44 PROFESSOR KELLAND ON A PROCESS 












b2r (r+28) (2742s) a78+3r & 
F 2s437r—1 (r+ 2s—7r yp) (2Zr+2s—r or+2s—r ae 
/28+3r—1 B) K) 
@ re ety g{ Ge—1 Gere) ete 
dz Ago. | ae = 2s (2s—r) pat 
or Depron Be" (r+2 5s) (QaeE ie ors aa ene 
7 eetr=1 + Ber8r—-1 (r+2e—rp) 2rt+2e—r pi) + &e.} 
BD pe nee OOO gn BY (Ce ae 
aaa ax aoe dx 28 (2s—r) | [2s—2r 
Ogg Be (r +28) (2r+2 8) 2s42r 
Lay as + Braise (7+28—r fl) (Qr+2s—rp) s &e. } 
(2 s—r pt) (2s—r—7 pf) 23-27 raft y 
<8 “Ds (@s—r) Be—2r ie 
1 
If Syne | 
Saree 
if es g 2s= rf) (2s—r—r p) 2t- Fae) Pali 
: 28(2s—r) /2s—2r 7m Qs 
eee | 28 
ral a 
Sieh aes 
(ry ca 
Therefore, generally, if y=d* cos az, we have 
rete 
dz} dx ee real 

Se 
d pe gn ey a =aly ay: 
or, if x“ y=z, the equation may be written 
d-! rid a 2 2 
(—, x ae FI z=(—a’)’z,...(C) 

a form which exhibits its relation with the differential equation resulting from ¢* 
11. There exist numerous relations between the differential coefficients of a 
function ; such as the following :— 



D 
be bn [-2en 
Since = c= az) va (-rf u; 
[oor 
Dyfi ae 
let ¢ (>) = 5-; then 
