DIFFERENTIAL EQUATIONS OF THE SECOND ORDER, 

 which hold whatever be the value of p. But from 3 = we have 

 33 . 33 /7 . v , 93 / , 93 n ... 33 . 



+ - <* + w) + (o + a?) + (/< +fp) + (j/ + ep) 



...+ 



dc 



= o, 



and 



33 33 



37 + 37 



33 



33 



33 



33 rfrt 33* 



3ff f/?/ 3r- </// 



For our immediate purpose, p = q ; hence, subtracting, we hav 



33 33 . 33 



3^ - 37 + 37 



33 



3/ 



33 



37 



_ 



31 



which, being free from p and q, must be satisfied in virtue of the above three 

 equations. This being the case, it must, when we substitute for 



da da 



dti dk 



dc 



df. 



Iff ' 



be satisfied independently of the values of 



tlh dk 



( 1L .. (] L 

 d:>; fiii ' 



df/ 

 dz 



Assigning the necessary conditions, we find 



- 

 36 



3/ ' ' 3A ' 



33 33 33 _ 

 3 3</ 3c " " ' 



33 33 , 33 



a^ ~ + 37 



33 



33 



371 



33 



33 



33 



