E C L 



from which expression may be deduced values of the time, correspond- 

 ing to any assigned values of c, as in the following instances. 



(j) To determine the time at which the moon first enters the penum- 

 bra, for c put P -f- P + IT + "5" > ^ nas * wo va l ues > an d the second value 

 will denote the time at which the moon quits the penumbra. 



(jj) To determine the time at which the moon enters the umbra, put 



(jjj) To determine the time when the whole disk has just entered tha 

 shadow, we must deduct d from the preceding value, and make c = P-f. 



p - -- j and similarly for other phases. 



(Jijj) To find the middle of the eclipse, we have t X Sin ' 8 g , and in 

 that case the distance of the centres (c) is = Pi cos. 6. 



(v) The nearest approach of the centres being known, the magnitude 

 of the eclipse is easily ascertained. Thus on the supposition that A cos. 9 



is less than the distance (P -f- p 4- -~- j at which the moon's 



limb just touches the shadow, some part of the moon's disk is eclipsed -, 

 and the portion of the diameter of the eclipsed part is 



The portion of the diameter of the non-eclipsed part is the moon's ap- 

 parent diameter d t minus the preceding expression, and therefore is 



A cos. 8+ ^ 4.5_p~p. 



If this expression should be equal nothing, the eclipse would be just a 

 total one. If the expression should be negative, the eclipse may be eaid 

 to be more than a total one, since the upper boundary of the moon's disk 

 would be below the upper boundary of the section of the shadow. 



(vj) If in the expression 



sin. 6 V (c* A* cos.* 0). 

 n 



we substitute for <*, P 4- p 4- -5- -5- we have the time from the moon's 



A A 



first entering to her finally quitting the shadow or umbra. And if in th 

 95 F2 



