OP ELLIPSOIDS OF VARIABLE DENSITIES. 209 



where for simplicity the indices at the foot of the letters ( and a 

 have been omitted, and their accents transferred to the letters 

 themselves. Moreover all the finite integrals are supposed taken 

 from 1 to s + 1. 



By making h in the last expression we immediately get 

 V'^>, and if for a moment, to prevent ambiguity, we write b r in 

 the place of the original a r ' and omit the lower indices as before, 

 we obtain 



where to avoid all risk of confusion r has been changed into r", 

 and the double accent of this index transferred to the letters f 

 and b themselves. 



We will now conceive the expression (32) to be written in 

 the abridged form 



the order of the terms remaining unchanged. 



If then we recollect that the accents have no other office to 

 perform than to keep the various finite integrations quite dis- 

 tinct, and consequently that in the final results they may be 

 permuted in any way at will, we shall readily get 



14 



