ASTRONOMY LIBRARY

'TABLES

OF THE MOON;

CONSTRUCTED FOR THE USE OF

THE AMERICAN EPHEMERIS AND NAUTICAL ALMANAC.

BY

PROFESSOR BENJAMIN PEIRCE, LL. D.

PUBLISHED BY AUTHORITY OF THE SECRETARY OF THE NAVY.

BUREAU OP NAVIGATION,

WASHTNOTON.

18C5.

I* a'* **t*»* * • •

.7, ' >i' v: •; • .; :

• ' 3* ** * ft '*'

UNIVERSITY PRESS: WELCH, BIGELOW, AND COMPANY, CAMBRIDGE.

PREFACE

TO THE SECOND EDITION.

ONE of the first steps in the preparation of the American Ephemeris and Nautical Almanac, founded by Congress in March, 1849, was the collection of materials for new Tables of the Moon. The work was completed, and the first edition of the American Tables was published in 1853.

Since this preliminary step, however indispensable, unavoidably delayed the appearance of the Almanac, I am very solicitous to make known, here and elsewhere, the great obli- gations which American astronomical science is under to Hon. John P. Kennedy, then the Secretary of the Navy, for his just estimate of the magnitude and importance of this work. Although the processes by which it was conducted had formed no part of his study, its objects and value were perfectly understood by a scholar who had already adorned the literature of his own country by his writings.

The American Tables, 'as is stated in the title-page of the first edition, are " constructed from Plana's theory, with Airy's and Longstreth's corrections, Hansen's two inequalities of long period arising from the action of Venus, and Hansen's values of the secular variations of the mean motion and the motion of the perigee."

The formulas of Plana's theory were taken, not from Plana's own work, but from pages Ixxiv. - Ixxx. of the Introduction to the Eeduction of the Observations of the Moon, made at the Royal Observatory, at Greenwich, from 1750 to 1830.

These formulas were adopted because they claimed to be corrected by Plana himself^ and, what is of more importance, because they had been compared with observation, and formed the basis of Airy's corrections of the elements of the Moon.

The term 0".8 sin [23], which occurs in that formula, is very different from the cor- responding term 3".3 sin [23], which is originally given by Plana ; but it appears from the remarks given on page Ixxxi. of the Introduction to the Lunar Observations, that this correction was adopted with the assent of Plana, and it was, therefore, attributed to Plana in the American Tables.

Airy's corrections of the Lunar elements were adopted from his Memoir in Vol. XVII. of the Memoirs of the Eoyal Astronomical Society. In making these corrections, the two inequalities given at that time by Hansen, and produced by the disturbing force of Venus, were introduced in the comparison. Therefore it was necessary to introduce these terms also into the American Tables, in order to have the theory which had been verified

3

PREFACE.

by observation. Very different values of these terms have since been given by Hansen, and are introduced into his Tables. A new set of corrections of the Lunar elements has also been made by Airy ; but these corrections were published several years after the appearance of the American Tables.

Just before the final preparation of the American Tables, and when the first volume of the American Ephemeris was on the eve of completion, Longstreth's empirical correc- tions of Plana's formula for the Moon's longitude were communicated to me by their author ; they were accompanied by a table of comparisons (published in the Memoirs of the American Philosophical Society for 1853) which sufficiently attest their value and propriety, and the forthcoming volume of the Ephemeris was delayed until the corre- sponding changes were computed and applied.

The present edition of the American Tables of the Moon is the same as the first, with the exception of the correction of typographical errors ; the substitution of the Tables of the Moon's Parallax constructed from Walker's and Adams's formulas, in the place of the original Parallax Tables' ; and the addition of a Table adapted to a convenient modifica- tion of the method of computing the latitude, by Professor J. D. Runkle.

A third edition will shortly be issued, of which the basis will still be Plana's theory, while the Tables will be corrected to conform to the new Solar Parallax, and the corrected elements of the Moon's orbit.

WAOHIHOTON. Nary Department, March, 1865.

C. H. DAVIS. JRear-Admiral, and Chief of the linreau of Navigation.

INTRODUCTION.

I. CONSTRUCTION OF THE TABLES.

THESE tables are constructed from the theory of PLANA, modified by the theoretical investigations of HANSEN, and the empirical corrections of AIRY and LONGSTRETH.

The moon's mean longitude is also to be corrected by the two terms of long period, arising from the action of Venus, which were discovered by HANSEN, and printed in the Astronomische Nachrichten, No. 597, and which are expressed by

8h. 6 = the correction of the mean longitude of the moon arising from the action of Venus.

*/ The following notation is adopted,

6 = the mean longitude of the moon, or = the longitude of the moon's perigee, 17 = the longitude of the moon's node, 6, = the mean longitude of the sun, or. = the longitude of the sun's perigee.

ff, ff,., w',., and i)' = the respective daily motions of d, or, 6,., or.., and 17.

00, «•„, 0..o, ar.,0, Vo = the values of 6, or, 6,,, or.., and ij at any assumed epoch, as the beginning of the nineteenth century.

The values of 0, v, Sac., at any number of days i from this epoch are, from the formulae of PLANA, with the corrections given by HANSEN in the Astronomische Nachrichten, No. 597,

6 =6t + ffi + .8'.'.598 (10)-»i3 + 3".6483 (10)-" i3 vr =*,, + «'» — 27".217 (10)-* *" — 13".750 ( 10)-" i3, 6.. = 6.., + ff.. i + 0".91584 ( 10)~» f -f 0".03879 ( 10)-" f, «V = w..o + «V t + 0".91584 ( 10)-" f + 0".03879 (10)-" f, i? = la + n' i + 6».0355 10-" i2 + 2".3744 (10)-" f.

The values of 00, *0, &c., and of 0'0, «'„, &c., derived, for the mean noon of Washington of the date 1801, Jan. 0, from the values obtained by AIRY in his Memoir upon the Cor- rections of the Elements of the Moon's Orbit, published in the Memoirs of the Eoyal As- tronomical Society, Vol. XVIL, and from BESSEL'S Tables of the Sun, are

6, = 107 55 40*5, ff = 13 635.02808897,

v, = 266 4 51.3, v1 = 0 401.05783886,

0.0 = 279 52 44.3, ff^ = 0 3548.32999304,

or. 0=279 31 10.4, ^ = 0 0.16947241,

17, = 135552.6, ,' =_0 190.63366070.

INTRODUCTION.

The ass.Hmgd- "Western Longitude of Greenwich from Washington is 18h 51m 48''. -'

noation

g" = the mean anomaly of Venus,

z = the mean anomaly of the sun = 0,. — ar..,

v = the uncorrected mean longitude of the moon = 6 — 8b. 6,

c = the mean anomaly of the moon = 6 — w,

y = the mean argument of the latitude = 0 -*— qt

t = the argument of variation = 6 — tft,

« = the true longitude of the moon,

J 1= the true argument of the latitude,

9 = the mean heliocentric longitude of Venus,

© = the mean heliocentric longitude of the earth = 180° -j~ £..»

}[ = the mean heliocentric longitude of Jupiter,

H=8g"— 13z-f 315° 3(X,

H'= 18 g" — 16 z — x + 35° 2(K2,

•

gives the following formulae for the longitude, latitude, and horizontal parallax of the moon.

In writing these formulae, most of the arguments are expressed by numbers, in which the digit occupying the place of units is the coefficient of x, that in the place of tens is the coefficient of t, that in the place of hundreds is the coefficient of z, that in the place of thousands is the coefficient of y, and that in the place of tens of thousands is the co- efficient of «. The accents upon the numbers indicate that the coefficient is negative. Thus the number of the argument [14' 253'] denotes

u — 4y + 2z + 5< — 3*.

•

The form of the formula of the longitude is modified simply by substituting the term dependent upon the true arguments of the latitude, instead of the equivalent terms. This is accomplished by adding to the formula of longitude the equation,

0 = — 416".7 sin 2 J + 411".7 sin 2y -f 4".l sin (2y + 2x),

-f 0".9 sin (2y — 2x) — 46".0 sin (2y — *) + 45".2 sin (2y -f «),

+ 0".3sin (2y + 3i) — 9".3 sin (2y + r — 2<) + 8".8sin(2y — z-f2<),

• + 0".9sin (2y-f x + 2t)+Q".l sin (2y — x— 2*) — 0".4 sin (2y + 2* — 2t),

— 0".5sin (2y — 2 * + 2 <) + 5".7 sin (2y -f 2<) — 3".8 sin (2y — 2<),

— 0".4 sin (2y — x + z) — 0".4 sin (* -f z — 2 y) — 0".2 sin (2y — 4 1 + *), + 1".0 sin (2 y — t) — 0".7 sin (2 y + z) -f 1".3 sin (2y — z),

— 0".4 sin (* — 2< + z + 2y) + 0".3 sin (2( + 2y — z) -f- 0".3 sin (2* — z — 2y).

The form of the formula for latitude is modified in a way which is evident from in- spection of the formula, and which is designed to obviate the necessity of correcting the arguments for the change from mean to true longitude. The formula of parallax is re- tained in PLANA'S form.*

«

The terms of the various equations are given in the first column of the following tables of the formulae united with the constants which are employed in the construction of the tables. The second column contains the initial letter of the authority for the corresponding coefficients of the equation, whether PLANA, AIRY, or LONGSTRETH. The letter is accented when the value of the coefficient is modified by the present form of the tables. The thitd column contains the period of the argument expressed in mean solar days. The fourth column contains the number of the argument. The fifth column contains the number of the table which gives the values of the equation.

* See Formula, page 805. 6

INTRODUCTION.

EQUATION.	M		1		EQUATION.	|		u
	PERIOD.	s	W	o	PERIOD.	^	U
		H		o	M					o	•
« = the moon's true longitude.	D			H	Equations of Longitude con-			1	£
= nutation						tinued.	5
					d.
	- u —,,8° 3135".	2	A.			2	+ 6.8 sin [1'2]	P.	25.82638	27	32
	-22655.226			d.		6		- 0.9 sin [2'4]	P.			32
	-22639.2 sin	ri	A.	27.55455245	i	6	+ 7.5				33
	- 769.5 sin	'2'	P.			6	4- 7.5 sin [2'21'1	P.	38.52204	28	33
	36.7 sin	3'	P.			6	.4- 6.3				34
	2.0 sin	'4'	P.			6		- 6.3 sin [2'021]	P'.	32.76364	29	34
	0.1 - sin	5	P.			6	+ 3.8				35
	- 4587.4					7	4- 3.8 sin [IW]	P.	10.37093	30	35
	- 4586.9 sin	'21']	A.	31.81193574	2	7	4- 3.0				36
	_ 31.2 sin	42']	L.			7		- 3.0 sin [31']	P.	15.31442	31	36
+ 2457.02					8		- 3.0				37
_ 122.1 sin	10	P.	29.53058800	3	8		- 3.0 sin [1'42']	L.	16.63016	32	37
+ 2371.0 sin	"20=	A.			8		- 2.1				38
+ 0.9 sin	30'	P.			8		- 2.1 sin [2'01]	P.	32.45058	33	38
+ 14.4 sin	!40'	P.			8		- 2.0				39
+ 670.5					9		- 2.0 sin f221']	P.	27.09271	34	39
— 670.3 sin	;ioo]	A.	365.259687	4	9	+ 1.2				40
7.9 sin		P.			9		- 1.2 sin [201]	P.	23.94223	35	40
+ 225.3					10		P 1.0				41
4- 18.0 sin	I'1]	P.	411.78517	5	10		- 1.0 sin [111]	P.	13.71881	36	41
— 212.4 sin	;2'2]	P.			10		- 0.5				42
+ 206.9					11		- 0.5 sin [43']	P.	37.62533	37	42
	- 206-9 sin	'1'21']	L.	34.84689	6	11		- 0.4				43
	- 192.1					12		- 0.4 sin [121	P.	9.39439	38	43
	- 192.1 sin	[21]	P.	9.61372	7	12	+ 0.6				44
	- 165.9					13		- 0.6 sin [32']	P.	34.47528	39	44
	p 165.9 sin [1'20]	P.	15.38731	8	13	+ 0.4				45
	- 148.1					14	4- 0.4 sin [1'03]	P.	9.42177	40	45
	- 148.1 sin	[I'Ol]	P.	29.80283	9	14	-j- 0.4				46
	- 110.0					15		- 0.4 sin [103]	P.	8.95955	41	46
— 110-0 sin	[101]	L.	25.62170	10	15		P 0.3	•			47
4- 85.0					16		- 0.3 sin [2'21]	P.	10.14791	42	47
— 85.0 sin [2001']	L'.	26.87829	11	16		- 0.6				48
+ 58.7					17		- 0.6 sin [1'221	P.	7.26893	43	48
— 58.7 sin [202'0]	P'.	173.31006	12'	17	+ 0.3				49
4- 38.0 4- 38-0 sin 4- 28.8	[41']	P.	10.08460	13	18 18 19	_ 0.3 sin [12'3] + 0.2 — 0.2 sin [2021]	P. P'.	22.78614 5.63335	44 45	49 50 50
— 28.8 sin [121']	P.	29.26328	14	19	+ 0.4				51
+ 25.0					20		- 0.4 sin [2'1011	P'.	29.01328	46	51
— 25.0 sin [120]	L.	14.19161	15	20	+ 1.3				52
+ 21-0					21	+ 1.3 sin [21'00]	P'.	14.13256	47	52
— 8.2 sin	[11]	P.	14.25418	16	21	+ 0.5				53
+ 14.1 sin	[22]	P.			21		- 0.5 sin [2'022]	P.	14.96709	48-	53
	- 17.2		P.			22	+ 0.2				54
	- 17.2 sin [110]	P.	27.32168	17	22	— 0.2 sin [202'2]	P'.	12.76271	49	54
	14.0					23	+ 0.4				55
	- 14.0 sin [1'21]	P.	9.87359	18	23	- 0.4 sin [2101']	P'.	25.03597	50	55
	12.8					24	+ 0.2				56
— 12.8 sin [2'3]	P.	24.30220	19	24		- 0.2 sin [2001]	P'.	9.10846	51	56
9.6					25	+ 1.0				57
9.6 sin [1'02]	P.	14.31731	20	25	4- 1.0 sin [201'0]	P'.	25.23137	52	57
+ 9.2					26	+ 2.6				58
— 9.2 sin [12'2]	L.	131.67112	21	26		- 2.6 sin [212'0]	P'.	117.53942	53	58
+ 8.1					27	+ 1.2				59
— 0.4 sin [I'lO]	P.	32.12809	22	27	4- 1.2 sin [1'40]	P.	7.53494	54	59
+ 7.8 sin [2'20] + 9.8	P.			27 28	+ 0.9 » — 0.9 sin [141']	P.	9.81365	55	60 60
— 9.8 sin [202'1]	L'.	23.77463	23	28	+ 0.7				61
+ 7.3					29		- 0.7 sin [2100]	P'.	13.11748	56	61
— 7.3 sin [102]	P.	13.27650	24	29	+ 0.8				62
+ 2.9					30	4- 0.8 sin [23]	P.	5.66247	57	62
— '2.9 sin [121]	P.	9.36717	25	30	+ 0.5				63
+ 1.9					31		- 0.5 sin ri42'l	P.	15.24221	58	63
1.9 sin [41]	L.	5.82261	26	31	+ 0.6 " "				64
+ 1.6					32		- 0.6 sm [204'1]	P'.	38.96397	59	64

INTRODUCTION.

EQUATION	g M		|	EQUATION.	"		u
0	PERIOD.	•	(d		0	PERIOD.	^	a
Equations of Longitude con-	1		o	$	Equations of Latitude con-	B		1	a s
tinned.					tinued.
4- d.4		A		65	4- o".2		d.		104
	- 0.4 sin [212'1]	P'.	22.32171	60	65	— 0.2 sin [1021]	p.	7.1041	87	104
	- 0.4				66		- 0.2				105
	- 0.4 sin [4000]	P.	6.80305	61	66		- 0.2 sin [1021']	p.	14.6664	88	105
	- 0.3				67		- 0.2				106
	- 0.3 sin [21-20]	P'.	7.22100	62	67		- 0.2 sin [1'022]	p.	9.6561	89	106
	- 0.3				68		- 0.2				107
-	- 0.3 sin- [11000]	P.	13.63340	63	68	— 0.2 sin [1'021]	p.	32.2808	90	107
-- 0.3				69	4- 6.2				108
	- 0.3 sin [2'1'21]	P.	35.99212	64	69	— 6.18 sin 38	p.		77	108
4- 0.2				70	4- 9.1				109
	- 0.2 sin [140]	P.	7.23638	65	70	4- 2.17 cosu	A.			109
4-0.2				71	— 8.80 sin «	A.			109
	- 0.2 sin [2'030]	P.	35.59582	66	71
+ i.o				72	In which the values of A. and B. are given by the fol-
	- 1.0 sin [I'lOOl]	A.	27.44332	67	72	lowing formulae :
+ 0.7 4- 0.7 sin [ll'OOl] * ' " *	A.	27.66669	68	73 73 74	A =	17600.0 - 846.0	A'.	d.
— 2.2 sin [1'2'2]	L.	471.89326	69	74		- 527.5 cos [20'20]	P.	173.31006	12"	83
4- 1.5				75		- 25.7
4- 1.5 sin [21*2'0]	P.	329.79056	70	75		- 25.7 cos [2002'] ,i.i i	P.	1095.1653	73'"	84
_	- 13				76		- 22.1
— 1.1 sin (?-©)		583.921	71	76	— 22.1 cos [212'0] + 1 • »	P.	117.5394	53'	85
4- 0.4 sin 2 (9-©) 4- 0.8				76 77	1.3 — 1.3 cos [1]	P.	27.5546	V	86
4- 0.7 sin (©-#)		398.884	72	77 77	4- 10.3 — 10.3 cos [21'2'0]	P.	329.7906	70'	87
4- 2.0				78	4- 6.63
4- 2.0 sin [2002']	P.	1095.1653	73'	78	— 1.3 cos [100]	P'.	365.2597	4	89
4- 0.5				79	4- 4.7
0.5 sin [111']	P.	3232.8202	74	79	4- 4.7 cos [2'2]	P.	205.8926	5'	90
4- 53.2				80
4- 23.2 sin H.		84753.24	75	80	B = —1000.
4- 6565				81	4- 846.0
-}- 27.4 sin H.		95489.94	76	81	— 527.5 sin [202'0]	P.	173.31006	12'	83
—416.9 sin 2$. 4- 6.38 sin (u-y)			77	82 8U	4- 25.7 — 25.7 sin [2002']	P.	1095.1653	73"	84
— 0.97 cos (u-y)			8U	4- 22.1 — 22.1 sin [212'0]	P.	117.5394	53	85
•The	Moon's Latitude = -f- A sin ff + B cos y *	4- 1.3
-60.	— 1.3 sin [1]	P.	27.5546	1	86
	- 15.8				92	4- 10.3
	- 15.8 sin [102'1]	P.	188.2015	78	92	4- 10.3 sin [21'2'0]	P.	329.7906	70	87
	- 22.2				93	4- 88.9
	- 14.4 sin [1001']	P.	2190.3306	73	93	4- 48.9 sin [100]	P'.	365.2597	4	88
-	- 0.6				94	4- 4.7
	- 0.6 sin [lOl'O]	P.	346.6201	12'"	94	4- 4.7 sin [2'2]	P.	205.8926	5	90
4- 0.2				95	4- i.o
— 0.2 sin [I'lOl]	P.	438.3608	79	95	— 1.0 sin [1*1]	P'.	411.7852	5	91
4- 0.1				96
	- 0.1 sin [1101']	P.	313.0547	80	96
:	h 0.7 - 0.7 sin [112'1]	P.	124.2016	81	97 97	•The Moon's Equatorial Horizontal Parallax =*
	- 1.8				98	3000.
	- 1.8 sin [1*021]	P.	14.8655	s-J	98	4- 348.0		d.		110
	- 0.7	4			99		- 186.8 cos [1]	P.	27.55455	1"	110
	- 0.7 sin [1*2*20]	P.	39.2116	83	99		- 10.3 cos [21	P.			110
	- 0.6				100		0.6 cos [3]	P.			110
	- 0.6 sin [10021	P'.	9.5717	84	100		- 28.6				111
4-0.5 "				101	— 0.9 cos flO]	P.	29.53059	3	111
	- 0.5 sin [I'Olll	P.	29.9342	48	101		- 27.6 cos [20]	P.			111
4-0.4 "				102		- 0.1 cos [40]	P.			111
:	f- 0.4 sin [803*0] [• 0.3 f 0.3 sin [1042*]	P. P.	23.5193 38.2830	85 86	10-2 103 103		- 34.2 - 33.9 cos [21'] - 0.3 cos [42'J	P. P.	31.81194	2	112 112 112

* See Table cixxvii.

* See Formula, page 305.

INTRODUCTION.

	H EQUATION.	R U		EQUATION.	i
	o	PERIOD.	W	0	PERIOD.	s
The	Moon's Equatorial Hori- 5	1'	3 3	P The Moon's Equatorial Hori- §	1	m
zo	ital Parallax continued.			zontal Parallax continued
	H			n	d.
	- 1.4	d.	113	— 0.6 cos [120] P.	14.1916 15	121
	- 1.4 cos [1'21'] P.	36.8469 6	113		- 0.3	1	122
	- 3.1		114		- 0.3 cos [22] P.	7.1271 16	122
	- 3.1 cos" [21] P.	9.6137 7	114		- 0.2		123
	- 2.2		115		- 0.2 cos [1'21] P.	9.8736 18	123
	- 2.2 cos [1'20] P.	15.3873 8	115		- 0.1		124
	- 1.2		116		- 0.1 cos [2'2] P.	24.3022 19'	124
	- 1.2 cos [101] P.	29.8028 9	116		- 0.4		125
	- 0.9		117	— 0.4 cos [100] P.	365.2597 4	125
	- 0.9 cos [I'Ol] P.	25.6217 10	117	+ 0.2		126
	- 1.2		118	4- 0.2 cos [22'] P.	205.8926 5	126
	- 1.2 cos [2001'] P.	26.8783 11	118	+ 0.2		127
	- 0.5		119	— 0,2 cos [20'20] P.	173.3101 12'	127
-1	- 0.5 cos [41'] P. - 0.2 - 0.2 cos [121'] P.	10.0846 13 29.2633 14	119 120 120	The Moon's Equatorial Semidiameter = The Horizontal Parallax.
+ 0.6		121	X 0.272274 | B.	128
This value of the Moon's Semidiaraeter is that deduced by BCTRCKHARDT from eclipses and occultations, and should be used for the computation of these phenomena. But for Meridian Observations it seems to vary with the telescope ranging from 2" to 3" greater than the value here given.
The Principal Terms of the Second and Fourth Differences of the Longitude for a Quarter of a Day are given
in the following formulae.
EQUATION.	ARGUMENT.	TABLE.	EQUATION.	ARGUMENT.	TABLE.
Second Difference of the Longitude				Second Difference, continued.
for a Quarter of a Day =				+ 0.35		23"
—130.				— 0.354 sin [1'21]	18	23"
-f 76.0		6"	+ 0.05		24"
— 73.563 sin [1	1	6"	4- 0.054 sin [2'3]	19	24"
	- 9.993 sin 2		6	a	+ 0.11		25"
	- 1.071 sin [3'		6	a	— 0.115 sin [1'02]	20	25"
	- 0.104 sin [4'		6	"	+ 0.07		27"
	- 0.008 sin 15'		6"	— 0.074 sin [2'20]	22	27"
+ 11.2 — 11.180 sin [21'] — 0.304 sin [42'1	2	7" 7" 7"	+ 0.10 + 0.102 sin [102] -j- 0.08	24	29" 29" 30"
+ 31.16		8"	— 0.081 sin [121]	25	30"
H- 0.345 sin [10	3	8"	+ 0.14		31"
— 20.808 sin [20'		8"	— 0.137 sin [41]	26	31"
	- 0.023 sin [30		8"	+ 0.19		35"
	- 0.650 sin [40		8"	— 0.087 sin [1'41']	30	35"
+ 0.42 — 0.42 sin [l'21'l	6	11" 11"	Fourth Difference of the Longitude for a Quarter of a Day =
+ 5.12		12"	— i'.oo
	- 5.117 sin [21]	7	12"		- 0.45		6	IV.
+ 1.73 ' '		13"		- 0.239 sin [1	1	6	IV.
	- 1.727 sin [21']	8	13"		- 0.130 sin [2'		6	IV.
+ 0.41 " "		14	a		- 0.031 sin [3'		6iv.
	- 0.411 sin [1*011	9	14"		- 0.005 sin 4		6	V.
	- 0.41		15"		- 0.03		7iv.
	- 0.413 sin [101] - 0.29	10	15" 16"		- 0.027 sin [21'] - 0.003 sin [42']	2	7iv. TIT.
	- 0.288 sin [2001']	11	16	it		- 0.31		giv.
	- 0.92		18	n		- 0.303 sin [20]	3	giv.
	- 0.920 sin [41']	13	18	"		- 0.006 sin [30]		giv.
	- 0.08		19	H		- 0.029 sin [40]		giv.
	- 0.083 sin [121']	14	19	II		- 0.14		12'v.
	- 0.31		20	II		- 0.136 sin [21]	7	12IV-
	- 0.306 sin [120]	15	20"		- 0.02		13	v-
	- 0.80		21	II		- 0.018 sin [21']	8	131V
	- 0.100 sin [11] - 0.680 sin [221	16	21" 21"		- 0.02 - 0.022 sin [41']	.13	18'v-
+ 0.06 " "		22	II		- 0.03		21	v.
	— 0.057 sin [110]	17	22"		- 0.033 sin [22] 16	21'v-

INTRODUCTION.

Since HANSEN'S inequalities of long period, arising from the action of Venus, affect the mean longitude of the moon, they must be applied to the several arguments contained in Tables \a. or V6., and to render these corrections always additive the arguments in Tables Ha. and 116. have been diminished by the following constants: —

Arg. 1 by 0.001859,

Arg. 2 by 0.001410,

Arg. 3 by 0.001214,

Arg. 6 by 0.0013,

Arg. 7 by 0.0011,

Arg. 8 by 0.0012, Arg. 9 by 0.0012, Arg. 10 by 0.0010, Arg. 11 by 0.0011, Arg. 13 by 0.0012.

And Tables Va. and V6. have been constructed by the formulae, —

Corr. Arg. 1	0.0005(
Corr. Arg. 2	0.0006(
Corr. Arg. 3	0 0005!
Corr. Arg. 6	0.0006
Corr. Arg. 7	0.0002
Corr. Arg. 8	0.0003
Corr. Arg. 9	0.0005
Corr. Arg. 10	0.0005
Corr. Arg. 11	0.0005
Corr. Arg. 13	0.0002

TABLE Vo.

-f- 0.000498 4- 0.000569 4- 0.000529 -f 0.00062 -f 0.00017 4- 0.00028 4- 0.00053 4- 0.00046 4- 0.00048 4- 0.00018

TABLE VA.

slnH	+ 0.001359 + 0.0005826 sin H>,
sin H	4- 0.00081 4- 0.000673 sin If,
sin H	4- 0.000684 4- 0.000624 sin If,
sin H	4- 0.0007 4- 0.00074 sin If,
sin H	4- 0.0009 4- 0.00021 sin H',
sin H	4- 0.0009 4- 0.00033 sin H'
sin H	4- 0.0007 4- 0.00053 sin H',
sin H	4- 0.0005 4- 0.00054 sin H,
sin H	4- 0.0006 4- 0.00056 sin If,
sin H	4- 0.0010 4- 0.00021 sin If.

II. DESCRIPTION OF THE TABLES.

TABLES la., 16., and Ic. are Tables of Astronomical Dates in mean solar days reckoned from the beginning of the Julian Period, from which the date of any event can be reduced to days and decimals of a day when it is originally given in the usual form with reference to the Christian Era.

Tables Ila. and 116. contain the values of the mean longitude, the negative of the longitude of the node, and all the arguments for the mean Washington noon of every thousandth day from 2300000 to 2500000.

Tables Ilia, and III6. contain the motions of the mean longitude, and of the lon- gitude of the node for every interval of days and fractions of a day less than 1000 days, and the first ten multiples of all the periods.

Table IV. contains the constants by which the mean longitude, and the longitude of the node, and the various arguments, can be reduced, from the interval from 2400000 to 2500000 days to any previous time after the commencement of the Julian Period.

Tables Va. and V6. contain the corrections of the various arguments for HANSEN'S term of long period in the action of Venus.

Tables VI. to LXXXII. inclusive contain the different equations of the moon's lon- gitude.

Tables VI". to XXXVII". inclusive contain the second differences for a quarter of a day of the moon's longitude.

Tables VI.IV to XVI.IV inclusive contain the fourth differences for a quarter of a day of the moon's longitude.

Tables LXXXIII. to CIX. inclusive contain the terms of the moon's latitude.

Tables CX.. to CXXVII. inclusive contain the terms of the moon's horizontal par- allax.

Table CXXVIII. contains the table for the moon's semidiameter.

10

INTRODUCTION.

III. USE OF THE TABLES.

1. Eeduce the instant for which the moon's place is to be computed to its date in days and decimals of a day from Washington mean noon, by means of Tables la., 16., and Ic. The number of days for the beginning of the year is to be found in Table la., that for the day of the year in Table 16., and the decimal of the day in Table Ic.

2. Find the longitudes and arguments for the date from Tables Ila., 116., Ilia., III6., Va., and V6.

If the date is contained within the interval 2300000 to 2500000 days,

Find the value of the longitude or argument for the preceding thousandth day in Table Ila. or 116., in the column headed with the name of the longitude or argument; multiply the number which is contained in the column headed with the accented name of the longitude or argument by one thousandth part of the excess of the date over that of the preceding thousandth day. Find in Table Ilia, the motion of the longitude for this excess of days.

The sum of the three numbers thus found for each longitude is the mean longitude for the date, and the sum of the two numbers for each argument and of the excess of the date over that of the preceding thousandth day is the argument for the date. The argument thus found must be reduced by substituting as many entire multiples of the period of the argu- ment as it contains, and Table III6. will facilitate this process of reduction. Finally, cor- rect the argument by the addition of the corrections contained in Tables Va. and V6.

If the date is less than 2300000 days,

Change the hundred thousands of the date to 24 ; find the longitude and arguments by the preceding process for the changed date, with the exception of the corrections contained in Tables Va. and V6. Take from Table IV. the constants of longitude and argu- ment which correspond to the hundred-thousandth day next preceding the given date. Multiply the excess of the date over the next preceding hundred-thousandth day by the accented number of which the logarithm is given in the column of Table IV. next follow- ing the longitude or argument to which it corresponds when it is. of sufficient magnitude to be noticed. Multiply the square of this excess by the doubly accented number of which the logarithm is given in the column of Table IV. next following that of the singly ac- cented number, when it is of sufficient magnitude to be noticed. The sum of these two products, added to the constant, and corrected by the addition of the correction of Tables Va. and V6. is the total addition to be made to the longitude or argument obtained by the preceding process.

3. Find, by means of the several arguments, the equations of longitude contained in the Tables VI. - LXXXI.4. inclusive, and add their sum to the value of u already obtained.

It is to be observed, in entering Tables XVII., LIIL, and LXXVIIL, that

Arg. 12' = Arg. 12, but that the period is half as long. Arg. 48' = Arg. 48 — 6J-.26, and it has a half-period. Arg. 73' = Arg. 73 -f 173'-.792, and it has a half-period.

4. To the sum of u and the equations of longitude add the value of y — u already ob- tained, and this sum is y, which is the argument with which Table LXXXII. is to be entered for the final equation of longitude, which is to be added to the sum of u and the other equations in order to obtain the true longitude, il, of the moon.

11

INTRODUCTION. 5. Find the value of A by entering

.1.

Table LXXXIII. with the Arg. 12" = Arg. 12 — 43.3275,

Table LXXXIV. with the Arg. 73'"= Arg. 73 + 47.5826,

Table LXXXV. with the Arg. 53' = Arg. 53 — 29.38,

Table LXXXVI. with the Arg. 1' = Arg. 1 -f 6.89,

Table LXXXVII. with the Arg. 70' = Arg. 70 — 82.45, Table LXXXIX. with the Arg. 4

Table XC. with the Arg. 5' = Arg. 5 + 51.47.

The value of A is the sum of the equations thus obtained increased by 17600".

6. Find the value of B by entering Tables LXXXIII. to XCI. inclusive (excepting Table LXXXIX.) with the arguments respectively written above them.

The sum of the equations thus obtained diminished by 1000" is the value of B.

7. Find the remaining equations of the moon's latitude by entering Tables XCII. to CIX. inclusive with the arguments respectively written above them.

The sum of the equations thus obtained, diminished by 60", and added to the sum of the products of A by sin y, and of jB by cos. y, is the moon's latitude.

8. The moon's equatorial horizontal parallax is found by entering tables CX. to CXXVII. inclusive with their respective arguments, and adding 3000" to the sum of the equations thus obtained.

9. The moon's equatorial semidiameter is found by multiplying the equatorial horizontal parallax by 0.272274, which product may be readily obtained by means of Table CXXVIII.

This value is to be used for the computation of eclipses, but in the reduction of meridian observations it should be increased by 2".5 in the case of a telescope for which no special investigation has been made, or by whatever constant may be found suitable by a special investigation for each telescope.

10. Directions for the Computation of an Ephemeris. The longitude, exclusive of nuta- tion and the equation of Table LXXXIL, should be found for each successive noon ; and also the second and fourth differences of the equations for a quarter of a day from the Tables .VI." to XXI.IV inclusive.

If then the following notation is adopted,

«, = the longitude for the time t in days, exclusive of nutation and the equation of Table LXXXIL

A, = the sum of all those equations for which tables of second differences are given. A', = the sum of all those equations for which tables of second differences are not given.

B, = the sum of all the tabular second differences from those tables for which tables of fourth differences

are given. B't == the sum of all the tabular second differences from those tables for which tables of fourth differences are

not given. B", = B,+ B',.

C, = the sum of all the tabular fourth differences for all the equations for which they are given. A" V, = the nth differences of the series of n + 1 numbers

V, _ | „ + j, V, _ j „ + !, &c..,

of which the first corresponds to the date preceding the date t by | n days, and the last cor- responds to the date which follows the date t by \ n days, and the intermediate numbers are at intervals of a quarter of a day apart.

A" V, = the nth quarter difference of the values of the n -f- 1 numbers

of which the first corresponds to the date which precedes the date t by i n days, and the last corresponds to the date which follows the date t by $ n days, the intermediate numbers

12

IXTHODUOTIOX.

occurring at intervals of a day. In taking these quarter differences, all the terms of each order of difference are to be divided by four, before their quarter differences are obtained in the same way.

In the following computations it will be sufficiently accurate to put

A' V, = A« F,,

A» V, = A'3 F, — J A" F,.

Find for each noon and interpolate by differences for every six hours

A* M, = C, + A' Bt + A« A't — 1". Test the accuracy of Bt by the formula

A' B,= c.-fjA'C,— 1". Find for each noon

A' w, = B", + A' A', — 130".

Find for each day and for the instant fths of a day after the noon A' K/+, = A JB", + t -f A' A't + t + j A4 «,+i.

Interpolate the remaining third differences of ut by means of the fourth differences, being careful to adopt a judicious distribution of the small changes which are required in the fourth differences to accomplish this interpolation.

Interpolate the second differences of ut with a similar regard to changes of the third differences.

Test the accuracy of A, by the formula

A» A, = B", + 1 c, + | A" B'( — 130", Find for each day and the instant f ths of a day after the noon

A «, + , = 3° 1058".757 + A At + t + A A',+t + J A3 vl+t — J A« u, + J.

Interpolate the first differences of u, by the aid of the second differences, and by them interpolate the values of ut.

The values of y should be obtained for each quarter of a day, and thence the equations from Table LXXXII.

The various terms of the latitude and horizontal parallax need only be found for each noon, except A. sin y, which, after the interpolation of A., should be computed for each quarter of a day.

11. Example.

Find the moon's longitude, latitude, equatorial horizontal parallax for the date B. C. 413, August 27, at 6 o'clock in the afternoon, mean solar time at Athens.

Solution. The western longitude of Athens from Washington being 17b> 16m- 53'-, the given date is in Washing- ton time — 413 August 26d 23b- 16"1- 53'-. This is reduced to the Julian date in days by Tables la., 15., and Ic.

— 500 years is in Julian date in days 1538798.

13 B. 31777.

Aug. 26 238.

23"- 0.958333333

16-- 0.011111111

„ 53* 0.000613426

—413 Aug. 26d- 23"- 16ra- 53" 1570813.970057870

By substituting 2400000 for the 1500000, the date becomes 2470813.970057870. whence from Tables II. to V. inclusive the arguments are obtained as follows :

13

INTRODUCTION.

y-u ARGUMENT 1.

3.

From Table 116., for 2470000,

Correction X .81397, From Table JIIn., or the excess of date,

From Table IV. for I.'.IMH.

Accented No. X 70813.97,

Doubly accented Xo. X (70813.97)*,

Correction from Table Va.,

Correction from Table V4., Greatest Multiple of Period for Subtraction, Mean Longitude or Argument for date,

22 2502.58 1.29

285 6'.i2.C,o

4 27i is. s:;

—1035.81

—4.94

312 12C4.55

43

•2-20

T.-.s.:,

—0.9

370.1

1207.8

730.4

3.2

35 3069.1

10.9057714 1142

813.971 " i;,7'.i

14.9092:><>6

—5031

335

16989

826.6365734 13.0588844

21.243406 —58

813.9701 i:,,x

22.915317 57954

840 C,l

1202

827.110329 31.077951

8.500660 263

813.97(1058

3.859920

—80960

—112

30

1048

797.325876 28.985031

ARGUMENT 4.

6.

9.

10.

From Table II*., for 2470000,

Correction X .81397,

The excess of date, From Table IV., Accented No. X 70813.97, Doubly ace. No. X (70813.97)",

Correction from Table Va.,

Correction from Table V6., Or. Mult, of Period for Subtr., Argument for date,

281.3878 0

813.9701

365.1 2" 76 0 0 0 0 1095.7791

364.7064

316.3339 13

813.9701

168.9847

—1.0665

—60

0

0

1235.3555 62.8620

5.6456 0

813.9701

25.1207

656

8

0

11

836.3254 8.4785

9.8725

0

813.9701

7.7149

—454

—2

0

10

826.7797 4.2882

4.7758 0

813.9701

4.0279

—219

— 1

0

11

815.5275 7.225 1

26.1947 0

813.9701

16.1365

—984

—5

0

10

834.4791 21.7243

23.6165 0

813.97IH

13.8541

—846

—5

1

8

845.51(50 5.8405

ARGUMENT 1 1.

12.

13.

14.

15.

16.

IT.

From Table 116., for 2470000, The excess of date,

From Table IV.,

Ae,-ei,ted N'o. X 70813.97,

Doubly ace. No. X (70813.97)', Correction from Table Vc., Correction from Table V6.,

Gr. Mult, of Period for Subtr.,

Argument for date,

0.9587

813.9701

19.0676

761

4

0

9

833.2270 0.8468

20.6699

813.9701

171.4161

1642

G93.2KI2 312.9810

3.2232

813.9701

9.9006

51

0

0

11

826.9369 0.1632

5.760

818.970

21.068

59

0

0

0

819.872 21.485

5.5ft

8 i:i.97o

3.704

—21

0

0

0

823.113 0.117

4.981

813.970

9.575

—61

0

0

0

826.743 •1.672

15.347

813.970

3.560

—21

0

0

0

819.656 13.206

ARGUMENT i§.

19.

2O.

21.

22.

23.

24.

Fro,,, Table 116., for 2470000,

The excess of date, From Table IV., Accented No. X 70813.97.

•hilt, of Period for Subtr., Argument for dat-'.

4.364 813.970

7.935

—80 819.508

6.711

3.891 813.970

8.791

—207 826.875

0.170

1.189

818.970

1.178

—101

81C,.0,S7

0.099

r.'.i.'.i I 813.97 108.02

— 73 921.70

69.50

28.372

K1.-J.970

4.212

—24

835.330

11.200

17.824 813.970

12.603

—60

882.112

12.225

1.155

81 ,".970

1.086

—!>1

.SO'.I.HCC.

6.25]

4.760 818.970

7.5 1C,

—47

824.811

1.888

ARGUMENT 26.

2T.

28.

29.

30.

32.

33.

From Table 116., for 2470000,

Tlic exee-i of date. From Table IV..

ited No. X 70813.97, (ir. Mull, of Period for Subtr., Argument for date,

3.087 81.V.I70

0.868

—38 815.165

2.222

818.97 24.56 —16

826.44

1 2.27

24.849

818.970

27.868

—78

847.484

19.120

21.177

81.V.I70

18.084

— 149

is:, i .s:,:, 1.527

1.760

8l:!.i»70

10.188

:,

819.804 6.618

9.15

813.97

18.08

2

826.98

!i. 1 9

ll.ol

813.97

7.35

7

881.51 0.89!

15.84 818.97

1 7.58

—12

648.72

3.05

Ai:«,rMi.\r

35.

36.

37.

39.

40.

41.

Table 1 1/,., tor -..'170000, The exee-- .,)' date. Froa, Table IV..

it.-d No. / 7"Si:;.«.»7. ( ir. .Mult, of Period for Sublr.. Argument for date.

25.51 81897

i '.'.:> I 6

19.17

18.42

818.97

L2.98

— 8 887.98

7.2(1

12.65

818.97

9.22

f

*-_':;. i:i 12.66

86.4

814.0

88.9

3

L9.S

17.71 818.97

2.17

—10

826.7 1

7.04

18.1

81 1.0

10.7

—2

827.4

10.2

] C.2C,

818.97

4.65 II

829. 1 2

5.87

7.85

818.97

L89

11

824.2H 1 .5 1

INTRODUCTION.

ARGUMENT 42. 43. 44. 45. 46. 47. 4§. 49.
From Table II J., for 2470000, The excess of date, From Table IV., Accented No. X 70813.97, Gr. Mult, of Period for Subtr., Argument for date,	4.08 813.97 8.11 —5 821.98 4.13	3.31 813.97 9.77 —6 814.12 12.87	0.5 814.0 8.2 0 820.3 2.4	6.42 813.97 11.54 0 828.10 3.83	5.3 814.0 20.4 0 812.4 27.3	11.98 813.97 3.54 0 819.69 9.80	26.58 813.97 1.51 —12 838.16 3.78	2.2 814.0 1.2 0 816.8 0.6
ARGUMENT SO. 51. 52. 53. 54. 55. 56. 57.
From Table 115., for 2470000, The excess of date, From Table IV., Accented No. X 70813.97, Gr. Mult, of Period for Subtr., Argument for date,	20.9 814.0 17.6 0 851.2 1.3	8.23 813.97 7.20 —4 819.76 9.60	16.97 813.97 3.04 0 832.64 1.34	15.27 813.97 116.22 12 940.32 5.26	5.10 813.97 3.93 0 813.77 9.23	12.40 813.97 9.63 0 824.35 11.65	12.36 813.97 3.25 0 826.40 3.18	2.93 813.97 10.20 0 815.40 11.70
ARGUMENT 58. 59. 6O. 61. 62. 63. 64. 65.
From Table Hi., for 2470000, The excess of date, From Table IV., Accented No. X 70813.97, Gr. Mult, of Period for Subtr., Argument for date,	11.51 813.97 6.71 0 823.08 9.11	32.28 813.97 28.49 0 857.21 17.53	14.74 813.97 11.84 0 825.90 14.65	0.26 813.97 3.40 0 816.37 1.26	7.82 813.97 11.09 0 823.19 ' 9.69	0.35 813.97 8.73 0 818.00 5.05	20.93 813.97 19.88 0 827.82 26.96	12.82 813.97 3.83 0 824.95 5.67
ARGUMENT 66. 67. 68. 69. 7O. 71. 72. 73.
From Table 116., for 2470000, The excess of date, From Table IV., Accented No. X 70813.97, Gr. Mult, of Period for Subtr., Argument for date,	26.4 814.0 5.1 0 818.7 26.8	27.20 813.97 4.21 —8 823.30 22.00	6.94 813.97 25.69 —11 830.00 16.49	281.5 814.0 387.5 —26 1415.7 64.7	61.7 814.0 0.4 —3 659.6 216.2	201.5 814.0 406.6 0 1167.8 254.3	179.3 814.0 281.4 0 1196.7 78.0	1231.1 814.0 184.3 7.2 2190.2 46.4
ARGUMENT 74. 75. 76. 78. 79. 8O. 81. 82.
From Table 116., for 2470000, The excess of date, From Table IV., Accented No. X 70813.97, Gr. Mult, of Period for Subtr., Argument for date,	1691 814 1905 9 3233 1186	54809 814 32286 0 84753 3156	77263 814 52991 0 95490 35578	60.489 813.970 170.305 —.427 941.008 103.329	282.2 814.0 401.3 0 1315.1 182.4	68.3 814.0 26.2 0 626.1 282.4	14.23 813.97 112.35 —28 869.43 70.84	10.000 813.970 2.633 0 817.603 9.000
ARGUMENT 83. 84. 85. 86. 87. 88 89. 9O.
From Table IB., for 2470000, The excess of date, From Table IV., Accented No. X 70813.97, Gr. Mult, of Period for Subtr., Argument for date,	12.80 813.97 24.97 0 823.44 28.30	17.33 813.97 8.28 0 823.17 16.41	9.53 813.97 14.44 0 823.18 14.76	24.78 813.97 31.21 842.22 27.74	1.01 813.97 4.82 0 809.87 9.93	4.42 813.97 5.08 0 821.32 2.15	1.92 813.97 4.68 0 811.11 9.46	15.3 814.0 20.4 0 839.3 10.4
HE-NCE:
Arg. 12' = 139.6709 Arg. 73' = 220.2 Arg. 1' = 19.95 Arg. 12" = 96.3434 Arg. 73" = 367.8 Arg. 70' = 133.7 Arg. 48'= 12.49 Arg. 73'"= 94.0 Arg. 5' = 114.33 Arg. 12'" =292.9810 Arg. 53' = 93.42

15

INTRODUCTION.

TABLE.	EQUATION.	TABLE.	EQUATION.	TABLE.	A.	R
VI.	45193.81	XLV.	0.04	LXXXIII.	1359.62	72f>!'75
VII.	71.73	XLVI.	0.02	LXXXIV.	0.72	31.78
VIII.	1655.54	XLVII.	0.04	I.XXXV.	26.83	43.0'J
IX.	1340.46	XLVIII.	0.13	LXXXVI.	1.07	0.01
X.	206.06	XLIX.	0.26	LXXXVII.	13.42	20.11
XI.	176.80	L.	0.04	LXXXVIII.		40.00
XII.	360.58	LI.	0.40	LXXXIX.	6.66
XIII.	823.57	LII.	2.59	xc.	0.00	4.73
XIV.	170.69	LIII.	0.25	XCI.		2.00
XV. XVI. XVII.	130.22 169.81 45.31	LIV. LV. LVI.	0.22 0.41 0.01	1 Constant, A	17600. = 19008.32 B	—1000. = — 131.93
XVIII.	4.56	LVII.	0.92
XIX. XX.	23.67 48.53	LVIII. LIX.	5.14 2.16	TABLE.	EQUATION.	TABLE.	EQUATION.
V YT	07 ZA	T X	fl J.'i
JVJV1. XXII. XXIII. XXIV. XXV. XXVI. XXVII. XXVIII. XXIX. XXX. XXXI.	Ot .Jt 34.12 20.49 25.40 0.51 0.00 10.81 0.02 0.45 4.33 3.16	.IJ.A.. LXI. LXII. LXIII. LXIV. LXV. LXVI. LXVII. LXVIIL LXIX. LXX.	l/.^tt* 1.39 0.55 0.03 0.04 0.38 0.30 0.59 0.10 0.20 0.36	XCII. XCIII. XCIV. xcv. XCVI. XCVII. XCVIII. XCIX. c.	31.50 7.!IO 0.67 0.23 0.11 0.77 3.44 0.87 0.90	CI. CII. cm. CIV. cv. CVI. CVII. cvm. CIX.	0.98 0.47 0.39 0.00 0.00 0.39 0.26 5.50 15.79
XXXII.	1.78	LXXI.	0.13	Constant,		—CO.
XXXIII.	14.92	LXXII.	0.10	Sum,		10.17
XXXIV.	0.49	LXXIII.	1.19	A sin y,		714.C2
X XXV.	2.05	LXXIV.	4.40	Bcosy,		— 18L88
XXXVI.	0.16	LXXV.	2.93	3>'s Latitude =		-V.i2.96
xxxvn.	0.13	LXXVI.	1.49	=		9' 52.96
XXXVIII.	0.02	LXXVII.	1.33
XXXIX.	0.03	LXXVIII.	1.55		EQUATION.	TABLE.
XL.	2.38	LXXIX.	0.50	TABLE.	EQUATION.
XLI.	1.35	LXXX.	31.26
XLII.	0.99	I.XXXI.	81.62			i
XLIII.	0.56	LXXXL4.	—4.52	cx	867".08	CXXII I.	0.17
XLIV.	0.73			CXI.	57.27	CXXIV.	<>.<•:;
	CXII.	28.73	cxxv.	d.l 1
	CXIII.	2.88	CXXVI.	0.08
	CXIV.	4.57	CXXVII.	0.01
	cxv.	2.51	CXXVIII.	0.0'J
	CXVI.	0.02	('XX IX.	(1.07
Sum of Equations of Longitude, 0 50222.76 or, 18 3422.76 Mean Longitude, 312 12C I..V, Longitude in Orbit, 326 1087.31 y — u, 35 3069.1 y, 2 556.4	CXVII. ' CXVIII. CXIX. (XX. (XXI. CXXII.	0.02 0.67 0.31 0.46 0.42 0.21	(XXX. ('XXXI. CXXXII. (XXXIII. CXXXIV.	(MHi 0.11 0.40 0.68 0.01
Table LXXXII., —31.33	Constant,		3000.
Nutation of Equinox, 10.54	sin j)'s Horizontal Parallax =	8466.95
u = true Longitude = 326 1066.52	Table CXXXV.,		0.16
	}>'s Horizontal Parallax,	3467.11
i

16

TABLE la.

Dute of Jan. 0 in Common Years, and of Jan. 1 in Bissextile Years.

Year.	Dale in Mean .Solar Days.	Year.	Date in Mean Solar Days.	YEA : IN THE CENTURY.	Days from previous Centennial Date.	YEAR IN THE CKNTURY.	Days from previous Cen- tennial Date.
If Negative.	If Positive.	If Negative.	If Positive.
	—47 135.	0	—1000	1356173	100	1	0	50	51	18262
	—4712	365	— 900	1392698	99	2	365	495.	525.	18628
	—4711	730	— 800	1429223	as	3	730	48	53	18993
	—4710	1095	— 700	1465748	975.	45.	1096	47	54	19358
	—47095.	1461	— 600	1502273	96	5	1461	46	55	19723
	—4708	1826	— 500	1538798	95	6	1826	455.	565.	20089
	—4707 s.	2191	— 400	1575323	94	7	2191	44	57	20454
	— 1706	2556	— 300	1611848	935.	85.	2557	43	58	20819
	— 47055	2922	— 200	1648373	92	9	2922	42	59	21184
	—4704	3287	— 100	1684898	91	10	3287	415.	605.	21550
	—4703	3652	1	1721423	90	11	3652	40	61	21915
	—4702	4017	101	1757948	895.	125.	' 4018	39	62	22280
	—47015.	4383	201	1794473	88	13	4383	38	63	22645
	—4700	4748	301	1830998	87	14	4748	375.	645.	23011
	— 4600	41273	401	1867523	86	15	5113	36	65	23376
	—4500	77798	501	1904048	855.	165.	5479	35	66	23741
	—4400	114323	601	1940573	84	17	5844	34	67	24106
	— 4300	150848	701	1977098	83	18	6209	335.	685.	24472
	—4200	187373	801	2013623	82	19	6574	32	69	24837
	—4100	223898	901	2050148	815.	205.	6940	31	70	25202
	—4000	^ 260423	1001	2086673	80	21	7305	30	71	25567
	—3900	296948	1101	2123198 '	79	22	7670	295.	725.	25933
	—3800	333473	1201	2159723	78	23	8035	28	73	26298
	—3700	369998	1301	2196248	775.	245.	8401	27	74	26663
	—3600	406523	1401	2232773	76	25	8766	26	75	27028
	—3500	443048	1501	2269298	75	26	9131	255.	765.	27394
	—3400	479573	1583	2299238	74	27	9,496	24	77	27759
	—3300	516098	1584B.	2299604	735.	285.	9862	23	78	28124
	—3200	552623	1585	2299969	72	29	10227	22	79	28489
	—3100	589148	1586	2300334	71	30	10592	215.	805.	28855
	—3000	625673	1587	2300699	70	31	10957	20	81	29220
	—2900	662198	15885.	2301065	695.	325.	11323	19	82	29585
	—2800	698723	1589	2301430	68	33	11688	18	83	29950
	—2700	735248	1590	2301795	67	34	12053	175.	845.	30316
	— 2.600	771773	1591	2302160	66	35	12418	16	85	30681
	—2500	808298	15925.	2302526	655.	365.	12784	15	86	31046
	—2400	844823	1593	2302891	64	37	13149	14	87	31411
	—2300	881348	1594	2303256	63	38	13514	135.	885.	31777
	—2200	917873	1595	2303621	62	39	13879	12	89	32142
	—2100	954398	15965.	2303987	615.	405.	14245	11	90	32507
	—2000	1090923	1597	2304352	60	41	14610	10	91	32872
	—1900	1127448	1598	2304717	59	42	14975	95.	925.	33238
	— 1800	1163973	1599	2305082	58	43	15340	8	93	33603
	—1700	1200498	16005.	2305448	575.	445.	15706	7	94	33968
	—1600	1237023	1601	2305813	56	45	16071	6	95	34333
	—1500	1273548	1701	2342337	55	46	16436	55.	965.	34699
	— 1400	1210073	1801	2378861	54	47	16801	4	97	35064
	— 1300	1246598	1901	2415385	535.	485.	17167	3	98	35429
	—1200	1283123			52	49	17532	2	99	35794
	—1100	1319648			51	50	17897	15.	1005.	36160
	—1000	1356173			50	51	18262		100	36159

17

TABLE Ib.

Number of Days from Jan. 0 in Common Tears, and Jan. 1 in Bissextile Years.

													15§S.
		JANUARY.	FEBRUARY.
										1		H	i n	Bj	tl 3 &	fi H a
	Da/	Com-	BWn	Com-	Bissex-	9) 1	J	^	M	,j	o	1	8	t*	9	n	S u	S
	of	mon	tile	mon	tile		cu	2j	g	t^	8	B	^	0	B	R	o	a
	Month.	Year.	Year.	Year.	Year.			H					o	55	Q	o	K	s
	1	1	0	32	31	60	91	121	152	182	213	244	274	305	335	274	295	325
	2	2	1	33	32	61	92	122	153	183	214	245	275	306	336	275	296	326
	3	3	2	34	33	62	93	123	154	184	215	246	276	307	337	276	297	327
	4	4	3	35	34	63	94	124	155	185	216	247	277	308	338	277	298	328
	5	5	4	36	35	64	95	125	156	186	217	248	278	309	339		299	329
	6	6	5	37	36	65	96	126	157	187	218	249	279	310	340		300	330
	7	7	6	38	37	66	97	127	158	188	219	250	280	311	341		301	331
	8	8	7	39	38	67	98	128	159	189	220	251	281	312	342		302	W>
	9	9	8	40	39	68	99	129	160	190	221	252	282	313	343		303	333
	10	10	9	41	40	69	100	130	161	191	222	253	283	314	344		304	334
	11	11	10	42	41	70	101	131	162	192	223	254	284	315	345		305	335
	12	12	11	43	42	71	102	132	163	193	224	255	285	316	346		306	33()
	13	13	12	44	43	72	103	133	164	194	225	256	286	317	:t i?		307	337
	14	14	13	45	44	73	104	134	165	195	226	257	287	318	348		308	338
	15	15	14	46	45	74	105	135	166	196	227	258	288	319	349	278	309	339
	16	16	15	47	46	75	106	136	167	197	228	259	289	320	350	279	310	340
	17	17	16	48	47	76	107	137	168	198	229	260	290	321	351	280	311	341
	18	18	17	49	48	77	108	138	169	199	230	261	291	322	352	281	312	312
	19	19	18	50	49	78	109	139	170	200	231	262	292	323	353	282	313	343
	20	20	19	51	50	79	110	140	171	201	232	263	293	324	354	283	314	344
	21	21	20	52	51	80	111	141	172	202	233	264	294	325	355	284	315	345
	22	22	21	53	52	81	112	142	173	203	234	265	295	326	35(5	285	316	346
	23	23	22	54	53	82	113	143	174	204	235	266	296	327	357	286	317	:U7
	24	24	23	55	54	83	114	144	175	205	236	267	297	328	358	287	318	348
	25	25	24	56	55	84	115	145	176	206	237	268	298	329	359	288	319	349
	26	26	25	57	56	85	116	146	177	207	238	269	299	330	360	289	320	350
	27	27	26	58	57	86	117	147	178	208	239	270	300	:{.'( l	361	290	321	35 1
	28	28	27	59	58	87	118	148	179	209	240	271	301	:!.'(-,;	862	291	322	352
	29	29	28		59	88	119	149	180	210	241	272	302	333	:»;:(	292	323	:{;-,:<
	30	30	29			89	120	150	181	211	242	273	303	334	364	293	324	354
	31	31	30			90		151		212	243		304		365	294		355
	t

18

TABLE lc.

To Reduce Hours, Minutes, and Seconds of Time to Decimals of a Day.

Hours an.l Minutes.	Decimal of a Day.	Minutes.	Decimal of a Day.	Minutes and Seconds.	Decimal of a Day.	Seconds.	Decimal of a Day.
	h.		m.		m.		s.
	1	.041666667	13	.009027778	50	.034722222	23	.000266204
	2	.083333333	14	.009722222	51	.035416667	24	.000277778
	3	.125000000	15	.010416667	52	.036111111	25	.000289352
	4	.166666667	16	.011111111	53	.036805556	26	.000300926
	5	.208333333	17	.011805556	54	.037500000	27	.000312500
	6	.2.50000000	18	.012500000	55	.038194444	28	.000324074
	7	.291666667	19 ,	.013194444	56	.038888889	29	.000335648
	8	.333333333	20	.013888889 .	57	.039583333	30	.000347222
	9	.375000000	21	.014583333	58	.040277778.	31,	.000358796
	10	.416666667	22	.015277778	59	.040972222	32	.000370370
	11	.458333333	23	.015972222	60	.041666667	33	.000381944
	12	.500000000	24	.016666667			34	.000393519
	13	.541666667	25	.017361111			35	.000405093
	14	.583333333	26	.018055556			36	.000416667
	15	.625006000	27	.018750000			37	.000428241
					S.
	16	.666666667	28	.019444444	I	.000011574	38	.000439815
	17	.708333333	29	.020138889	2	.000023148	39	.000451389
	18	.750000000	30	.020833333	3	.000034722	40	.000462963
	19	.791666667	31	.021527778	4	.000046296	41	.000474537
	20	.833333333	32	.022222222	5	.000057870	42	.000486111
	21	.875000000	33	.022916667	6	.000069444	43	.000497685
	22	.916666666	34	.023611111	7	.000081019	44	.000509259
	23	.958333333	35	.024305556	8	.000092593	45	.000520833
	24	1.000000000	36	.025000000	9	.000104167	46	.000532407
			37	.025694444	10	.000115741	47	.000543981
	ni.
	i	.000694444	38	.026388889	11	.000127315	48	.000555556
	2	.001388889	39	.027083333	12	.000138889	49	.000567130
	3	.002083333	40	.027777778	13	.000150463	50	.000578704
	4	.002777778	41	.0-28472222	14	.000162037	51	.000590278
	5	.003472222	42	.029166667	15	.000173611	52	.000601852
	6	.004166667	43	.029861111	16	.000185185	53	.000613426
	7	.001861111	44	.030555556	17	.000196759	54	.000625000
	8	.005555556	45	.031250000	18	.000208333	55	.000636574
	9	.006250000	46	.031944444	19	.000219907	56	.000648148
	10	.006944444	47	.032638889	20	.000231481	57	.000659722
	11	.007638889	48	.033333333	21	.000243056	58	.000671296
	12	.008333333	49	.031027778	22	.000254630	59	.000682870
	13	.009027778	50	.034722222	23	.000266204	60	.000694444

19

TABLE II«.

Epochs and Arguments for each Thousandth Day, from 2300000 to 2400000. For Washington Mean Noon.

juiuMod. ii u' y-u (y-u') ARG. 1. I'. 8. «'.
							0.000		0.000
	2300000	315 909.18	It -1.34	130 248.9	+0.9	22.4927509	—1188	24.229050	+079
	2301000	171 2335.93	1.32	183 83.5	0.9	2.9741917	1173	6.247185	078
	2302000	28 162.69	1.30	235 3518.1	0.9	11.0101863	1158	20.077254	077
	2303000	244 1589.47	1.29	288 3352.7	0.9	19.0461825	1143	2.095387	076
	2304000	100 3016.27	1.27	341 3187.2	0.9	27.0821802	1128	15.925454	075
	2305000	317 843.09	1.26	34 3021.8	0.9	7.5636269	1113	29.755521	074
	2306000	173 2269.92	1.24	87 2856.4	0.8	15.5996276	1097	11.773650	073
	2307000	30 96.77	1.22	140 2690.9	0.8	23.6356298	1082	25.603715	072
	2308000	246 1523.64	1.21	193 2525.4	0.8	4.1170810	1067	7.62 1843	071
	2309000	102 2950.52	1.19	246 2359.9	0.8	12.1530862	1052	21.451905	070
	2310000	319 777.42	1.17	299 2194.4	0.8	20.1890929	1037	3.470031	069
	2311000	175 2204.34	1.15	352 2028.9	0.8	0.6705487	1022	17.300092	068
	2312000	32 31.27	1.13	45 1863.4	0.8	8.7065584	1007	31.130151	067
	2313000	248 1458.23	1.12	98 1697.8	0.8	16.7425697	0992	13.148273	066
	2314000	104 2885.19	1.10	151 1532.3	0.8	24.7785824	0977	26.978331	065
	2315000	321 712.18	1.09	204 1366.7	0.8	5.2600442	0962	8.996451	064
	2316000	177 2139.18	1.07	257 1201.1	0.7	13.2960600	0946	22.826507	063
	2317000	33 3566.20	1.05	310 1035.6	0.7	21.3320773	0931	4.844626	062
	2318000	250 1393.24	1.04	3 870.0	0.7	1.8135436	0916	18.674680	061
	2319000	106 2820.29	1.02	56 704.4	0.7	9.8495639	0901	0.692797	060
	2320000	323 647.37	1.00	109 538.6	0.7	17.8855856	0886	14.522848	059
	2321000	179 2074.45	0.98	162 373.0	0.7	25.9216089	0871	28.352899	058
	2322000	35 3501.56	0.96	215 207.4	0.7	6.4030813	0856	10.371013	057
	2323000	252 1328.68	0.95	268 41.7	0.7	14.4391077	0841	24.201061	056
	2324000	108 2755.82	0.93	320 3476.0	0.7	22.4751355	0826	6.219173	055
	2325000	325 582.98	0.92	13 3310.4	0.7	2.9566124	0811	20.049220	.054
	2326000	181 2010.15	0.90	66 3144.7	0.6	10.9926433	0795	2.067329	053
	2327000	37 3 137.31	0.88	119 2979.0	0.6	19.0286756	0780	15.897374	052
	2328000	254 1264.55	0.87	172 2813.2	0.6	27.0647095	0765	29.727418	051
	2329000	110 2691.77	0.85	225 2647.5	0.6	7.5461925	0750	11.745524	050
	2330000	327 519.02	0.83	278 2481.8	0.6	15.5822294	0735	25.575566	049
	2331000	183 1946.28	0.81	331 2316.0	0.6	23.6182678	0720	7.593* 171	048
	2332000	39 3373.55	0.79	24 2150.3	0.6	4.0997553	0705	21.423711	047
	2333000	256 1200.85	0.78	77 1984.5	0.6	12.1357967	0690	3.441814	046
	2334000	112 2628.16	0.76	130 1818.7	0.6	20.1718397	0675	17.271851	015
	2335000	329 455.48	0.75	183 1652.9	0.6	0.6533317	0660	31. 10 ISSN	044
	233<;ooo	185 1882. s:»	0.73	236 1IS7.I	0.5	8.68!):t777	0644	13.11!i!>ss	0 13
	•-2:07000	41 3310.19	0.71	289 1321.3	0.5	16.7254252	0629	26.950023	012
	2888000	258 1137.57	0.70	3J2 1155.4	0.5	24.7614742	0614	8.96812]	041
	2339000	114 2564.96	0.68	35 989.6	0.5	5.2429723	0599	22.798153	040
	•^:!IOOOO	331 392.38	0.66	88 823.7	0.5	13.2790243	0584	4.816249	039
	8841000	187 IMii.sl	0.64	141 657.8	0.5	21.315077N	0569	18.6102SO	038
	23 12000	43 3247.25	0.62	194 491.9	0.5	1.7965804	055 1	0.66 1373	037
	3848000	260 1071.72	0.61	247 326.0	0.5	9.8326370	0538	14.494402	036
	234 1000	116 2502.20	0.59	300 160.1	0.4	17.8686951	0523	28.324430	035
	23 15000	333 329.70	0.58	352 3594.2	0.4	25.9047547	0508	10.342521	034
	23 IfiOOO	189 1757.21	0.56	45 3428.3	0.4	6.3862634	0493	24. 1725 Hi	033
	23 17000	45 31S1.75	0.54	98 3202.3	0.4	14.422326 1	0478	6.190035	032
	2348080	262 1012.30	0.53	151 3096.3	0.3	22.4583902	0462	20.02065!)	031
	2849000	us 2i3!>. MI	0.51	204 2930.4	0.3	2.9399035	0447	2.038746	030
	3850000	335 207. 15	-0.49	257 2764.4	+0.3	10.9759706	-0432	15.868767	+029

20

TABLE Ha.

Epochs and Arguments for each Thousandth Day, from 2300000 to 2400000. For Washington Mean Noon.

juiianPeriod. u u' y-u (y-u') ARG. 1. 1'. 2. 2'.
							0.000		0.000
		O II	If	O ft	II	d.		d
	2350000	335 267.45	-0.49	257 2764.4	+0.3	10.9759706	-0432	15.868767	+029
	2351000	191 1695.05	0.47	310 2598.4	0.3	19.0120393	0417	29.698788	028
	2352000	47 3122.67	0.45	3 2432.4	0.3	27.0481095	0402	11.716872	027
	2353000	264 950.30	0.44	56 2266.4	0.3	7.5296288	0387	25.546891	026
	2354000	120 2377.96	0.42	109 2100.3	0.3	15.5657021	0372	7.564973	025
	2355000	337 205.63	0.41	162 1934.3	0.3	23.6017769	0357	21.394990	024
	2356000	193 1633.31	0.39	215 1768.2	0.2	4.0833007	0341	3.413069	023
	2357000	49 3061.02	0.37	268 1602.2	0.2	12.1193785	0326	17.243084	022
	2358000	266 888.74	0.36	321 1436.1	0.2	20.1554579	0311	31.073098	021
	2359000	122 2316.48	0.34	14 1270.0	0.2	0.6369863	0296	13.091175	020
	2360000	339 144.23	0.32	67 1103.9	0.2	8.6730686	0281	26.921186	019
	2361000	195 1572.01	0.30	120 937.8	0.2	16.7091525	0266	8.939261	018
	2362000	51 2999.80	0.28	173 771.6	0.2	24.7452379	0251	22.769271	017
	2363000	268 827.60	0.27	226 605.5	0.2	5.2267724	0235	4.787344	016
	2364000	124 2255.43	0.25	279 439.3	0.2	13.2628608	0220	18.617351	015
	2365000	341 83.27	0.24	332 273.2	0.2	21.2989508	0205	0.635422	014
	2366000	197 1511.13	0.22	25 107.0	0.1	1.7804898	0190	14.465428	013
	2367000	53 2939.00	0.20	77 3540.8	0.1	9.8165828	0175	28.295432	012
	2368000	270 766.90	0.19	130 3374.6	0.1	17.8526773	0159	10.313500	Oil
	2369000	126 2194.81	0.17	183 3208.4	0.1	25.8887734	0144	24.143503	010
	2370000	343 22.73	0.15	236 3042.2	0.1	6.3703184	0129	6.161569	009
	2371000	199 1450.68	0.13	289 2875.9	0.1	14.4064175	0114	19.991569	oca
	2372000	55 2878.64	0.11	342 2709.7	0.1	22.4425181	0099	2.009633	007
	2373000	272 706.62	0.10	35 2543.4	0.1	2.9240678	0083	15.839632	006
	2374000	128 2134.62	0.08	88 2377.2	0.1	10.9601715	0068	29.669629	005
	2375000	344 3562.63	0.06	141 2210.9	+0.1	18.9962766	005^	11.6876^0	004
	2376000	201 1390.66	0.04	194 2044.6	0.0	27.0323833	0037	25.517686	003
	2377000	57 2818.71	0.02	247 1878.3	0.0	7.5139391	0022	7.535745	002
	2378000	274 646.77	-0.01	300 1711.9	0.0	15.5500488	-0007	21.365738	+001
	2379000	130 2074.85	-i-O.Ol	353 1545.6	0.0	23.5861601	+0008	3.383795	000
	2380000	316 3502.95	0.03	46 1379.2	0.0	4.0677201	0021	17.213787	-001
	2381000	203 1331.07	0.05	99 1212.9	0.0	12.1038347	0039	31.043777	002
	2382000	59 2759.20	0.07	152 1046.5	0.0	20.1399505	0054	13.061831	003
	2383000	276 587.35	0.08	205 880.1	0.0	0.6215154	0070	26.891820	004
	2384000	132 2015.52	0.10	258 713.7	0.0	8.6576343	0085	8.909872	005
	2385000	348 3443.71	0.11	311 547.3	0.0	16.6937547	0100	22.739858	006
	2386000	205 1271.91	0.13	4 380.9	-0.1	24.7298766	0115	4.757908	007
	2387000	61 2700.13	0.15	57 214.5	0.1	5.2114476	0130	18.587893	008
	2388000	278 528.37	0.16	110 48.0	0.1	13.2475726	0146	0.605940	009
	2389000	134 1956.62	0.18	162 3481.6	0.1	21.2836990	0161	14.435923	010
	2390000	350 3384.89	0.20	215 3315.1	0.1	1.7652747	0176	28.265904	Oil
	2391000	207 1213.18	0.22	268 3148.6	0.1	9.8014042	0191	10.283949	012
	2392000	63 2641.49	0.24	321 2982.1	0.1	17.8375353	0206	24.113929	013
	2393000	280 469.81	0.25	14 2815.6	0.1	25.8736679	0222	6.131972	014
	2394000	136 1898.15	0.27	67 2649.1	0.2	6.3552496	0237	19.961949	015
	2395000	352 3326.51	0.28	120 2482.6	0.2	14.3913852	0252	1.979990	016
	2396000	209 1154.88	0.30	173 2316.1	0.2	22.4275224	0268	15.809965	018
	2397000	65 2583.27	0.32	226 2149.5	0.2	2.9091087	0283	29.639940	019
	2398000	282 411.68	0.33	279 1983.0	0.3	10.9452489	0299	11.657978	020
	2399000	138 1840.11	0.35	332 1816.4	0.3	18.9813907	0314	25.487950	021
	2400000	354 3268.55	+0.37	25 1649.8	-0.3	27.0175339	+0329	7.505986	-022

21

TABLE Ha.

Epochs and Arguments for each Thousandth Day, from 2300000 to 2400000. For Washington Mean Noon.

juiS^Veriod. ARG. 3. 3'. 4. S. 5'. 6. 7. 8. 9.
		d.	0.0000	d.	d.	0.00	d.	d.	d.	d.
	2300000	16.095387	-27	127.1121	383.5901	-14	23.6328	8.7464	3.8010	21.5098
	2301000	12.065368	27	31.3631	148.2332	14	13.0730	8.9197	3.6257	8.2136
	2302000	8.015349	27	300.S 137	324.6615	14	2.5132	9.0931	3.4504	24.7202
	2303000	3.975330	26	205.0647	89.3046	14	26.8004	9.2663	3.2750	11.4240
	2304000	29.465900	26	109.2856	265.7329	14	16.2406	9.4395	3.0997	27.9306
	2305000	25.425882	26	13.5065	30.3761	14	5.6808	9.6128	2.9244	14.6345
	2306000	21.385865	25	282.9872	206.8044	13	29.9679	0.1724	2.7491	1.3383
	2307000	17.345848	25	187.2081	383.2328	13	19.4081	0.3457	2.5738	17.8449
	2308000	13.305831	24	91.4290	147.8760	13	8.8483	0.5190	2.3984	4.5487
	••>:«>9000	9.265815	24	360.9097	324.3044	13	33.1354	0.6922	2.2231	21.0554
	2310000	5.225799	24	265.1306	88.9476	13	22.5756	0.8655	2.0478	7.7592
	2311000	1.185783	23	169.3515	265.3761	12	12.0158	1.0388	1.8725	24.2659
	2312000	26.676355	23	73.5725	30.0193	12	1.4560	1.2121	1.6972	10.9697
	2313000	22.636340	23	343.0531	206.4478	12	25.7431	1.3853	1.5218	27.4763
	2314000	18.596325	22	247.2741	382.8763	12	15.1833	1.5586	1.3465	14.1801
	2315000	14.556311	22	151.4950	147.5196	12	4.6235	1.7319	1.1712	0.8840
	2316000	10.516297	22	55.7159	323.9482	12	28.9106	1.9052	0.9959	17.3906
	2317000	6.476284	21	325.1966	88.5915	11	18.3508	2.0785	0.8206	4.0945
	2318000	2.436270	21	229.4175	265.0201	11	7.7910	2.2517	0.6452	20.6011
	2319000	27.926845	21	133.6384	29.6635	11	32.0781	2.4250	0.4699	7.3050
	2320000	23.886833	20	37.8594	206.0923	11	21.5183	2.5983	0.2946	23.8116
	3831000	19.846820	20	307.3400	382.5209	11	10.9585	2.7716	15.5066	10.5154
	2322000	15.806809 20	211.5609	147. Kill	10	0.3987	2.9449	15.3313	27.0221
	2323000	11.766797	19	115.7819	323.5930	10	24.6858	3.1182	15.1560	13.7260
	2324000	7.726786	19	20.0028	88.2365	10	14.1260	3.2915	14.9807	0.4298
	2325000	3.686775	19	289.4835	264.6652	10	3.5662	3.4648	14.8053	16.9365
	3826000	29.177352	18	193.7044	29.3087	10	27.8533	3.6380	14.6300	3.6403
	2327000	25.137342	18	97.9253	205.7374	10	17.2934	3.8113	14.4547	20.1470
	2328000	21.097332	18	2.1463	382.1662	09	6.7336	3.9846	14.2794	6.8508
	2329000	17.057323	17	271.6269	146.8098	09	31.0207	4.1579	14.1041	23.3575
	2330000	13.017314	17	175.8478	323.2386	09	20.4609	4.3312	13.9288	10.0613
	•J.'i.-ilOOO	8.977305	16	80.0688	87.8822	09	9.9011	4.5045	13.7535	26.56SO
	2882000	4.937296	16	349.5494	264.3110	09	34.1882	4.6778	13.5782	13.2719
	2383000	0.897288	16	253.7703	28.!).-, 17	09	23.6283	4.8511	13.4029	29.7785
	2334000	26.387869	15	157.9913	205.3835	08	13.0685	5.0244	13.2276	16.48v> I
	2335000	22.347861	15	62.2122	381.8124	08	2.5087	5.1977	13.0522	3.1863
	2336000	18.307854	15	331.6929 Mli. l.Vil	08	26.7958	5.3710	12.8769	19.6930
	3837000	14.267847	14	235.9136	322.NS50	08	16.3860	5.6443	12.7016	6.3968
	233Mioo	10.227841	14	110.1317	87.6286	08	5.6761	5.7176	12.5263	22.9035
	233<)000	e.lsls:;:.	14	11.3557	263.9577	07	29.9632	5.8909	12.3510	9.6074
	23 10000	2.147829	13	813.8868	28.6015	07	19.4034	6.0642	12.1757	26.1141
	•j:ui(XM)	27.638413	13	218.0579	205.0305	07	8.8436	6.2375	12.0004	12.8179
	2342000	23.598401	13	123.2782	381.4595	07	33.1306	6.4108	11.825)	29.3216
	2843000	19.558402	12	36.4991	1 Hi. 1033	07	22.6709	6.5841	11.6498	16.0285
	2344000	16.618396	12	295.9797	3v.",'. 5323	07	12.0110	6.7574	11.4745	2.732 1
	2946000	11.478894	12	200.2007	87.1762	06	1.4611	6.9307	11.2991	19.2391
	2846000	7.438391	11	104.4216	263.6053	06	26.7883	7.1041	11.1238	5.9429
	•-i:t I7(ii HI	3.:i!is:isi	11	8.6436	28.2 192	06	15.1784	7.2774	10.0 is.,	22.4-496
	2348000	28 -ss97:»	11	278.1232	204.IJ7S3	06	4.6ls:>	7.4507	10.7732	9.1535
	2349000	24J848970	10	182.3441	381.1074	06	28.9056 7.W 10	10.5979	25.6602
	2860000	•„'(). SOS9I.M -10	86.5651	145.7514	-08	|K 3i:.7	7.7973	10.4226	12.3641

TABLE

Epochs and Arguments for each Thousandth Day, from 2300000 to 2400000. For Washington Mean Noon.

juiiKiod. ARG. 3. 3'. 4. 5. 5. 6. 7. 8. 9.
		d.	0.0000	d.	d.	0.00	d.	d.	d.	d.
	2350000	20.808968	-10	86.5651	145.7514	-05	18.3457	7.7973	10.4226	12.3641
	2351000	16.768966	10	356.0457	322.1805	05	7.7859	7.9706	10.2473	28.8708
	2352000	12.728965	09	260.2666	86.8245	05	32.0730	8.1439	10.0720	15.5747
	2353000	8.688963	09	164.4876	263.2537	05	21.5131	8.3172	9.8967	2.2786
	2354000	4.648963	08	68.7085	27.8977	05	10.9533	8.4905	9.7214	18.7853
	2355000	0.608962	08	338.1891	204.3270	05	0.3934	8.6638	9.5460	5.4892
	2356000	26.099550	08	242.4101	380.7562	04	24.6805	8.8372	9.3707	21.9959
	2357000	22.059550	07	146.6310	145.4003	04	14.1207	9.0105	9.1954	8.6998
	2358000	18.019551	07	50.8520	321.8296	04	3.5608	9.1838	9.0201	25.2065
	2359000	13.979552	07	320.3326	86.4737	04	27.8479	9.3571	8.8448	11.9104
	2360000	9.939553	06	224.5536	262.9030	04	17.2880	9.5304	8.6695	28.4172
	2361000	5.899555	06	128.7745	27.5472	04	6.7282	0.0900	8.4942	15.1211
	2362000	1.859557	06	32.9954	203.9765	03	31.0152	0.2633	8.3189	1.8250
	2363000	27.350147	05	302.4760	380.4059	03	20.4554	0.4366	8.1436	18.3317
	2364000	23.310150	05	206.6970	145.0501	03	9.8955	0.6100	7.9683	5.0356
	2365000	19.270153	05	110.9179	321.4795	03	34.1825	0.7833	7.7930	21.5424
	2366000	15.230156	04	15.1389	86.1238	03	23.6227	0.95G6	7.6177	8.2463
	2367000	11.190160	04	284.6195	262.5532	02	13.0628	1.1300	7.4424	24.7530
	2368000	7.150164	04	188.8404	27.1975	02	2.5030	1.3033	7.2671	11.4569
	2369000	3.110169	03	93.0614	203.6270	02	26.7900	1.4766	7.0918	27.9636
	2370000	28.600762	03	362.5420	380.0565	02	16.230-2	1.6499	6.9165	14.6676
	2371000	24.560767	03	266.7629	144.7008	02	5.6703	1.8232	6.7412	1.3715
	2372000	20.520772	02	170.9839	321.1303	02	29.9573	1.9965	6.565SJ	17.8783
	2373000	16.480778	02	75.2048	85.7747	01	19.3975	2.1699	6.3906	4.5822
	2374000	12.440784	01	344.6854	262.2043	01	8.8376	2.3432	6.2153	21.0889
	2375000	8.400791	01	248.9064	26.8487	01	33.1246	2.5165	6.0400	7.7929
	2376000	4.360798	01	153.1273	203.2783	01	22.5648	2.6899	5.8648	24.2996
	2377000	0.320805	00	57.3483	379.7079	-01	12.0049	2.8632	5.6895	11.0035
	2378000	25.811401	-00	326.8289	144.3524	00	1.4450	3.0366	5.5142	27.5103
	2379000	21.771409	+00	231.0498	320.7820	00	25.7321	3.2099	5.3389	14.2142
	2380000	17.731417	01	135.2708	85.4265	00	15.1722	3.3832	5.1636	0.9181
	2381000	13.691425	01	39.4917	261.8562	00	4.6123	3.5565	4.9883	17.4249
	2382000	9.651434	01	308.9723	26.5007	00	28.8993	3.7299	5.8130	4.1288
	2383000	5.611444	02	213.1933	202.9305	00	18.3395	3.9032	4.6377	20.6356
	2384000	1.571454	02	117.4142	379.3602	-t-01	7.7796	4.0766	4.4624	7.3395
	2385000	27.062052	02	21.6352	144.0048	01	32.0666	4.2499	4.2871	23.8463
	2386000	23.022062	03	291.1158	320.4346	01	21.5067	4.4232	4.1118	10.5502
	2387000	18.982073	03	195.3367	85.0792	01	10.9469	4.5966	3.9365	27.0570
	2388000	14.942084	03	99.5577	261.5090	01	0.3870	4.7699	3.7612	13.7610
	2389000	10.902095	04	3.7786	26.1537	01	24.6740	4.9433	3.5859	0.4649
	2390000	6.862107	04	273.2592	202.5835	02	14.1141	5.1166	3.4106	16.9717
	2391000	2.822119	04	177.4802	379.0134	02	3.5542	5.2899	3.2353	3.6757
	2392000	28.312720	05	81.7011	143.6581	02	27.8413	5.4633	3.0600	20.1824
	2393000	24.272733	05	351.1817	320.0880	02	17.2814	5.6366	2.8847	6.8864
	2394000	20.232746	05	255.4027	84.7327	02	6.7215	5.8100	2.7094	23.3932
	2395000	16.192759	06	159.6236	261.1627	03	31.0085	5.9833	2.5341	10.0971
	2396000	12.152773	06	63.8446	25.8075	03	20.4486	6.1566	2.3589	26.6039
	2397000	8.112788	06	333.3252	202.2374	03	9.8887	6.3300	2.1836	13.3078
	2398000	4.072802	07	237.5461	378.6674	03	34.1757	6.5033	2.0083	0.0118
	2399000	0.032817	07	141.7671	143.3123	03	23.6158	6.6767	1.8330	16.5186
	2400000	25.523420 -+-08	45.9880	319.7423	+03	13.0559	6.8500	1.6577	3.2226

23

TABLE lie

Epochs and Arguments for each Thousandth Day, from 2300000 to 2400000. For Washington Mean Noon.

jJKod. ARG- IOt '*• I2' 13' 14' l5' 16' l7'
	2300000	23.5709	6.1437	211.1477	9.3568	a. 25.412	6.884	0.887	10.837
	2301000	24.3246	11.6470	171.2876	0.8971	1.197	13.471	2.544	27.256
	2302000	25.0784	17.1501	131.4274	2.5220	6.246	5.866	4.751	16.355
	2303000	0.2104	22.6538	91.5673	4.1470	11.295	12.454	6.958	5.451
	2304000	0.9642	1.2788	51.7072	5.7719	16.343	4.849	9.165	21.871
	2305000	1.7179	6.7822	11.8470	7.3968	21.392	11.437	11.371	10.969
	2306000	2.4716	12.2856	318.6070	9.0217	26.440	3.832	13.578	0.067
	2307000	3.2254	17.7890	278.7469	0.5620	2.226	10.419	1.531	16.486
	2308000	3.9791	23.2923	238.8867	2.1870	7.274	2.815	3.738	5.584
	2309000	4.7329	1.9174	199.0266	3.8119	12.323	9.402	5.945	22.005
	2310000	5.4866	7.4208	159.1665	5.4368	17.371	1.798	8.152	11.101
	2311000	6.2403	12.9242	119.3063	7.0617	22.420	8.385	10.359	0.199
	2312000	6.9941	18.4276	79.4462	8.6866	27.468	0.781	12.566	16.619
	2313000	7.7478	23.9309	39.5860	0.2269	3.254	7.368	0.519	5.717
	2314000	8.5016	2.5560	346.8460	1.8519	8.303	13.955	2.726	22.136
	2315000	9.2553	8.0593	306.4858	3.4768	13.351	6.351	4.933	11.234
	2316000	10.0091	13.5627	266.6257	5.1017	18.400	12.938	7.140	0.332
	2317000	10.7629	19.0661	226.7655	6.7267	23.448	5.334	9.347	16.752
	2318000	11.5166	24.5694	186.9053	8.3516	28.497	11.921	11.554	5.849
	2319000	12.2704	3.1945	147.0451	9.9765	4.282	4.316	13.761	22.269
	2320000	13.0241	8.6978	107.1850	1.5168	9.330	10.905	1.714	11.366
	2321000	13.7779	14.2011	67.3248	3.1417	14.379	3.299	3.921	0.464
	8828000	14.5316	19.7045	27.4646	4.7666	19.428	9.886	6.128	16.884
	2323000	15.2854	25.2078	334.22 Hi	(i.3915	24.476	2.282	8.335	5.982
	2324000	16.0391	3.8329	294.3644	8.0165	0.262	8.869	10.542	22.401
	2325000	16.7929	9.3362	254.5042	9.6414	5.310	1.265	12.749	11.499
	2326000	17.5167	11.8396	214.6440	1.1817	10.359	7.852	0.702	0.597
	2327000	18.3004	20.3429	174.7838	2.8067	15.407	0.248	2.909	17.016
	2:528000	19.0542	25.8463	134.9236	4.4316	20.456	6.835	5.116	6.114
	2329000	19.8079	4.4713	95.0634	6.0565	25.505	13.422	7.323	22.534
	2:i:»oooo	20.5617	9.9746	55.2032	7.6814	1.290	5.817	9.530	11.631
	2331000	21.8156	15.4780	15.3130	9.3063	6.338	12.405	11.737	0.729
	2332000	22.0693	20.9818	322.1029	0.8466	11.887	4.800	13.944	17.149
	2333000	22.N23 1	26.4847	282.2 127	2.4715	16.435	11.388	1.897	6.247
	2334000	23.5768	5.1097	2 12.3S2.-.	4.0965	21.484	3.785	4.104	22.666
	•885000	24.3306	10.6130	202.5223	5.7214	26.532	10.370	6.311	11.7(11
	2336000	25.0844	16.1M4	162.6621	7.8463	2.318	2.766	8.518	0.862
	3887000	0.2164	21.6197	122.8018	8.9713	7.366	9.355	10.725	17.282
	2888600	0.9702	0.2447	82.9416	0.5116	12.415	1.749	13.983	6.379
	•-J339000	l.794t	5.7481	43.0814	2.1365	17.464	8.336	0.885	22.799
	23 10000	2^778	11.2513	3.2212	3.7614	22.512	0.732	3.092	11.897
	2:iilOOO	3.28W	16.7547	309.9811	5.386U	27.560	7.818	5.299	0.995
	3849000	8.98S4	22.25SO 270.] -JO!)	7.0112	&346	13.906	7.506	17.414
	2:u:t<MM>	4.7392	O.NS30 230.2606	s.(i:i(ii	s.3!ii	6.802	9.713	6.512
	2:! 11000	5. mo	6.8Kti3	190.4004	0.1764	13.443	12.889	11.920	22.932
	9845000	<;.2Ki7	11.8MI7	150.5102	1.8013	18.491	5.285	14.127	12.029
	2846000	7.0005	17.3930 110.li7!l!l	&4S68	23.540	11.893	2.080	1.127
	8847000	7.7.r)i:<	22>!Mi:i 70.8197	r>.o:,i2	28.588	4.267	4.287	17.547
	3848000	-.,()>! 1.5213 30.9594	6.6761	4.375	10.855	6.494	6.645
	9848000	!i.2<Jl!i 7.02 Hi	8S7.7198	8.3010	!». 122	8.350	8.701	23.064
	8SD0006	lO.Oir,-; 12.5279	297.8590	9.9259	14.471	9.837	10.908	12.162

24

TABLE Ha.

Epochs and Arguments for each Thousandth Day, from 2300000 to 2400000. For Washington Mean Noon.

Dayof ARG. IO. 11. 12. 13. 14. 15. 1C. 17. Juliun Period.
	2350000	10.0157	d. 12.5279	297.8590	cl. 9.9259	d. 14.471	d. 9.837	d. 10.908	12.162
	2351000	10.7695	18.0313	257.9988	1.4662	19.519	2.233	13.115	1.260
	2352000	11.5233	23.5346	218.1385	3.0911	24.568	8.820	1.068	17.679
	2353000	12.2771	2.1596	178.2782	4.7160	0.353	1.216	3.275	6.777
	2354000	13.0309	7.6629	138.4180	6.3410	5.401	7.805	5.482	23.197
	2355000	13.7847	13.1662	98.5577	7.9659	10.450	0.199	7.690	12.295
	2356000	14.5385	18.6695	58.6974	9.5908	15.498	6.786	9.897	1.393
	2357000	15.2923	24.1728	18.8372	1.1311	20.547	13.374	12.104	17.812
	2358000	16.0461	2.7978	325.5970	2.7561	25.595	5.769	0.057	6.910
	2359000	16.7999	8.3011	285.7367	4.3810	1.381	12.357	2.264	23.329
	2360000	17.5537	13.8044	245.8764	6.0059	6.429	4.752	4.470	12.427
	2361000	18.3075	19.3077	206.0161	7.6308	11.478	11.339	6.677	1.525
	2362000	19.0613	24.8110	166.1558	9.2557	16.526	3.734	8.885	17.945
	2363000	19.8151	3.4360	126.2956	0.7960	21.575	10.322	11.091	7043
	2364000	20.5690	8.9393	86.4353	2.4209	26.623	2.717	13.299	23.462
	2365000	21.3228	14.4426	46.5750	4.0458	2.409	9.304	1.252	12.560
	2366000	22.0766	19.9459	6.7147	5.6708	7.457	1.700	3.459	1.658
	2367000	22.8305	25.4492	313.4745	7.2957	12.506	8.287	5.666	18.077
	2368000	23.5843	4.0742	273.6142	8.9206	17.554	0.683	7.873	7.175
	2369000	24.3381	9.5774	233.7539	0.4609	22.603	7.270	10.080	23.595
	2370000	25.0919	15.0807	193.8936	2.0858	27.651	13.858	12.287	12.693
	2371000	0.2240	20.5840	154.0333	3.7107	3.437	6.253	0.240	1.790
	2372000	0.9778	26.0873	114.1729	5.3356	8.485	12.841	2.447	18.210
	2373000	1.7317	4.7123	74.3126	6.9605	13.534	5.236	4.654	7.308
	2374000	2.4855	10.2156	34.4523	8.5855	18.582	11.825	6.861	23.727
	2375000	3.2393	15.7188	341.2121	0.1258	23.631	4.219	9.068	12.825
	2376000	3.9932	21.2221	301.3518	1.7507	28.679	10.806	11.275	1.923
	2377000	4.7470	26.7254	261.4914	3.3757	4.464	3.201	13.482	18.343
	2378000	5.5009	5.3504	221.6311	5.0006	9.513	9.789	1.435	7.440
	2379000	6.2547	10.8536	181.7708	6.6255	14.561	2.184	3.642	23.860
	2380000	7.0085	16.3569	141.9104	8.2504	19.610	8.772	5.849	12.958
	2381000	7.7623	21.8602	102.0501	9.8753	24.659	1.167	8.056	2.056
	2382000	8.5162	0.4852	62.1897	1.4156	0.444	7.755	10.263	18.475
	2383000	9.2700	5.9884	22.3294	3.0405	5.492	0.150	12.470	7.573
	2384000	10.0239	11.4917	329.0892	4.6654	10.541	6.737	0.423	23.993
	2385000	10.7777	16.9950	289.2288	6.2903	15.589	13.325	2.630	13.091
	2386000	11.5316	22.4983	249.3685	7.9153	20.638	5.720	4.837	2.188
	2387000	12.2855	1. 1232	209.5081	9.5402	25.686	12.308	7.044	18.608
	2388000	13.0393	6.6265	169.6477	1.0805	1.472	4.703	9.252	7.706
	2389000	13.7932	12.1298	129.7874	2.7054	6.520	11.291	11.458	24.125
	2390000	14.5470	17.6330	89.9270	4.3303	11.569	3.686	13.665	13.223
	2391000	15.3008	23.1363	50.0666	5.9552	16.617	10.273	1.618	2.321
	2392000	16.0547	1.7612	10.2063	7.5801	21.666	2.669	3.826	18.741
	2393000	16.8086	7.2615	316.9660	9.2050	26.714	9.256	6.033	7.839
	2394000	17.5624	12.7677	277.1056	0.7453	2.499	1.652	8.240	24.258
	2395000	18.3163	18.2710	237.2453	2.3702	7.548	8.239	10.447	13.356
	2396000	19.0702	23.7743	197.3849	3.9952	12.596	0.635	12.654	2.454
	2397000	19.8240	2.3992	157.5245	5.6201	17.645	7.222	0.607	18.873
	239NOOO	20.5779	7.9025	117.6641	7.2450	22.693	13.810	2.814	7.971
	2399000	21.3317	13.4057	77.8037	8.8699	27.742	6.205	5.021	24.39 1
	2400000	22.0856	18.9090	37.9133	0.4102	3.527	12.792	7.228	13.489

25

TABLE

Epochs and Arguments for each Thousandth Day, from 2300000 to 2400000. For Washington Mean Noon.

,^ A,. ,, ... *, ... *,. «. «. «. 3«.
	d.	d.	d.	d.	d.	d.	d.	d.	d.
	2300000	7.892	22.048	4.908	57.34	18.074	6.402	6.714	0.194	5.702
	2301000	0.786	1.356	2.696	3.97	22.104	7.868	10.976	7.274	4.214
	230-2000	3.553	4.966	0.484	82.27	26.133	9.333	1.963	4.987	2.725
	2303000	6.320	8.576	12.589	28.90	30.162	10.799	6.225	2.699	1.237
	2304000	9.086	12.185	10.378	107.20	2.063	12.264	10.487	0.412	5.572
	2305000	1.980	15.795	8.166	53.83	6.093	13.730	1.474	7.491	4.083
	2306000	4.747	19.405	5.954	0.46	10.122	15.196	5.736	5.204	2.595
	2307000	7.513	23.014	3.742	78.76	14.152	16.661	9.999	2.916	1.107
	2308000	0.407	2.322	1.530	25.39	18.181	18.127	0.985	0.6-29	5.441
	2309000	3.174	5.932	13.635	103.70	22.210	19.592	5.247	7.708	3.953
	2310000	5.942	9.542	11.423	50.33	26.239	21.058	9.510	5.422	2.465
	2311000	8.708	13.151	9.211	128.63	30.268	22.524	0.495	3.134	0.977
	2312000	1.602	16.761	6.999	75.26	2.170	0.215	4.758	0.847	5.311
	2313000	4.369	20.371	4.787	21.89	6.199	1.680	9.021	7.926	3.823
	8814000	7.136	23.981	2.575	100.19	10.228	3.146	0.007	5.639	2.335
	2315000	0.029	3.288	0.363	46.82	14.258	4.612	4.269	3.352	0.847
	2316000	2.796	6.898	12.468	125.12	18.287	6.077	8.532	1.064	5.181
	2317000	5.563	10.508	10.256	71.75	22.316	7.543	12.794	8.144	3.693
	2318000	8.330	14.117	8.044	18.38	26.346	9.008	3.780	5.857	2.204
	2319000	1.224	17.727	5.832	96.69	30.375	10.474	8.042	3.569	0.716
	2320000	3.991	21.337	3.620	43.32	2.277	11.940	12.305	1.282	5.051
	2321000	6.758	0.644	1.408	121.62	6.305	13.406	3.292	8.361	3.563
	8839000	9.525	4.254	13.513	68.25	10.335	14.871	7.554	6.074	2.074
	8888000	2.419	7.864	11.301	14.88	14.364	16.337	11.816	3.786	0.586
	2321000	5.186	11.474	9.090	93.18	18.393	17.802	2.803	1.499	4.921
	2325000	7.952	15.084	6.878	39.81	22.423	19.268	7.065	8.579	3.432
	2326000	0.816	18.693	4.666	118.11	26.452	20.734	11.3-27	6.291	1.944
	23-27000	3.613	22.305	2.454	64.74	30.481	22.199	8.314	4.004	6.279
	2328000	6.380	1.611	0.242	11.37	2.382	23.665	6.576	1.717	4.790
	2329000	9.146	5.221	12.347	89.67	6.412	1.355	10.838	8.796	3.302
	2330000	2.041	8.830	10.135	36.30	10.441	2.821	1.825	6.509	1.814
	2331000	4.808	12.440	7.923	114.61	14.471	4.287	6.088	4.221	0.326
	8889000	7.574	16.050	5.711	61.24	18.500	5.753	10.350	1.934	4.660
	2333000	0.468	19.660	3.499	7.87	22.529	7.218	1.336	9.014	3.172
	2334000	3.235	23.269	1.287	86.17	26.558	8.684	5.599	6.727	1.684
	2335000	Mm	2.577	13.392	32.80	30.588	10.150	9.861	4.481	0.1 96
	8889000	8.769	6.187	11.180	111.10	2.489	11.615	0.847	'2.151	4.530
	8887000	1.663	9.797	8.969	57.73	6.518	13.081	5.110	9.231	8.041
	8888000	4.430	13.407	6.757	4.36	10.547	14.546	9.372	6.944	1.664
	233UOOO	7.196	17.016	4.545	82.66	14.577	16.012	0.358	4.656	0.065
	23 10000	0.090	20.626	2.333	29.29	18.606	17.478	4.621	2.369	4.400
	8841000	2.857	24.236	0.121	107.60	22.636	18.944	8.884	0.082	2.912
	8848000	5.624	3.544	12.226	51. "23	26.665	20.410	13.146	7.161	1.423
	23 13000	8.391	7.154	10.014	0.86	30.694	21.875	4.13-2	4.874	5.758
	23 11000	1.285	10.765	7.803	79.16	2.5»5	23.341	8.395	2.586	4.270
	23 15000	4.052	14.375	5.591	25.79	6.625	1.032	12.657	0.299	2.781
	8849000	6.818	17.!)N:. 3.379 104.09 10.654	2.497	3.644	7.379	1.293
	23 17000	9.585	21.595 1.167, 50.72	14.683	3.963	7.906	5.091	5.628
	231 MM id	2.479	0.900 13.272 129.03	18.713	5.428	12.16H	2.804	4,189
	8849000	5.2 It!	4.510	11.061 75.66	22.742	6.894	3.155	0.517	2.651
	8850000	8.013	8.120	8.848 22.29	26.771	8.360	7.417	7.596	1.163
1

26

TABLE Ila.

Epochs and Arguments for each Thousandth Day, from 2300000 to 2400000. For Washington Mean Noon.

juiia^rioa ARG. 18. ID. 2O. 2L. 22. 23. 24. 23. 26.
	2350000	8.013	d. 8.120	d. 8.848	d. 22.29	d. 26.771	d 8.360	d 7.417	7.596	ii. 1.163
	2351000	0.907	11.730	6.636	100.59	30.801	9.826	11.679	5.309	5.498
	2352000	3.674	15.340	4.424	47.22	2.702	11.292	2.666	3.021	4.010
	2353000	6.411	18.950	2.212	125.52	6.731	12.757	6.929	0.734	2.521
	2351000	9.208	22.560	0.000	72.15	10.761	14.223	11.191	7.814	1.033
	2355000	2.102	1.868	12.106	18.78	14.790	15.689	2.177	5.526	5.368
	2356000	4.869	5.478	9.894	97.09	18.819	17.154	6.440	3.239	3.879
	2357000	7.636	9.088	7.682	43.72	22.849	18.620	10.702	0.951	2.391
	2358000	0.530	12.697	5.470	122.02	26.878	20. )85	1.688	8.031	0.903
	2359000	3.297	16.307	3.258	68.65	30.907	21.551	5.951	5.744	5.238
	2360000	6.064	19.917	1.046	15.28	2.809	23.017	10.214	3.457	3.749
	2361000	8.830	23.527	13.151	93.58	6.838	0.708	1.200	1.169	2.261
	2362000	1.724	2.835	10.940	40.20	10.867	2.174	5.463	8.250	0.773
	2363000	4.491	6.445	8.728	118.51	14.897	3.639	9.725	5.961	5.107
	2364000	7.258	10.055	6.516	65.14	18.926	5.105	0.711	3.674	3.619
	2365000	0.152	13.665	4.304	11.78	22.955	6.571	4.974	1.387	2.131
	2366000	2.919	17.274	2.092	90.08	26.984	8.036	9.236	8.466	0.643
	2367000	5.686	20.884	, 14.197	36.71	31.014	9.502	0.223	6.179	4.977
	2368000	8.452	0.192	11.985	115.01	2.915	10.967	4.485	3.892	3.489
	2369000	1.347	3.803	9.774	61.64	6.944	12.433	8.748	1.604	2.001
	2370000	4.113	7.412	7.562	8.27	10.974	13.899	13.010	8.684	0.513
	2371000	6.880	11.022	5.350	86.57	15.003	15.365	3.997	6.396	4.847
	2372000	9.647	14.632	3.138	33.20	19.032	16.831	8.259	4.109	3.359
	2373000	2.541	18.242	0.926	111.51	23.062	18.296	12.521	1.822	1.871
	2374000	5.308	21.852	13.031	58.14	27.091	19.762	3.508	8.901	0.383
	2375000	8.075	1.160	10.819	4.77	31.120	21.228	7.770	6.614	4.717
	2376000	0.96:,	4.770	8.607	83.07	3.022	22.693	12.033	4.327	3.229
	2377000	3.736	8.379	6.396	29.70	7.051	0.384	3.019	2.039	1.741
	2378000	6.503	11.989	4.184	108.00	11.080	1.849	7.282	9.119	0253
	2379000	9.270	15.599	1.972	54.63	15.110	3.315	11.544	6.831	4.587
	2380000	2.164	19.209	14.077	1.27	19.139	4.781	2.531	4.544	3.099
	2381000	4.931	22.819	11.865	79.57	23.168	. 6.247	6.793	2.257	1.611
	2382000	7.697	2.127	9.653	26.20	27.198	7.713	11.055	9.337	0.123
	2383000	0.591	5.737	7.442	104.50	31.227	9.178	2.042	7.049	4.457
	2384000	3.358	9.347	5.230	51.13	3.128	10.644	6.305	4.762	2.969
	2385000	6.125	12.957	3.018	129.43	7.158	12.110	10.568	2.475	1.481
	2386000	8.892	16.567	0.806	76.06	11.187	13.575	1.555	0.187	5.815
	2387000	1.786	20.177	12.911	22.70	15.216	15.041	5.816	7.267	4.327
	2388000	4.553	23.787	10.699	101.00	19.245	16.506	10.078	4.980	2.839
	2389000	7.319	3.095	8.487	47.63	23.275	17.972	1.065	2.692	1.351
	2390000	0.214	6.705	6.276	125.93	27.301	19.438	5.327	0.405	5.685
	2391000	2.981	10.315	4.064	72.56	31.331	20.904	9.590	7.484	4.197
	2392000	5.748	13.925	1.852	19.19	3.235	22.370	0.576	5.197	2.709
	2393000	8.514	17.535	13.957	97.50	7.264	0.060	4.839	2.910	1.221
	2394000	1.408	21.145	11.745	44.13	11.294	1.526	9.102	0.622	5.555
	2395000	4.175	0.453	9.534	122.43	15.323	2.992	0.088	7.702	4.067
	2396000	6.942	4.063 7.322	69.06	19.352	4.457	4:350	5.415	2.579
	2397000	9.709	7.673 5.110	15.69	23.381	5.923	8.613	3.127	1.090
	2898000	2.603	11.283 2.898	93.99	27.411	7.388	12.875	0.840	5.425
	2399000	5.370	14.893 0.686	40.62	31.410	8.854	3.862	7.920	3.937
	2100000	8.137	18.503 12.791	118.93	3.342	10.320	8.124	5.633	2.449

27

TABLE II«.

Epochs and Arguments for each Thousandth Day, from 2300000 to 2100000. For Washington Mean Noon.

JulKriod. AK(J- 97' 28' "' 30< 3I> 33t 33> 34< 35<
	2300000	it 15.42	22.494	32.009	2.076	d. 14.53	d. 4.53	23.94	d. 5.18	8.26
	2301000	8.19	20.922	16.336	6.466	3.78	6.72	17.97	2.75	2.69
	2302000	0.96	19.350	0.662	0.486	8.34	8.91	12.00	0.32	21.06
	2303000	19.56	17.778	17.753	4.877	12.91	11.10	6.04	24.98	15.48
	2301000	12.33	16.205	2.080	9.267	2.15	13.29	0.07	22.55	9.91
	2305000	5.10	14.633	19.171	3.287	6.71	15.48	26.55	20.12	4.34
	230GOOO	23.70	13.061	3.497	7.678	11.28	1.04	20.58	17.69	22.70
	2307000	16.47	11.488	20.588	1.697	0.52	3.23	14.61	15.26	17.13
	2308000	9.24	9.916	4.915	6.087	5.09	5.42	8.65	12.83	11.56
	2309000	2.01	8.344	22.006	0.107	9.65	7.61	2.68	10.40	5.98
	2310000	20.61	6.772	6.332	4.498	14.22	9.80	29.16	7.97	0.41
	2311000	13.38	5.200	23.424	8.888	3.46	11.99	23.19	5.54	18.78
	2312000	6.15	3.628	7.750	2.908	8.02	14.18	17.22	3.11	13.21
	2313000	24.75	2.055	24.841	7.299	12.59	16.37	11.25	0.68	7.63
	2314000	17.52	0.483	9.168	1.318	1.83	1.93	5.29	25.34	2.06
	2315000	10.29	37.433	26.259	5.709	6.40	4.12	31.77	22.91	20.43
	2316000	3.06	35.860	10.585	10.099	10.96	6.31	25.78	20.48	14.85
	2317000	21.66	31.288	27.676	4.119	0.21	8.50	19.81	18.05	9.28
	2318000	14.43	32.715	12.003	8.509	4.77	10.69	13.84	15.62	3.70
	2319000	7.20	31.143	29.094	2.529	9.33	12.88	7.88	13.19	22.07
	2320000	25.80	29.571	13.421	6.919	13.90	15.07	1.91	10.76	l(i..r)()
	2321000	18.57	27.999	30.511	0.939	3.14	0.63	28.41	8.33	10.93
	2322000	11.34	26.427	14.838	5.329	7.71	2.82	22.44	5.90	5.35
	2323000	4.11	24.854	31.929	9.720	12.28	5.01	16.47	3.47	23.72
	2324000	22.71	23.282	16.256	3.740	1.52	7.20	10.51	1.04	18.15
	2325000	15.48	21.710	0.582	8.130	6.08	9.39	4.54	25.70	12.57
	232(5000	8.25	20.137	17.673	2.149	10.64	11.58	31.02	23.27	7.00
	2327000	1.02	18.565	2.000	6.540	15.21	13.77	25.05	20.84	1.42
	2:^8000	19.62	16.992	19.091	0.560	4.46	15.96	19.08	18.41	19.79
	2329000	12.39	15.420	3.418	4.951	9.02	1.52	13.12	15.98	11.22
	2330000	5.16	13.848	20.509	9.341	13.59	3.72	7.15	13.55	N.I;.-,
	a.-wooo	23.76	12.276	4.835	3.361	2.83	5.91	1.18	11.12	3.07
	2:t:<2000	16.53	10.704	21.926	7.751	7.39	8.10	27.66	8.69	21.lt
	2333000	9.30	9.132	6.253	1.771	11.95	10.29	21.69	6.26	15.87
	2334000	27.90	7.559	23.344	6.161	1.20	12.48	15.72	3.83	10.29
	•BS500Q	20.67	5.987	7.671	0.181	5.77	14.67	9.76	1.40	4.72
	233GOOO	13.44	4.415	24.763	4.572	10.33	0.23	3.79	26.06	23.08
	2337000	6.21	2.842	9.088	8.962	14.90	2.42	30.27	23.63	17.51
	2338000	24.80	1.270	26.179	2.982	4.14	4.61	•J 1.30	21.20	11.91
	2339000	17.58	38.220	10.506	7.372	8.70	6.80	18.33	18.77	6.37
	2310000	10.35	36.648	27.597	1.392	13.27	8.99	12.37	16.34	0.79
	•j:illOOO	3.12	35.076	11.924	5.782	2.51	11.18	6.10	13.91	19.16
	gttaooo	21.71	33.504	29.015	10.173	7.08	13.37	0,13	11.48	18.59
	BM80M	14.49	31.931	13.312	4.193	11.64	15.56	26.91	9.05	8.01
	2:1 1 1000	07.26	30.359	30.433	8.583	0.89	1.12	20.94	6.62	2.44
	•j:tt:.o»i)	0.02	28.787	14.760	2.603	5.45	331	14.98	4.19	20.81
	•j:tiiiiio()	18.62	27.214	31.850	6.993	10.01	.r)..r)()	9.01	1.76	15.24
	23 17000	11.1(1	25.612	16.178	1.013	14.58	7.69	3.01	26.42	9.66
	•J:UM)OO	4.17	210li9	0.504	5.403	BJBt	9.88	29.52	23.99	4.09
	23i!>ooo	22 76	22. 1!I7	17.595	9.794	8.:i<»	12.07	23.55	21.56	22.45
	•j:t:»oooo	15.54	8OM0	1.922	3.814	12.95	14.26	17.59	19.13	16.88

TABLE Ha.

Epochs and Arguments for each Thousandth Day, from 2300000 to 2400000.

For Washington Mcau Noon.

JulKiod. AttG- 27' 3S' "' 30' 3I< 3a< 33« 31' 35'
	2350000	d. 15.54	20.925	d. 1.922	d. 3.814	d 12.95	14.26	d. 17.59	19.13	1688
	2351000	8.31	19.353	19.013	8.204	2.20	16.45	11.62	16.70	11.31
	2352000	1.08	17.780	3.340	2.224	6.76	2.01	5.65	14.27	5.73
	2353000	19.67	16.208	20.431	6.614	11.32	4.20	32.13	11.84	24.10
	2354000	12.45	14.635	4.757	0.634	0.57	6.39	26.16	9.41	18.53
	2355000	5.23	13.063	21.848	5.024	5.13	8.58	20.20	6.98	12.96
	2356000	23.81	11.491	6.175	9.415	9.70	10.77	14.23	4.55	7.38
	2357000	16.58	9.918	23.266	3.435	14.26	12.96	8.26	2.12	1.81
	2358000	9.36	8.346	7.593	7.825	3.51	15.15	2.29	26.78	20.18
	2359000	2.13	6.773	24.684	1.845	8.07	0.71	28.77	24.35	14.60
	2360000	20.72	5.201	9.011	6.235	12.64	2.90	22.81	21.92	9.03
	2361000	13.50	3.629	26.102	0.255	1.88	5.09	16.84	19.49	3.46
	2362000	6.27	2.057	10.429	4.645	6.44	7.28	10.87	17.06	21.82
	2363000	24.86	0.484	27.520	9.036	11.01	9.47	4.90	14.63	16.25
	2364000	17.63	37.434	11.846	3.056	0.25	11.66	31.38	12.20	10.68
	2365000	10.41	35.862	28.938	7.446	4.82	13.85	25.42	9.77	5.10
	2366000	3.18	34.289	13.265	1.466	9.38	16.04	19.45	7.34	23.47
	2367000	21.77	32.717	30.355	5.856	13.95	1.60	13.48	4.91	17.90
	2368000	14.54	31.144	14.682	10.247	3.19	3.79	7.51	2.48	12.32
	2369000	7.32	29.572	31.773	4.266	7.75	5.99	1.54	0.05	6.75
	2370000	0.08	28.000	16.100	8.657	12.32	8.18	28.03	24.71	1.18
	2371000	18.68	26.428	0.427	2.676	1.56	10.37	22.06	22.28	19.55
	2372000	11.46	24.856	17.518	7.067	6.13	12.56	16.09	19.85	13.97
	2373000	4.23	23.283	1.845	1.087	10.69	14.75	10.12	17.42	8.40
	2374000	22.82	21.711	18.936	5.477	15.26	0.31	4.15	14.99	2.82
	2375000	15.59	20.139	3.263	9.868	4.50	2.50	30.64	12.56	21.19
	2376000	8.37	18.566	20.354	3.887	9.06	4.69	24.67	10.13	15.62
	2377000	1.14	16.994	4.682	8.278	13.63	6.88	18.70	7.70	10.04
	2378000	19.73	15.421	21.772	2.298	2.87	9.07	12.73	5.27	4.47
	2379000	12.50	13.849	6.099	6.688	7.44	11.26	6.76	2.84	22.84
	2380000	5.28	12.277	23.190	0.708	12.00	13.45	0.80	0.41	17.27
	2381000	23.87	10.705	7.516	5.098	1.25	15.64	27.28	25.07	11.69
	2382000	16.64	9.132	24.608	9.489	5.81	1.20	21.31	22.64	6.12
	2383000	9.42	7.560	8.934	3.508	10.37	3.39	15.34	20.21	0.54
	2384000	2.19	5.987	26.026	7.899	14.94	5.58	9.37	17.78	18.91
	2385000	20.78	4.415	10.352	1.918	4.19	7.77	3.41	15.35	13.34
	2386000	13.55	2.843	27.444	6.309	8.75	9.96	29.89	12.92	7.77
	2387000	6.33	1.270	11.770	0.329	13.31	12.15	23.92	10.49	2.19
	2388000	24.92	38.220	28.861	4.719	2.56	14.34	17.95	8.06	20.56
	2389000	17.69	36.647	13.188	9.110	7.12	16.53	11.98	5.63	14.99
	2390000	10.47	35.075	30.279	3.129	11.68	2.09	6.02	3.20	9.41
	2391000	3.24	33.503	14.606	7.520	0.93	4.28	0.05	0.77	3.84
	2392000	21.83	31.931	31.697	1.539	5.49	6.47	26.53	25.43	22.21
	2393000	14.61	30.358	16024	5.930	10.06	8.66	20.56	23.00	16.63
	2394000	7.38	28.786	0.351	10.321	14.62	10.85	14.59	20.57	11.06
	2395000	0.14	27.214	17.442	4.340	3.87	13.04	8.63	18.14	5.49
	2396000	18.74	25.641	1.769	8.731	8.43	15.23	2.66	15.71	23.85
	2397000	11.53	24.069	18.860	2.750	13.00	0.79	29.14	13.28	18.28
	2398000	4.29	22.496	3.187	7.141	2.24	2.98	23.17	10.85	12.71
	2399000	22.88	20.924	20.278	1.161	6.80	5.17	17.20	8.42	7.13
	2400000	15.66	19.352	4.605	5.551	11.37	7.36	11.24	5.99	1.56

29

TABLE Ha.

Epochs and Arguments for each Thousandth Day, from 2300000 to 2400000.

For Washington Mean Noon.

r,-n*Tp°r-^ ARG. 36. 37. 38. 39. 4O. 41. 49. 43. 44. Julian Period.
	2300000	d. 2. 1 1	d. 27.6	18.63	d. 10.6	d. 3.86	d. 5.90	d. 1.84	d. 8.97	d. 7.8
	2301000	0.96	11.8	4.04	10.8	5.14	2.43	7.34	5.86	5.3
	2302000	13.21	33.5	8.23	11.0	6.44	16.88	2.70	2.74	2.7
	2303000	11.74	17.6	12.42	11.2	7.73	13.41	8.20	14.18	0.1
	230 1000	10.26	1.8	16.62	11.5	9.03	9.94	3.56	11.06	20.3
	2305000	8.79	23.5	2.02	11.7	10.32	6.47	9.06	7.95	17.7
	2306000	7.32	7.6	6.22	11.9	11.61	3.01	4.43	4.83	15.1
	2307000	5.84	29.4	10.41	12.2	12.91	17.45	9.92	1.72	12.5
	2808000	4.37	13.5	14.61	12.4	14.20	13.98	5.29	13.15	9.9
	2309000	2.90	35.2	0.01	12.6	15.49	10.51	0.64	10.04	7.3
	2310000	1.42	19.3	4.21	12.8	16.78	7.05	6.15	6.92	4.7
	2311000	13.67	3.4	8.40	13.0	18.07	3.58	1.51	3.81	2.1
	2312000	12.20	25.2	12.60	13.2	0.52	0.11	7.00	0.70	22.4
	2313000	10.72	9.3	16.79	13.4	1.82	14.55	2.37	12.13	19.8
	2314000	9.25	31.0	2.19	13.7	3.11	11.08	7.87	9.01	17.2
	2315000	7.78	15.2	6.39	13.9	4.40	7.61	3.23	5.90	11.6
	2316000	6.30	36.9	10.58	14.1	5.70	4.14	8.73	2.79	12.0
	2317000	4.83	21.0	14.78	14.4	6.99	0.67	4.10	14.23	9.4
	2318000	3.36	5.1	0.18	14.6	8.29	15.12	9.59	11.10	6.8
	2319000	1.88	26.9	4.38	14.8	9.58	11.65	4.95	7.99	4.2
	2320000	0.41	11.0	8.57	15.0	10.87	8.19	0.31	4.88	1.6
	2321000	12.66	32.7	12.77	15.2	12.16	4.72	5.82	1.77	21.8
	2322000	11.18	16.8	16.96	15.4	13.15	1.25	1.17	13.19	19.2
	2323000	9.71	1.0	2.37	15.6	14.74	15.70	6.68 10.08	16.6
	2324000	8.23	22.7	6.56	15.9	16.04	12.22	2.04	6.97	14.1
	2325000	6.76	6.8	10.76	16.1	17.33	8.75	7.53	3.86	11.5
	2326000	5.29	28.6	14.95	16.3	18.62	5.28	2.90	0.75	8.9
	2327000	3.82	12.7	0.35	16.6	1.08	1.81	8.39	12.17	6.3
	2328000	2.34	34.4	4.55	16.8	2.37	16.26	3.76	9.06	3.7
	2329000	0.87	18.5	8.75	17.0	3.66	12.79	9.26	5.95	1.1
	2330000	13.12	2.6	12.94	17.2	4.95	9.33	4.62	2.84	21.3
	2331000	11.64	21.1	17.13	17.4	6.24	5.H6	10.12	14.27	18.7
	2332000	10.17	8.5	2.54	17.6	7.53	2.39	5.48	11.15	16.1
	2333000	8.69	30.2	6.73	17.8	N.N2	16.84	0.84	K.OI	18.5
	2334000	7.22	14.4	10.93	18.0	10.12	13.37	6.35	4.93	10.9
	2335000	5.75	36.1	15.12	18.3	11.41	' 9.90	1.70	1.82	8.3
	2336000	4.28	20.2	0.53	18.5	12.70	6.43	7.20	13.21	6.8
	2337000	2.80	4.3	4.72	18.7	14.00	2.96	2.56	10.13	8.2
	2888000	1.33	26.1	8.91	18.9	15.29	17.41	8.06	7.02	0.6
	2839000	13.58	10.2	13.12	19.1	16.58	13.94	3. 13	8.91	20.8
	23 10000	12.10	31.9	17.31	19.8	17.87	10.47	8.94	0.79	18.2
	2841000	10.63	16.0	2.7 1	19.5	0 32	7.00	4.29	12.22	15.6
	2842000	9.15	0.2	6.90	19.7	1.61	3.53	9.79	9.11	13.0
	23 13000	7.68	21.9	11.10	19.9	2.91	0.0(5	5.15	(i.OO	10.4
	23 1 1000	6.21	6.0	15.29	20.2	4.20	14.51	0.51	2.88	7.8
	2845000	4.73	27.8	0.70	20.4	5.1!)	11.04	6.01	14.32	5.2
	2846000	3.26	1 1 .9	4.89	20.6	6.78	7.57	1.37	11.20	2.6
	2847000	1.79	88.6	9.09	20.9	8.07	4.10	6.81	8.09	0.0
	2348000	0.31	17.7	13.2s	21.1	9.87	0.61	2.23	4.97	20.3
	2349000	12.56	1.!)	17.48	21.3	10.66	15.0$	7.73	1.86	17.7
	2880000	11.09	23.6	2.88	21.5	11.95	11.61	3.09	13.29	J5.1

30

TABLE II«.

Epochs and Arguments for each Thousandth Day, from 2300000 to 2400000. For Washington Mean Noon.

junked. AR(i- 3G- 37- 38- 39- 40- 41« 42- 43. 44.
	2350000	11.09	d. 23.6	d. 2.88	d. 21.5	d. 11.95	d. 11.61	d. 3.09	d. 13.29	d. 15.1
	2351000	9.61	7.7	7.07	21.7	13.24	8.14	8.59	10.18	12.5
	2352000	8.14	29.4	11.27	21.9	14.53	4.67	3.96	7.06	9.9
	2353000	6.67	13.6	15.46	22.1	15.83	1.20	9.45	3.95	7.3
	2354000	5.19	35.3	0.87	22.4	17.12	15.65	4.82	0.84	4.7
	2355000	3.72	19.4	5.06	22.6	18.41	12.17	0.18	12.27	2.1
	2356000	2.25	3.5	9.26	22.8	0.86	8.70	5.68	9.15	22.3
	2357000	0.77	25.3	13.45	23.1	2.15	5.23	1.04	6.04	19.7
	2358000	13.02	9.4	17.65	23.3	3.45	1.76	6.54	2.93	17.1
	2359000	11.55	31.1	3.05	23.5	4.74	16.21	1.90	14.37	14.5
	2360000	10.07	15.2	7.25	23.7	6.03	12.74	7.40	11.24	12.0
	2361000	8.60	37.0	11.44	23.9	7.32	9.27	2.76	8.13	9.4
	2362000	7.13	21.1	15.64	24.1	8.61	5.80	8.26	5.02	6.8
	2363000	5.65	5.2	1.04	24.3	9.91	2.33	3.62	1.91	4.2
	2364000	4.18	27.0	5.23	24.5	11.20	16.78	9.12	13.34	1.6
	2365000	2.71	11.1	9.43	24.8	12.49	13.31	4.49	10.22	21.8
	2366000	1.24	32.8	13.62	25.0	13.78	9.84	9.98	7.11	19.2
	2367000	13.48	17.0	17.82	25.2	15.07	6.37	5.35	4.00	16.6
	2368000	12.01	1.1	3.22	25.4	16.37	2.90	0.70	0.89	14.0
	2369000	10.53	22.8	7.42	25.6	17.66	17.35	6.21	12.31	11.4
	2370000	9.06	6.9	11.61	25.8	0.11	13.88	1.57	9.20	8.8
	2371000	7.59	28.7	15.81	26.0	1.40	10.41	7.06	6.09	6.2
	2372000	6.11	12.8	1.21	26.2	2.69	6.94	2.43	2.98	3.7
	2373000	4.64	34.5	5.41	26.4	3.99	3.47	7.93	14.41	1.1
	2374000	3.17	18.6	9.60	26.7	5.28	0.00	3.29	11.29	21.3
	2375000	1.69	2.8	13.80	26.9	6.57	14.45	8.79	8.18	18.7
	2376000	0.22	24.5	17.99	27.1	7.86	10.98	4.15	5.07	16.1
	2377000	12.47	8.6	3.40	27.4	9.15	7.51	9.65	1.96	13.5
	2378000	11.00	30.4	7.59	1 27.6	10.45	4.04	5.01	13.38	10.9
	2379000	9.52	14.5	11.78	27.8	11.74	0.57	0.37	10.27	8.3
	2380000	8.05	36.2	15.98	28.0	13.03	15.02	5.88	7.16	5.7
	2381000	6.57	20.3	1.38	28.2	14.32	11.55	1.23	4.05	3.1
	2382000	5.10	4.4	5.58	28.4	15.61	8.08	6.73	0.94	0.5
	2383000	3.63	26.2	9.77	28.6	16.91	4.61	2.10	12.36	20.8
	2384000	2.15	10.3	13.97	28.9	18.20	1.14	7.59	9.25	18.2
	2385000	0.68	32.0	18.16	29.1	0.65	15.59	2.96	6.14	15.6
	2386000	12.93	16.2	3.57	29.3	1.94	12.12	8.46	3.03	13.0
	2387000	11.46	0.3	7.76	29.6	3.23	8.65	3.82	14.46	10.4
	2388000	9.98	22.0	11.95	29.8	4.53	5.18	9.32	11.34	7.8
	2389000	8.51	6.1	16.15	30.0	5.82	1.71	4.68	8.23	5.2
	2390000	7.03	27.9	1.56	30.2	7.11	16.16	0.04	5.12	2.6
	2391000	5.56	12.0	5.75	30.4	8.40	12.69	5.55	2.00	0.0
	2392000	4.09	33.7	9.95	30.6	9.69	9.22	0.90	13.43	20.2
	2393000	2.62	17.8	14.14	30.8	10.99	5.75	6.41	10.32	17.6
	2394000	1.14	2.0	18.34	31.0	12.28	2.28	1.76	7.21	15.0
	2395000	13.39	23.7	3.74	31.3	13.57	16.73	7.26	4.09	12.4
	2396000	11.92	7.8	7.93	31.5	14.86	13.25	2.63	0.98	9.9
	2397000	10.44	29.6	12.13	31.7	16.15	9.79	8.12	12.41	7.3
	2398000	8.97	13.7	16.32	31.9	17.45	6.32	3.49	9.30	4.7
	2399000	7.49	35.4	1.73	32.1	18.74	2.85	8.99	6.18	2.1
	2400000	6.02	19.5	5.92	32.3	1.19	17.30	4.35	3.07	22.3

31

TABLE IIfl.

Epochs and Arguments for each Thousandth Day, from 2300000 to 2400000.

For Washington Mean Noon.

,^A,,«. 4.. «. «. «,. «,. «. S8. *,
	d.	d.	d.	d	d.	d.	d.	ii.	d.
	2300000	3.87	23.2	12.49	22.74	1.5	15.1	8.53	0.73	94.82
	2301000	6.77J 7.7	9.08	4.98	6.0	13.7	6.60	Hi. 70	36.96
	2302000	9.661 21.2	5.67	17.15	10.4	12.2	4.67	7.45	96.65
	2303000	12.56| 5.8	2.25	29.32	2.2	10.8	2.74	23.42	38.79
	2301000	15.46	19.3	12.97	11.56	6.7	9.3	0.81	14.17	98.48
	2305000	1.46	3.9	9.56	23.73	11.3	7.9	17.09	4.92	40.62
	2306000	4.36	17.4	6.15	5.97	3.0	6.5	15.16	20.89	100.20
	2307000	7.25	2.0	2.74	18.14	7.5	5.0	13.2:	11.64	42.45
	8806000	10.15	15.5	13.46	0.38	12.1	3.6	11.30	2.38	102.13
	2309000	13.05	0.0	10.05	12.55	3.7	2.1	9.37	18.36	44.28
	2310000	15.95	13.6	6.64	24.73	8.3	0.7	7.44	9.10	103.96
	2311000	1.95	27.1	3.23	6.96	0.0	24.3	5.51	25.08	46.11
	2312000	4.84	11.7	13.95	19.14	4.5	22.9	3.58	15.83	105.79
	2313000	7.74	25.2	10.54	1.37	9.0	21.4	1.65	6.57	47.94
	2314000	10.64	9.8	7.13	13.55	0.8	20.0	17.93	22.55	107.62
	2315000	13.51	23.3	3.72	25.72	5.3	18.5	15.99	13.29	49.77
	2316000	16.44	7.8	031	7.96	9.8	17.1	14.07	4.04	109.45
	2317000	2.43	21.4	11.03	20.13	1.5	15.7	12.14	20.01	51.60
	2318000	5.33	5.9	7.62	2.37	6.0	14.2	10.21	10.76	111.28
	2319000	8.23	19.5	4.21	14.54	10.5	12.8	8.28	1.50	53.42
	2320000	11.13	4.0	0.79	26.71	2.3	11.4	6.35	17.48	113.11
	2321000	14.03	175	11.51	8.95	6.8	10.0	4.42	8.23	58.26
	3322000	0.02	2.1	8.10	21.12	11.3	8.5	2.49	24.20	114.94
	8323000	2.92	15.6	4.69	3.36	3.1	7.1	0.56	14.95	57.09
	2321000	5.82	0.2	1.28	15.53	7.6	5.6	16.84	5.69	116.77
	2325000	8.72	13.7	1200	27.70	12.1	4.2	14.91	21.67	58.92
	8336000	11.62	27.3	8.59	9.94	3.8	2.8	12.98	12.41	1.06
	•J.-U7000	14.51	II -	5.18	22.11	8.3	1.3	11.05	3.16	60.74
	2:WSOOO	0.51	25.3	1.77	4.35	0.1	24.9	9.12	19.14	2.89
	2329000	3.41	9.9	12.48	16.52	4.6	23.4	7.19	9.88	62.57
	2330000	6.31	23.4	9.08	28.70	9.1	22.0	5.26	0.63	4.72
	8331000	9.21	8.0	5.66	10.94	0.8	20.6	3.33	16.60	84.41
	8332000	12.10	21.5	2.25	23.11	5.3	19.1	1.40	7.35	6.55
	8333000	15.00	6.1	' 12.97	5.35	9.9	17.7	17.68	23.32	88.23
	8334000	0.99	19.6	9.56	17.52	1.6	16.2	15.75	14.07	8.38
	2335000	3.90	4.1	6.15	29.69	6.1	14.8	1382	4.81	68.06
	2336000	6.80	177	2.74	11.93	10.5	13.4	11.89	20.79	10.21
	•j:i:)7000	9.69	2.2	13.46	24.10	2.4	11.9	9.96	11.54	69.89
	2338000	12.59	15.8	10.05	6.34	6.9	10.5	8.03	2.28	18,04
	8339000	15.49	0.3	6.64	18.51	11.4	9.0	6.10	18.26	71.72
	8940000	1.49	18.8	3.23	0.75	3.1	7.6	4.17	9.00	13.87
	8311000	4.38	27.4	18.98	18.99	7.6	6.2	2.2 1	24.98	73.55
	ji KKI	7.98	11.9	10.51	86.09	12.2	4.8	0.31	15.72	15.70
	8343COO	10.18	25.5	7.12	7.88	3.9	3.3	16.59	(i. 17	76.38
	8344000	13.08	10.0	3.71	19.50	8.4	1.9	14.67	22.44	17.53
	8845000	15.98	23.6	0.30	1.74	0.1	0.4	12.73	13.19	77.21
	8346000	1.97	S.I	11.02	13.91	4.6	24.0	10.80	:i.!»i	l!).:ifi
	8347000	usn	21.6	7.61	26.08	9.2	22.6	S.N7	19.91	78.04
	•J.'ilM	7.77	6.2	4.20	8.89	0.9	21.1	6.94	10.66	21.19
	2349000	10. 67	19.7	0.79	20.49	5.4	19.7	5.01	1.40 SO.N7
	2850000	l:{.:>7 I .::	11.51	2.73	9.9 <