108 On the Generation of Statical Electricity. 
inches diameter, with four rubbers twelve inches long each, will 
be compared to a cylinder of twelve inches diameter, and eigh- 
teen inches long, with two rubbers eighteen inches long each. 
As the velocity of the portions of the glass passing under the 
rubbers is an increasing function of their respective distances 
from the axis of motion, the velocity of the circumference of that 
circle, which touches the centres of the cushions, will be taken 
for the mean; and this, multiplied into the total length of rub- 
ber, will repre the amount of glass surface subjected to il 
rubbing action for one revolution. Hence, 
Inches. 
(37:6992)48 = 1809-5616 for one half revolution of the plate. 
(37:6992 )36=1357-1712 for one revolution of the cylinder. 
It is assumed that the amount of force expended in each ma- 
chine for each unit of time is equal; hence but one half of a 
revolution of the plate is considered; for the diameter of its 
mean circle of resistance being twice the diameter of the cylin- 
der, it follows that the plate will make but one half of a revolu- 
tion, whilst the cylinder performs one entire revolution. Friction 
being directly proportional to pressure, it is evident that the sum 
of the pressures in each machine must be equal: hence the 
same amount of pressure is exerted on forty eight inches of rub- 
ber in one case as is applied to thirty six inches in the other; an 
inch of each is then pressed in the inverse ratio of these num- 
bers, oras 3 to 4. But by hypothesis, the greater pressure pro- 
duces the maximum effect; hence each inch of the plate rub- 
bers does not exert its greatest action; and as it has been assum- 
ed, that up to the maximum pressure for the same extent of sur- 
face the disengagement of electricity is directly proportional to 
the friction, it follows that the quantity given out by each inch 
of the rubbers of the plate, is to the quantity given out by each 
inch of the rubbers of the cylinder, as 3 to 4. But each of the 
rubbers of the same machine produces, by hypothesis, an equal 
effect on each equal portion of glass surface subjected to its ac- 
tion ; hence is obtained, for the total effective action for a unit of 
time of each machine, as follows : 
(1809:5616)3= 5428-6848 for the plate machine. 
(1357-1712)4=5428:6848 “ “ cylinder “ 
The machines are therefore equal in power. This result has 
been confirmed by accurate experiment. It is conceived that the 
