in Bramah’s Hydro-mechanical Press . SI 
This is the arrangement of the part ; and, in the next place, 
we have to explain the principle and manner of producing any 
assigned variation in the quantity of water to be injected at one 
stroke. 
In the machine we are describing, this is effected by making 
the two pumps of equal diameter, and equal length of stroke, 
and die wheels FF' of unequal diameters, the larger wheel F* 
having one tooth more than the smaller one F ; consequently, 
the wheel F, which has 80 teeth, will make one revolution and 
/gth part, while the wheel F' makes only one revolution, and 
the increase of / 5 th of a revolution at each stroke by the wheel 
F will, at the end of twenty strokes, cause the cranks to be at 
right angles to one another, supposing them to have been paral- 
lel at the commencement ; and* at the end of forty strokes, the 
one crank will be commencing its up stroke, when the other is 
commencing its down stroke, and as then their motions are in 
opposite directions, the one will counteract the effect of the other, 
excepting that small portion of effect which is due to the differ- 
ence of their velocities. Therefore, if the difference of their ve- 
locities be made small enough, a given power may be made ca- 
pable of producing any assignable degree of pressure at the 
completion of the time when the smaller wheel has gained half 
a revolution on the larger wheel. It is obvious, that the number 
of revolutions to produce this effect must be greater the smaller 
we make the difference between the velocities of the wheels. 
Let a denote that arc of a circle which the one wheel gains 
on the other at each revolution, or stroke of the pump ; then, if 
we make the machine commence when both the pistons are at 
the bottom, the water injected at any number n of revolutions 
of the large wheel will be proportional to 2 -f cos n a + cos 
For the pump acts effectively only during the time both pis- 
tons are descending. Therefore, if the machine begin with both 
its pistons at the lowest point, and the motion be continued till 
both begin to descend, it will be found that the crank of the 
small wheel has advanced half the arc a beyond the upper point, 
and consequently must begin its stroke from thence, while the 
crank of the larger wheel begins at the top. Also, when the 
crank of the large wheel has arrived at the distance a from the 
