168 Mr. Lubbock o;^ the Divergence of the numerical Coefficients 

 Table of Proportions in Quadrisulphuret of Lime. 



[To be continued.] 



XXV. On the Divergence of the numerical Coefficients of cer- 

 tain Inequalities of Longitude in the Lunar TJieory. By 

 J. W. Lubbock, Esq., F.E.S.\\ 



nPHE divergence of the numerical coefficients in the lunar 

 -*- theory, made manifest by M. Plana's development of the 

 expressions according to powers of m, presents a difficulty in 

 a complete numerical solution of the problem, that is, a solu- 

 tion intended to embrace all quantities which are sensible in 

 practically ascertaining the moon's place v^ith the accuracy 

 required for comparison with the best observations. But the 

 following questions naturally occur : Is there any method of 

 approximation which will serve to select the more consi- 

 derable terms, rejecting others ? Is the divergence due chiefly 

 to the development and expansion, according to powers of ?w, of 

 the divisors introduced by integration? In the latter case the 

 difficulty might be easily avoided ; but I fear that each of these 

 questions must be answered in the negative. 



In order to illustrate this point I have selected indifferently 

 two terms in the longitude amongst those in which this diver- 

 gence is met with, and I propose to examine their construc- 

 tion without introducing details which do not bear imme- 

 diately upon the point referred to. 



* Boiled in a flask loosely corked. 



t Lost some of the ingredients by boiling over ; hence a deficiency. 



i Boiled in a flask with great care. 



§ The oxygen was determined by especial care in these two cases. 



II Communicated by the Author. 



