390 
PROFESSOR H. S. HELE SHAW ON THE THEORY OE 
P describes upon the upper part of the curve say at M, a distance corresponding to 
upper boundary of element of width ax. Then : 
Reading of roller C= ^~y — Ax. 
Similarly when the pointer m traverses the lower boundary of the element at N, 
j2 
Reading of roller C=— — Ax 
£ 
being negative because the roller A is now returning, and its motion is reversed. 
Taking both results together 
Reading for element MN=^ + \\ J Ax 
=a(^ + bj Ax 
= moment of area of element MN about Ox. 
If now the whole distance moved through round the curve be taken where y 1 and y 3 
represent respectively b and (a + 6) at any point of the curve, then 
Reading of C= [ {yz~yi)^ x 
J x x 
= moment of area of whole curve about Ox. 
Fig. 26. 
Secondly, let three sets of spheres and rollers be employed, as in fig. 26,* 
1=moment of inertia of element MN about 0.r 3 
* The axis 7w, h' 2 should be perpendicular to its present direction in the figure. 
