56 C. V. L. Charlier 



Writing explicitly the limits we have 



D 



(119) I = j sin 'd- cos bcù db 



d 



where d= the least distance for a passage and B-= half the mean distance of 

 the stars. 



The relation between h and (assuming the law of Newton) was, according to (12), 



which gives 



1 h^oi^'x 

 cos = — , sin ' 



so that 



(120) I=k{ ^''"'^^ 



J 



,1 



For performing this integral we put 

 and get 



or 



n2n ^ j ^+w (J^-Qo^ 



We observe that J is not infinite for co = 0. Developing into powers of to, 

 or directly from (120), we find that, for small co, I is proportional to of. 



It is not permissible to put L) = co . The first term in (121) then is, indeed, 

 infinite whereas the second term accepts a finite value. 



We may, however, without inconvenience, and without altering materially the 

 value of the integral, put d — 0. 



For d = 0 I takes the form 



,122) ,^^l,„J, + ^'»*^ 



or, putting for a moment. 



0)' 



