400 PROFESSOR H. S. HELE SHAW OH THE THEORY OF 
Differentiating with respect to y and equating to zero gives the best angle for y, 
therefore 
T 
tany= £+§ cos </> 
once applied in practice. 
y=45°. 
tan y— 1 
(f)=5° 
cos (f>= '996. 
]l=l (nearly). 
Power Form. 
Figs. 32, 33, and 34 show three views of the “power form” of sphere and roller 
mechanism, which has been constructed to test the actual power transmitted. In this 
form an important modification, due to the author’s brother, Mr. Edward Shaw, 
Whitworth Scholar, Stud. Inst. C.E., has been introduced. It was mentioned that 
there was no necessity for the planes of rotation of the bearings to contain the centres 
of the sphere so long as their axes all passed through its axis of rotation. It is, 
therefore, possible instead of merely having sharp-edged disks to act as roller bearings 
(as in figs. 20 and 21) to have conical rollers. The elastic spherical surface yields to 
the very slight extent necessary to allow the flat edge of these rollers to form a 
straight line (instead of a point) of rolling contact passing through the apex of either 
of the cones, the fustra of which are shown in fig. 32. Every part of such a cone 
therefore , rolls upon the sphere. The action of these cones, which have a number of 
fine grooves round their peripheries, is even better than was anticipated. There are 
various points about this design which might be noticed. One is the construction of 
the frame F (fig. 34), which allows the pressure put upon the centres to close in its two 
sides and so maintain the requisite pressure on the sphere by means of the locked centre 
screw (H) without the use of expensive arrangements for springs, which were employed 
in the movable frame of the second integrating machine. The frame, though ribbed and 
otherwise rigid, is of smaller cross-section at h h (fig. 34) to allow this springing in or 
out to take place. The convenient nature of the supporting bracket or frame, which 
is self-contained, and which can be placed anywhere or in any position, is evident, 
and also the important point of its general simplicity of construction. 
It will be seen from the previous investigation that the loss of work in the trans- 
which result can be at 
In the model made 
Then 
This gives 
