392 
PROFESSOR H. S. HELE SHAW ON THE THEORY OF 
therefore, if 
So= reading of index for travel of the whole area of curve 
r«2 
So = £^2 yd A 
■'«i 
or with proper units 
fX 2 
=hh\ {yi—yi)dx 
S 3 = moment of area about Ox. 
With the addition of the third set of sphere and rollers 
Cx 2 
So— reading of index D z=lc 1 /cj Jc s y(dM ) 
J x 1 
=kjcjc, j {yi—yi)dx 
J x. 
= moment of inertia of area about Ox. 
Fig. 27. 
The three dials of B, C, and D may be arranged on the parallel ruler as shown in 
fig. 27 , and thus a compact and inexpensive instrument formed, which wih give on 
three dials simultaneously and without the necessity oj any calculation whatever^ the 
three quantities A, M, and I. 
But there are certain practical points of particular interest in this instrument which 
