960 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 



















ar 5 ‘a2 
Again, let ae JS 2 + aa 
8 dx JH 2.3m? 4% 2.3 5.6m+*t x® a 
then Y = 2 are yee 2 
2 2 3 m2 xt 9 3 5 6 Fi ae &e. 
a2 xy 5 
and dx : mnt 2 Eds Re 
ee ee ee 
a2 ok ax 
Py. = i dy, 5 ie 
d x? a mnt) da 42 
dy 2 2.5 
Also let ie tie 2 ee 
HN 2 
then La re Sma 3.8.23 iagege 
P/zy, 3 1 1 2 
and de 3 Dye iti. ia Bal s+ &e. 
we 1 dy, 
4a meat dx 
‘ d’ y, (;- il dy, Digi 
d x* 2 om =| da 42° 4x 
yee es Be * .g- 
Lastly, let di, Ge Cidpee See eee 
i 1 eS 
then =->=+——— - Sere 
Ys at 3.4m? at 3.4 Sree Me: 
; day + ee 
and ’ ae fat eo 4m! ae * ae 
1 dy, 
m? «i de 
Pace en eg 
7 da GS= oe 
Having found 7, ¥., y;, y, from these equations, we obtain 
Sy (89s. TE As dy,, Nw dy, 
—— a a ana ae dx ) 
The remarkable similarity between the equations which determine 4, y,, 
ys, Ys 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 differently in the two: the one 
function vanishes when #=o0, 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 


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