150 OUTLINES OF NATURAL PHILOSOPHY. 



== 3, and CD = A, and AD the distance of the 

 centres, which we may call?/ = V 3* + A* because 

 the triangle ACD may be regarded as rectilineal. 

 In practice, y may be found by a construction ; or, 

 if great accuracy is required, we may compute y 

 from the trigonometrical formula, cos y = cos 1 X 

 cos A* 



b. Let similar calculations be made for other two 

 instants, separated by equal intervals of time m \ so 

 that one may be near the middle, and another near 

 the end of the eclipse. Let the distances of the 

 centres found for these times be A, A 7 , A"; let 

 ''>Tf the differences of these distances be DandD'; 

 and let the second difference, or D D' = A. 



Then if y be the distance of the centres for any time 

 t 9 reckoned from the instant for which the first 

 computation is made, y = 



-* + 



m 



The distance of the centres is thus expressed in terms 

 of the time, and from this equation the time of the 

 beginning and end of the eclipse, and the quanti- 

 ty of greatest obscuration, may be determined. 



c. The time of the greatest obscuration is = 



w(D \ A) 



-D 



and this being substituted for t, the value of y will 

 give the nearest approach of the centres. 



d. This 



