which will happen on the 15th of May 1836. 37 
In procuring the preceding table of general data, I have used 
the method given by Professor Vince in his Astronomy, vol. iii. 
p. 52, for finding the horary motions in longitude and latitude, 
before and after the time for which the places are calculated. 
Mr. Vince remarks that this method is not perfectly correct, but 
sufficiently so for the longest eclipse. I am inclined to think it 
far from probable, that in any case, even when the moon is in 
her perigee, the half hourly change of her motion can vary in four 
hours in the ratio of 3,5, 7,9. In the example given by Mr. 
Vince, the equation of the second order in longitude is 1-24; 
from which, applying the arithmetical progression, we find that 
the horary motion at two hours preceding, is increased by 11’"16, 
and, at two hours following, diminished by the same quantity. 
Now, suppose the instant for which the places are calculated 
from the tables, to be an hour before the moon is in perigee; the 
horary motion will in this case increase for the first hour which 
follows, and then, having arrived at its maximum, it will begin 
to decrease. In such a case, therefore, I am at a loss to see how 
the above method could hold good. 
I have been induced to solicit the attention of your valuable 
correspondents to this point, from a hope that some of them will 
have the goodness to give, through the medium of your Maga- 
zine, some easy, and at the same time more accurate method of 
applying the equation of the second order, both in longitude and 
latitude. 
The following table exhibits the results of the principal steps 
of the calculations for Greenwich and Edinburgh. The times 
marked on the tops of the columns are the instants assumed. 
The line marked © contains the Sun’s longitude. 
—— A the Sun’s right ascension. 
»)) the Moon’s true longitude. 
L the Moon’s true latitude. 
R the right ascension of the meridian. 
———_——— H ——— the altitude of the nonagesimal. 
N 
P 
p 
D 
the longitude of the nonagesimal. 
the parallax in longitude. 
the parallax in latitude. 
——— the appar. diff. of long. of the © 
and ). 
—————— a the Moon’s apparent latitude. 
—_—-———— _ § —— the Moon’s apparent semidiameter, 
the Moon’s apparent motion in 60” 
of time. 
eS the errors from the instants as- 
sumed, where — shows the inst. too early, and’+ too late. 
The 
