372 
PROFESSOR H. S. HELE SHAW ON THE THEORY OF 
speed indicator, experienced no small difficulty in consequence of the powerful and 
expensive clockwork required to ensure a uniform speed of rotation. 
It is with combinations of this mechanism that the evil results of this loss of power 
are most evident, not merely because of the limited extent to which it can only in 
consequence be applied, but because of the unavoidable introduction of errors. 
(iii.) The third and last objection, first pointed out by Professor Clerk Maxwell, 
is perhaps the most serious of all. 
tig. 2. 
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Let A (fig. 2) be a plan of the roller, O being the centre of the disk which is 
turning in the direction indicated by the arrow N. Let A Q be the reaction to the 
force required to drive the roller round, acting at its periphery at the point of contact 
with the disk. This force though small must exist, and the result is that the 
displacement of the roller when the larger force A P (wdiich is that tending to alter its 
position radially on the disk) comes into operation is not radial but along A P. This 
line A R is the direction of the resultant of A P and A Q, and by moving along it the 
roller really slips through a circumferential distance R P, which represents the actual 
error thus introduced into the result. The total error is thus proportional to the 
distance moved sideways by the roller, that is, to its transverse displacement. It is 
this fact which is ignored in the tests of ergometers. The common method of 
procedure is to turn the instrument through a certain distance with a load deflecting 
the spring to a known and constant amount, and the roller consequently at one radial 
position on the disk. This is repeated for various other positions of the rofler when 
the record of work done is in each case found to be correct, and it is hard to see why 
it should be otherwise. These are not, however, the practical conditions of working, 
wdiich, as a rule, are totally different. In ergometers and steam engine integrators, 
for instance, a continual change takes place in the position of the roller due to 
fluctuations of power or steam pressure. This introduces an error in the way 
described which it does not appear possible to allow for even if the law of variation be 
known, without elaborate calculation. It certainly would be difficult to test an 
ergometer or similar instrument with a view’ to ascertaining and allowing for this 
