VECTOR DIFFERENTIATION. 
79 
ton and Tait, which makes (y — 1 R ) 2 = — r 2 or R 1 = r 2 , 
involves a negleet of the dimensions of the axis in the left- 
hand expression. Before differentiating, the power of the 
axis must be restored if the axis is variable. 
The next step is to find, how to differentiate ~ with respect 
to p. 
Since p — 
P 
— 1 absolutely, 
Therefore 
dp . — -f- p d (—^ — 0. 
P V P ) 
P d (—^ = — dp —, whence 
V p J p 
As do and p are at right angles to one another, the last two 
factors can be interchanged, provided the sign is changed; 
hence 
Here the remarkable fact is that no minus appears in the 
result; otherwise it is the same as 
(i) 
dr. 
To find how to differentiate -4- with respect to p : 
Since ~ = 1, therefore 
