HY'H THEOREM. 2!7 



+ - 







resolved parts of the rcqi n will be 



these three calculated results, multiplied respectively by 



be ca 



II I | I t | 



nay be shewn that there is only one ellipsoid which can 

 have its semi-axe- rig the conditions required 



I vory's theorem. 



; -pose that a, b t c are in descending order of magnitude* 



Put ' -c*.y, so that p and q 



ositive quantities. We have 



a^-p + t, b* 

 we obtain the following equation for determining t, 



lie chances of sigri of the expression which 

 member of this equation, we see that 

 there is a root between p and q, a root between q and 0, 

 and a root between and oo . Corresponding to the tirst root 

 we should obtain an h ypt'rboloid of two sheets ; correspond- 

 ing to the second root an hypcrboloid of one sheet ; ana cor- 

 iesj> the third root an ellipse 



of a body of any figure en a particle of which the distance 

 U wry gnat in comparison tri/A the greatest diameter of the 

 body, is very nearly the same, as if the particles 

 were condensed at their centre of <ind attracted ac- 



cording to the same law, whatever that law be* 



-or di nates be taken at the centre of 

 gravit attracting body, the axis -ugh the 



