334 On the Measurement of the Progress of an Eclipse, 8^c. 



' = T + 1 ±y(l)'+ <1± ^'-i^, (. being = 0) 



gives the beginning of the eclipse, 

 the end of the immersion, 

 the beginning of the emersion, 

 the end of the eclipse. 



The duration of the eclipse is = 2 / (-gj+ —^ — g 



The shortest distance between the centre of the moon and 

 of the section of the conns umhrce (occurring when t is equal to 



the time of the middle of the eclipse, or ^ = T + g ) will be 



o-iven by the value of D derived from the equation 



Lastly: any enlightened quantity of the moon or any distance 

 of the horns will be given by the formula 



'=T+W(4)' + - 



B 

 observing that in the foi'mer case D = t — tZ' + s. 



in the latter, D^ = A' + B'+ 2\/ A^ 

 A'=(t + c)(t-c) '&'={d' + c){d'-~c) 

 Thus we may have the time t expressed in function of c or in 

 function of e. The longitude of the place will be expressed in 

 time by the formula L = /— ^, in which t' represents the time 

 of the observations of s or c ; the longitude being east or west 

 according as L is positive or negative. Finally; substituting 

 the value of t, we have the longitude expressed in the time by 

 the formula 



1 have calculated M. de Humboldt's observation at Ibague* 

 by this formula, and tlie result would no doubt accord pre- 

 cisely with that in the text, were the elements it contains free 

 from errors ; for, after correcting the most palpable, my result 

 differs but 27' from that of M. Oltmans. The following 

 errors cannot b( disputed, and other lesser ones certainly 

 exist. 



It is impossible that 21'' 20' 45" at Paris, can be the mean 

 time, since the elements are calculated very near the opposi- 

 tion, and this happened, according to the text, at 19" 26' 41". 

 If we suppose for a moment that this latter element is inexact, 

 we may still convince ourselves that 21'' 20' 45" cannot be the 



* ^"JCS'' ^'^ Humbuldt, Astronondque. (2 vols. 4to,) vol. ii. p. ~55. 



correct 



