Latitude.

Elements of the Eclipse, by which it may be computed for any Place,

with the greatest accuracy.

% 57 28

15 57

45 50

53 2 0

5 10 15 20 25 30 35

1.219200
1.21762
1.151323
1.1063
1.0591412
1.012001
.961559
.917116
.869673
.822229
.77-1734
.727310
.679-91
.632147
.555001
.537554
490106
.4126.58
.393210
.317761
.300312
.232-63
.205114
.157965
.110515
.06.2065
.015615
031-34
.0792-1
.126734
.17111
.221633
269003
.31632
.36.981
,411130
.45678
.506326
,523774
.601221
.61667
.696114
.713360
.791005
.53430
Si-3
.93335
.94777
1.022217
1.073657
1.1296
1.170535
1.217972
1.65105
1 312-12
1.317276
1.407709

1.488793
1.480116
1.475176
1.16.261
1.461319
1.451131
1.447509
1.440385
1.4336.38
1.426729
1.419796
1.412861
1.405922
1.395981
1.392037
1.335091
1.378141
1.371199
1.36 1234
1.357276
1.330316
1.313353
1.336337
1.329413
1.322147
1.315173
1.31N197
1.301517
1.291533
1.257550
1.2-0563
1.273573
1.266501
1.239595
1.252537
1.21376
1.23-3-3
1.231576
1.221.569
1.217336
1.210.312
1.203.725
1.196306
1.1A9114
1.182159
1.175132
1.164102
1.161369
1.1.31331
1.147 297
1.110256
1.133214
1.126169
1.119121
1112071
1.105019
1.097963

.421081 .414176 .407263 .400358 .393114 .36529 .379611 .372691 .365768 .355542 .331914 .311983 .335050 .331115 .324177 .317237 .310295 .303351 .296404 .299154 -282502 .275517 .263591 .261632 .251671 .247707 .240741 .233773 .226-03 .219530 .212

55 .205377 .199897 .191915 .184931 .177914 .170955 .163964 .156970

149974 .142976 .135975 .128972 .121969 .114961 .107952 .100910 .0939 26 086909 .079-91 .072870 .065917 .058522 .051794 .044761 .037732 .030697

9.976 9.974 9.520 9.508
1536 7515 2799 7195
1376 7536 2634 7021
1396 7557

2166 6-17
1417 7577 2295 6674
1437

7599 2129 6500 1457

7619 1961 6326 1477 7639

1793

6153 1497 7660 1624 5979 1519 7681 1456 5905 1538 7702 1237 5632 1558 7723 1118 5158 1578 7711 0919 5234 1598 7761

0780 5110 1618 7705 0611 4936 1633

7806 | 0141 4762 1659 7826 0272 4587 1678 7047 *103 4113 1698 7869

9934

4239 1719 7889 | 9765 4061 1739 7910 9596 3989 1759

7931 9126 3715 1780

7953 9257 35 10 1800 7974 9088 3365 1920 7995 8919 3191 1841 8015 8750 3017 1861 8036 8591 2513 1882 8057 8111 2669 1902 8078 8212 2495 1923 8099 8073 2321 1913

8120 7903 2146 1961 8111

7733 1972 1941

8152 7561 1797 2001 8163 7394 1622 2025 8204 7221 1418 2015 8225 7055 1273 2065 9216 67-6 1039 2095

8266 6717 0922 2105 8297 65518 0717 2125

835 6378 0572
2115 8329 6209 0396
2165 8319 6010 (221
2185 8370 5970 *017
2205 8330 5700 9872
2225 $411 55:30 9699
2245 8132

5360 9523
2265
8153 5190

9319
2285
8174

5019 9174
2305 5435 4949 8999
2325 8516 4679 8821
2345 8537 4510 8619
2365 8558 4340 8474
2355 8579 4170 8299
2405 8600 4000 8124
2125 8621 3-30 7919
24:15 8612 3660 7771
2465 8663 3491 7599
2135 864 3321

0 2 12 3.3 3 27 3.7 4 42 4.1 5 57 4.6 7 12 5.0 827 5.5 9 42 5.9 10 57 6.4 12 12 6.8 13 27 7.3 14 42 78

8.2 17 12 8.7 18 27 9.2 19 42 9.6 20 57 10.1 22 12 10.6 23 27 11.0 24 42 11.5 25 57 12.0 27 12 12.4 28 27 12.9 29 42 13.4 30 57 13.8 32 12 14.3 33 27 14.8 34 42 15.2 35 57 15.7 37 12 16.2 38 27 16.6 39 42 17.1 40 57 17.6 42 12 18.0 43 27 18.5 44 42 19.0 45 57 19.4 47 12 19.9 48 27 20.3 49 42 20.8 50 57 21.2 52 12 21.7 53 27 22.2 54 42 22.6 55 57 23.1 57 12 23.6 58 27 24.0 59 42 21.5 60 57 24.9 62 12 25.4 63 27 23.8 64 42 26.3 65 57 56.7 67 12 27.2 69 27 37.6 69 42 28.1 70 57 28.5

These tables are adapted to computation by the following modification of Bessel's formulæ, which was suggested by T. Henry Safford, Jr.

d=the latitude of the place.

a=its eastern longitude from Greenwich.

log. e=8.9110835 log. (1-e?)=9.9971066

sin.y=esin. 0

h=sec, w cos. O

k=(1-e?) sec. y sin. O
a=A- h sin. (uta)
b=B- Ek +Hh cos. (u + a)
c=-C+ Fk-Gh cos. (r +2)

m=V (bc) If the instant for computation were correctly chosen at the time of begin. ning or end of the eclipse, m would be exactly equal to a. If m is not equal to a, the instant for a new computation, and which will be an approximation to the actual time of beginning, may be found by adding to the preceding time of computation an interval t, which may be obtained in seconds by the formulæ

log. u'=1.86167

log. H'=1.3757
tan. $y==

a'=A — M'h cos. (u +2)
b=B! + H h sin. (u +9)

1000000 (m-a)
a - U col.

and if y is taken of the same sign with a, it is a sufficiently near approximation to the angle of contact from the north towards the east. The magnitude of the eclipse is found by taking the difference (with regard to the signs) of V at the beginning and end of the eclipse, and if this difference is denoted by 29, the magnitude of the eclipse is

24.5 sin. '} y or 24.5 cos. 254 accordingly as o is acute or obtuse.

The value of y may also be obtained by the formulæ

tan.x=

p=4-X and the expression of t may be changed to

t=1000000.m-a cos. x sin.

a

sin.

sin. V

с

The elements of the sun for this table were derived from Bessel's tables, those of the moon from Damoiseau's tables corrected by Airy for Plana’s theory, and with the additional corrections given by Hansen's new terms and by Airy's comparison with the Greenwich Observations.

The following is an example under these tables for the computation of the beginning of the eclipse for the Washington Observatory.

A= lat. 38° 51' 391.25 sin. 6 9.7978800

B

1.462041 8.7089635

Ek

.591 152
sec. V
.0005692

Hh cos. (uta) .080875
k
9.7955558

b

.951764
h
9.8917198

с

.394136 for Oh. 29m. 30s.

Fk

.589272
ht

5° 49' 34".6 Gh cos. (u+a) .083057
long
–77 3 39.6

.112079
ta 288 45 55.0

b

9.9785292 sin. (uta) 9.9762786n

9.0495242 cos. (u+a) 9.5074402

9.5140267n h sin. (uta) 9.8679984n

tan. 54

9.5354975n
h cos. (n a) 9.3991600

-1.064186
G
9.5202146

h sin.(uta)

.737902
H
9.5086517

.326284
Gh cos. (u +2)8.9193746

.326608
Hh cos.(+2) 8.9078117 (m - a) 106 -324
E
9.9761435

d'h cos. (uta) 18.28 1.2609
9.9747596 H h sin.(uta)-17.53 1.2437n
Ek
9.7716993
A= 158.14

B= 23.06
Fk
9.7703154 al 139.86

5.53 V

322 71 b cos. y=-4.30 al - cos. y= 144.16

t=-28..2
Greenwich time of beginning =0h. 29m. 27.88.
Washington "

21

13.2

с

m

64