(97) 



& = l t — 3J S + 2l z + 180°, fll 



Tisskkand, however, has 



# — l _ si' + 2Z". 



The angle #, as defined by [1] is the angle to which the name 

 libration was first applied In Laplace, and which is by him called tu. 

 [Mécanique Celeste, Livre VIII, art. 15, Oeuvres, tome IV pages 75 

 and 79 of the edition of 1845). 



The differential equation determining the libration is 



d*& 



= — S 2 sin & [2 1 



dt* * L J 



This equation is derived by the combination of the three equations 



— = — Q 2 sin & ] r:3] 



df 



cPl. 



— = — Q, mm t) 



de 



We have thus 



jS' - Q, _ 3Q S + 2Q, [41 



From these equations the whole theory of the libration is derived 

 in the well known manner, on which, however, I will nol dwell. 

 my sole object being at present the determination of the quantities 

 <L Q 3 and Q t . 



For that purpose wc start from the formulas given by Tisserand at 

 the top of page '20, which must however be completed as follows: 



d*Q _ . 3 /dE t dR<\ 



W ~a> (lT + 17j [5] 



and two similar equations for q' and q". 



Introducing the same auxiliary angles u and u' that are used by 

 Tissbrand (formula (12) page 20), we get instead of Tisserand's 

 equations {B): 



