62 K F. DUPUrS 



Moreover we may divide the original hour spaces into intervals of 20 minutes by 

 employing the following formulae, x^, x.,, x.^ denoting as before, m, n being the terms 

 between a;, and x^ and p, q those between x., and x.^ 



m = ^(SXj+Sj-j — Xj) = 25"8-i 

 n = ^(2x^+8x^— X,) = 17-33 

 p = ^(2x^-i-8xs — x^) — 0.64 

 q = ^(5x^+5x2 — Xj) = — 7-53 



and similarly for y. 



In applying the preceding methods to the prediction of solar eclipses a few modifi- 

 cations are required. 



Thus for /T we employ (the moon's horizontal parallax) — (the sun's horizontal paral- 

 lax). 



For s we employ the siim of the semidiameters of the sun and moon. 



For H we take (moon's hourly motion in R. A.) — (sun's hourly motion in R. A.) 



For h we take (moon's hourly motion in declination) — (sun's hourly motion in 

 declination). 



If the sun and moon are moving in opposite directions, we take the sum instead of 

 the difference of their hourly motions in declination. 



As an example, we have for the solar eclipse of May 16th, 1882, as seen from Green- 

 wich, 



r = 19"-7 d = lD-2 M = 33-75 h = 4-4 N. ô = 19°-3 N. n = 58-1 s = 31-73 



For the hours 



« = 18 19 20 



we have 



a = 88"-! 73°-C 59°-2 



Thence we find by the tables, etc., 



Then drawing any line i, we take upon it a convenient point E as the sun's centre, and 

 set ofi" &A = 17-86, SB = 12-43, SC = 40-57. Then setting off downwards ^-XYIII = 

 3084, BXIX = 2347, CXX = 16-o3, and drawing a curve through the three points 

 thus found, we have the moon's apparent path. Taking SB = s = 31-78 {B being on 

 the moon's path) we find the time of beginning, JS, as 18 h. 11 m., and the time of ending, 

 E, as 19 h. 25 m. Drawing SiJf perpendicular to the moon's path gives the middle of the 

 eclipse, i.e., the time of the greatest phase, M, as 18 h. 46 m. 



With centre S and radius equal to the sun's semidiameter, 15-84, describe the circle 



/, and with M as centre and with a radius equal to the moon's semidiameter, 15-9, describe 



a circle g. The figure produced represents the appearance at greatest obscuration. 



Dividing the distance fg by the sun's diameter gives 0187 for the magnitude of the 



eclipse. 



The angle ASB+^d is the angle from the north point of the sun, toward the west, at 

 which first contact takes place. This angle is by measurement on the plot 158°. 



