MADE IN THE EFFICIENCY OF STEAM ENGINES IN CORNWALL. 129 
ence to the size of the wheels, and the logarithmic spirals may be inclined at 
any angle : at their ultimate limit the lines of the centres and of the tangents 
will coincide, producing equable velocities and avoiding friction ; but at this 
point the teeth or cogs disappear, and the wheels revolve with a contact of 
their peripheries. 
As cogs become oblique, their contact produces an increase of pressure with 
augmented friction on the axes : but I am induced to believe, from the results 
of such trials as I have been enabled to make, as well as from theory, that an 
uniform angular motion is the great object to be sought, especially in ponderous 
machinery, and above all where fly-wheels are applied. The expedient usually 
resorted to, of making the teeth small and consequently many in number, ren- 
ders attention to any precise curvature less necessary ; but this subdivision is 
limited by want of strength ; and I would venture to recommend the involute 
form, producing an equability of angular motion. 
When angular velocities are to be multiplied in large machines, the effect 
can scarcely be produced in any other way than by the usual one, of wheels 
unequal in diameter and consequently in the numbers of their teeth. 
The question then to be resolved is this : 
By the interposition of how many such pairs of wheels can the ultimate 
angular velocity be most advantageously produced ? 
Wishing to obtain a solution accurate to no further degree than what may 
be sufficient for the guidance of practical experiments, I omit to take any 
separate account of the friction caused by the teeth of the wheels as distinct 
from that of their axes, and I shall consider the wheels and axes throughout 
the train in a constant ratio to each other, although as the actual pressure 
becomes less, the axes maybe reduced in size, and thereby friction diminished. 
When two forces act on an axis from the peripheries of two wheels attached 
to it ; one for receiving motion, and the other for conveying it on through the 
train, the pressure on the axis may be the sum of the two forces, their differ- 
ence, or any intermediate quantity according to the positions of the points 
communicating with the preceding and with the subsequent wheels ; the pres- 
sure is most usually their sum, as convenience generally requires that the 
power should be received and carried forwards at opposite points. 
mdcccxxx. s 
