722 
Proceedings of the Boy at Society 
we need the moon’s distance, which has to he computed back 
from the parallax. I venture to suggest that it would greatly 
facilitate and improve the computation of eclipses and occupa- 
tions, to have the logarithm of the moon’s distance printed in the 
Almanac. 
The next step was to transpose the origin of co-ordinates from 
the earth’s centre to the place of observation. This is done by 
the simple addition or subtraction, as the case may be, of the 
co-ordinates of the locality, in which the earth’s oblateness and 
even the height above the sea-level may be taken into account. 
Lastly, from these local co-ordinates we deduce the moon’s 
apparent position, distance, semidiameter and parallaxes. Hence 
the sun’s parallaxes and apparent position, the distance between 
the centres and the separation of the limbs ; the item last named 
being that which determines the eclipse. These results, with 
their differences, are as under : — 
Gr. Time. 
Separation. 
5 1 
5 2 
5 3 
h. m. 
n 
18 20 
- 927 
n 
+ 146-8 
7/ 
30 
+ 54-1 
-48-1 
ft 
+ 98-7 
-4-5 
40 
+ 152-8 
+ 45-1 
-53-6 
-2-6 
50 
+ 197-9 
- 11-1 
-56-2 
+ 3-0 
19 00 
+ 186-8 
- 64-3 
-53-2 
+ 67 
10 
+ 122-5 
-110-8 
-46-5 
+ 9-2 
20 
+ 117 
-148*1 
-37-3 
30 
-136-4 
From this we see that the first contact will happen between 
18 h 20 m and 18 h 30 m . Putting t for the time in minutes reckoned 
from the epoch 18 h 30 m , and using differences of the third order, 
tlie separation has the value, 
- -000916/ 3 - -2405^ + 12-S666G, + 54T = sep n = 0’ . 
