VI 
Introduction 
An example of the author’s reduction sheet now follows: 
March 13, 1863. o h 46™ Clinton Mean Time 
(1) 
(2) 
(3) 
lg & 5 
(4) 
sin p sin P 
(5) 
sin cos P 
(6) 
sin or cos P 
(7) 
P 
(8) 
sin P 
(9) 
sin ( p — n ) 
sin p 
(10) 
P-N 
(11) 
cos(P-W) 
0 . 
i .7164c 
2.7168c 
9.7304c 
9 -9°55 n 
9.9198 
213° 45' 
9.9856 
~ 5 
189° 21' 
9.9942c 
Cl . 
1.710m 
2.7185c 
9.732 re 
9.8992c 
9-9I73 
214 14 
9.9818 
5 
189 50 
9.9936c 
b . 
1.2504c 
2.2788c 
9.2924c 
9-4395” 
9 .9108 
215 29 
95287 
19 
191 5 
9.9918c 
c . 
x.0334c 
2.1584C 
9.1720c 
9.2225c 
9-8733 
221 40 
9-3492 
20 
197 16 
9-9799” 
d . 
0.9269c 
X.6532C 
8.6668c 
9.1160c 
9.9742 
199 34 
9.1418 
20 
175 10 
9.9984c 
d 1 . 
0.7924c 
I.5682c 
8.5818c 
8.9815c 
9 .9680 
201 43 
9-OI35 
20 
177 19 
9-9995” 
d * . 
0.7597c 
O.9542C 
7.9678c 
8.7488c 
9.9976 
185 58 
8.9511 
20 
161 34 
9.9771c 
di . 
0.6180c 
I .3222C 
8-3358» 
8.8071c 
9-9765 
198 40 
8.8306 
20 
174 16 
9.9978c 
d 4 . 
0.30 IOC 
I .59IIC 
8.6074c 
8.4901c 
9.8993 
232 28 
8.7054 
20 
208 4 
9 - 9457 ” 
e 1 . 
1.0864 
1 - 477 1 
8.4907 
9-2755 
9.9942 
9 19 
9.2813 
20 
344 55 
9.9848 
e 2 . 
1 • 1I 73 
1.2041 
8.2177 
9.3064 
9.9986 
4 40 
9.3078 
20 
340 16 
9-9737 
1.2227 
1.4771c 
8.4007c 
9.4118 
9.9969 
353 
9.4149 
20 
328 46 
9.9320 
/. 
1.6808 
2.7924 
9.8060 
9.8699 
9.8791 
40 48 
9.9908 
4 
16 24 
9.9820 
8.1891 7.0136 “24° 24' 2.9864 
15 cos 5 1 N Igp 
S P S P 
(1) 
(12) 
sin (p—n) 
(13) 
sin(P-W) 
(14) 
(l2> + (l 3 ) 
=g sin 5 
(IS) 
cos (p—n) 
=g cos i 
(16) 
cos£ 
(17) 
i 
(18) 
B 0 +i 
(19) 
sin(Po-ff) 
(20) 
lg g 
(21) 
cos(B<,+£) 
a . 
9.9851 
9.2108c 
9.1959” 
9.4102 
9.9312 
-31 0 24' 
- 38 ° 34 ' 
9 - 7949 ” 
9.4790 
9.8931 
a 1 . 
9.9813 
9.2324c 
9.2137c 
9 4583 
9.9390 
-29 39 
-36 49 
9.7776c 
9-5193 
9.9034 
b . 
9.5268 
9.2838c 
8.8106c 
9-9739 
9.9990 
- 3 56 
— 11 6 
9.2845c 
9.9749 
9.9918 
9-3472 
9.4727” 
8.8199c 
9.9890 
9.9990 
- 3 52 
— 11 2 
9.2822c 
9.9900 
9.9919 
d . 
9.1398 
8.9256 
8.0654 
9.9958 
0.0000 
+ 0 40 
- 6 30 
9 -° 539 ” 
9.9958 
9.9972 
d* . 
9.0115 
8.6704 
7.6819 
9.9977 
0.0000 
+ 0 16 
- 6 53 
9 .0791c 
9.9977 
9.9968 
dK....' . 
8.9491 
9.5000 
8.4491 
9.9983 
9.9998 
+ 1 37 
- 5 33 
8.9855” 
9.9985 
9.9980 
d 3 . 
8.8285 
8.9996 
7.8281 
9.9990 
0.0000 
+ 0 23 
- 6 47 
9.0723c 
9.9990 
9.9969 
d-». 
8-7033 
9.6726c 
8-3759 
9.9994 
9.9999 
— 1 22 
- 8 32 
9.1714c 
9-9995 
9-9952 
e l . 
9.2793 
9 - 4153 ” 
8.6946c 
9.9920 
9.9994 
- 2 53 
-10 3 
9.2418c 
9.9925 
9-9933 
e 2 . 
9-3058 
9.5285c 
8.8343c 
9.9909 
9.9989 
- 3 59 
-11 9 
9.2864c 
9.9919 
9.9917 
e . 
9.4129 
9.7148c 
9.1277c 
9.9849 
9.9958 
- 7 54 
-15 4 
9.415 1 ” 
9.9891 
9.9848 
/. 
9.9904 
9.4508 
9.4412 
9-3179 
9.9025 
+ 53 1 
+ 45 5 i 
9-8559 
9-5387 
9.8429 
-7 0 10' 
Bo 
(1) 
(22) 
sin(p—n)X 
cos (P-N) 
(23) 
£ COS(Po + 0 
(24) 
sin(£— Lo) or 
cos(L—Lo) 
(25) 
L-Lo 
(26) 
£sin(P o + 0 
=sin 5 
(27) 
cos B 
(28) 
B 
(29) 
L 
(30) 
L' 
(31) 
Mar. 12 
(32) 
Mar. 14 
a... 
9 - 9793 ” 
9.3721 
9.9871 
-76° 
7 ' 
9.2739” 
9.9922 
— IO° 
5 °' 
185 0 
I' 
6 ° 
5 ' 
a 
_ 
a 1 . . 
9.9749c 
9.4227 
9.9836 
74 
20 
9.2969c 
9 - 99 I 3 
“ II 
26 
186 
48 
7 
52 
a3 
— 
b... 
9.5186c 
9.9667 
9.9740 
19 
37 
9 - 2 594 » 
9.9927 
— 10 
28 
241 
31 
62 
35 
c 
0 
c... 
9.3271” 
9.9819 
9.9896 
12 
29 
9.2722c 
9.9923 
— 10 
47 
248 
39 
69 
43 
d 
b 
d... 
9.1382c 
9.9930 
9.9958 
7 
57 
9.0497c 
9.9972 
— 6 
26 
253 
11 
74 
i 5 
e 
CiCj 
dK. 
9 .OIIOC 
9-9945 
9.9977 
5 
56 
9.0768c 
9.9968 
- 6 
5 i 
255 
12 
76 
16 
0 
0 
d>.. 
8.9262c 
9.9965 
9.9984 
4 
52 
8.9840c 
9.9981 
- 5 
32 
256 
16 
77 
20 
e 2 
c* 
d3.. 
8.8263c 
9-9959 
9 • 999 ° 
3 
52 
9.0713c 
9.9969 
- 6 
46 
257 
16 
78 
20 
63 
C 3 
d 4.. 
8 . 6490c 
9.9947 
9.9996 
2 
35 
9.1709c 
9 - 995 1 
- 8 
32 
258 
33 
79 
37 
0 
. . 
e 1 .. 
9.2641 
9.9858 
9.9923 
+ 10 
45 
9 - 2343 ” 
9-9935 
- 9 
53 
271 
53 
92 
57 
I 
d* ? 
9-2795 
9.9836 
9.9917 
11 
11 
9.2783c 
9.9919 
— 10 
57 
272 
19 
93 
23 
I 
e. . . 
9-3449 
9-9739 
9.9883 
13 
13 
9.4042c 
9.9856 
-14 
41 
2 74 
21 
95 
25 
f 
d 
/... 
9.9724 
9.3816 
9.9861 
75 
37 
9-3946 
9.9862 
+ 14 
22 
336 
45 
r 57 
49 
6 
261° 8' 181 0 4' 
L 0 —178 56 
long, of 
prime meridian 
from node 
The scheme of computation explains itself. In the ninth column the author sometimes gives n and sometimes 
sin ( p—n ) 
sin p 
sun’s rotation, as employed by the author, are: 
for either of which a table with argument sin p could easily have been constructed. The elements of the 
