434 

 lOa) 

 11 a) 



IX. DYNAMICS OF DEFORMABLE BODIES. 



,f 1 dgp 



9a) 



12 a) 



23 a) 



y := 2^=^> 



* _ 



~ 



1 Off X 



m^^ii 



1 dcp' y' 



2 "dy b 

 1 d(p' z' 



U7 = ~c 



In the cubic for the axes of <p, 

 26) k ii-l, f 



= 0, 



9 y f , C l 

 the three roots are proportional to the squares of the reciprocals of 

 the semi -axes (Note IV), 



Now by 25), and 24) 



and therefore 



222 _ 

 i 2 3 ~" 



^3 



_vl ume of strain -ellipsoid 

 volume of sphere 



But the product of the roots AiAgAg is equal to the constant term in 

 the cubic 26). that is. 



30) 



9, f> 

 The determinant of the coefficients of the substitution 9) accordingly 



represents the ratio of expansion, and since parallel lines are stretched 



V 

 in the same ratio, the ratio of expansion of volume -= is everywhere 



the same. 



