370 
PROFESSOR H. S. HELE SHAW ON THE THEORY OF 
dz 
__ co clt dz 
dx dx 
dt 
where dz and dx correspond respectively to the rates of change of the two variable 
quantities at any time t. 
The author three years ago applied this principle to the construction of a speed 
indicator. The disk was driven by a clock, and the screw by the body whose speed was 
to be indicated. In this case oq, the angular velocity of the shaft A, was constant. 
Then 
^1_ T T 
co=y^=yK. 
There were in the above instrument two screws of opposite pitch working inde¬ 
pendently upon one axis, so that each half of the diameter of the disk, available upon 
either side of its centre, could be employed. On either screw was a roller, working as a 
nut and connected with a corresponding index upon a dial, so as to always indicate its 
position upon the disk. One dial was arranged to indicate the speed of the engines 
of a steam vessel, while at the same time the other was indicating its corresponding 
speed through the water, so as to simplify the work of progressive speed trials. Two 
practical advantages may be noticed in connexion with such an instrument. The 
first is that a speed indicator of this kind may be placed in any part of the ship and 
communication made electrically, as was done in the above case. The second is that 
the slight and irregular variations in velocity which in most speed indicators, such as 
the strophometer of Hearson and the tachymeter of Buss, necessitate special arrange¬ 
ments of springs to diminish the oscillations of the index hand, are not recorded with 
this kind of instrument. This latter fact is the result of the gradual action of the 
screw, which may, however, be so arranged as to cause an indication of any required 
degree of sensitiveness. It is not necessary to further describe the instrument, which 
suffers from the inherent defects of the disk and roller, and the principle of which the 
author found had previously been suggested by two correspondents in ‘ Engineering/* 
and very possibly by others. Quite recently (May 24) a speed indicator of this kind 
was exhibited before the Physical Society by Mr. W. Golden and Sir A. Campbell, 
in which the disk was replaced by a cone, and on the same occasion Mr. N. Bailey 
described a speed indicator of his own which was no other than the simple disk and 
roller applied in this way.t 
Enough has been said to show that a great many attempts have been made to 
employ for practical purposes the invaluable principle of the disk and roller in two 
distinct ways, one of which is the converse of the other. J 
* ‘ Engineering,’ vol. xx., p. 314. 
f £ Nature,’ vol. xxx., p. 140. 
J There is, it is true, yet a third way of using the disk and roller, which is most important and 
