384 
PROFESSOR H. S. HERE SHAW ON THE THEORY OF 
(1.) No slipping must take place. 
(2.) Each set of rollers must always be in contact round the great circles 
formed by two perpendicular (not necessarily horizontal and vertical) 
diametral planes. 
(3.) The axes of all the rollers must intersect the line of intersection of the 
two planes. 
It will be observed that nothing is said about the planes of rotation of the rollers 
containing the centre of the sphere in the last condition, and the fact that this is not 
necessary is taken advantage of in the last application which is described in this paper. 
From the foregoing results it is evident that it is not the distribution of the rollers 
round the great circle that is important, but the direction of their axes. Therefore the 
rollers hitherto alluded to as movable centres do not require to be placed at the points 
of intersection of the diametral planes, and may be removed to such a position that 
they can never come into contact with the rollers round the horizontal great circle of 
contact. At the same time the top and bottom rollers which are not required to be 
in contact with the poles of the sphere may be removed to any other convenient 
position along their great circle of contact. 
Figs. 18 and 19 (p. 383) show respectively a diagrammatic plan and elevation of the 
sphere and rollers thus arranged, and the views are lettered to correspond with figs. 
11 and 12. Figs. 20 and 21 show the details of the mechanism designed to carry the 
above principles into operation. The rollers in contact with the horizontal circle are 
carried on a bracket, which is part of the fixed frame (I I). Those in contact 
with the vertical circle are carried in a strongly-ribbed movable frame (F F). The 
mode of attaining numerical results, if required, would be of course identical with 
that employed in the instruments already described, and would require the additional 
parts shown in connexion with them. 
The two kinds of defects shown at the commencement of this investigation to exist 
in the disk and roller have thus been practically eliminated. 
(1.) The results of friction are reduced to a minimum, for not only does the change 
of velocity ratio, i.e,, the relative position of the axes of rotation of the sphere to the 
fixed rollers, take place by rolling, but the sphere itself is entirely supported by 
rollers, and thus there is absolutely nothing but rolling contact. This was not the case 
with movable centres. The immediate result of this is that the hard, smooth surface 
of the sphere is no longer necessary, since no twisting now takes place, and the edges 
of the rollers transmitting the motion to be measured may now be serrated so as to 
form the envelopes of their teeth upon the elastic surface of the sphere. 
This effects a great reduction of friction, for the pressure which -was formerly 
necessary to ensure the transmission of rolling by frictional contact of the driving 
roller (A) in the fixed frame is now greatly reduced. The contact is now scarcely 
frictional contact at all, and the pressure on the bearings is so reduced that the most 
