2(J0 



Again, let 

 then 

 and 



Also let 



then 



and 



or 



Lastly, let 

 then 

 and 



or 



PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 



dx s'a: 2 .3?n?a;l~^2 .3.5 .6m^x 

 1 ii 



i/.,=2Jx + 



dri/x 



y^ =- 



1 



da? rri' X* 2 . 3»«'a?' 



2.3m^x^ 2 .3 .5 .6m*x 



+ &c. 





^i^ , (I ^ Yy. y,._f. 



dx^ \x ni'x' J dx 4x-~ 



dy 



cPt, 



dx 



= 1 - 



2 . 5 



J . J ni' x^ -I . I . I . V m* x^ 



- &c. 



,= X + 



f^y_s 





+ &c. 



3 1 _L 



dx- \x in' X*) dx 4x- 



3^ 



4:X 



i . -I 



dx x' 3 . 4 »«2a,S ■ 3 . 4 . 6 . 7 ^4 a,V 



-Tr+. 



r.+ &c- 



y, 



d^Vxy^ 



d'y. 



h 



J.f 



1^ 



x^ 3.im-x'^ 3.4.6.7OT^.r 



+ &c. 



7^4 &c. 



'?k2 a' 3 . 4 »»* a^ 

 >w- x5 dx 



da? 



\a; »«3 ^i j dx ^oc' 



Having found ?/i, y.,, y^, j/^ from these equations, we obtain 



\<^« »»•%/— I da/ Vrfa: Til's/ — 1 dx ) 



The remarkable similarity between the equations which determine y^, y.,, 

 y„ yi leads us to conclude that the form of this function is common to all similar 

 equations. It may be seen that the equations for y,, and y^ are identical : the 

 arbitrary constants must, however, be determined dififerently in the two : the one 

 function vanishes when ^=co , the other does not. By solving the equations in a 

 more general form, and by a more purely symbolical method, we shall be able to 



