108 Observations on Inclined Planes. 
tance of attrition and rolling unaffected by inertia. To do this, he 
‘introduces into his equations the weight of the wheels separately 
from the weight of the load, the wheels being increased in the ratio 
of SG to SO, SG being the radius of the wheel, or the distance of 
the center of gravity of the wheel from the circumference, and SO - 
being the distance of the center of oscillation from the same. ‘This 
latter point was found by causing the wheel to vibrate from a point 
in the circumference, and calculating from the times of vibration. 
Although this was necessary in Mr. Wood’s experiments, in order to 
obtain separately the amount of rubbing and rolling friction, yet it 
will readily be seen that many cases will occur in practice, where it 
will be inconvenient and sometimes impossible to ascertain the value 
of SG In the equations here given, the inertia is included in the 
general estimate of friction, for the sake of convenient application. 
‘xamples will be given hereafter. 
Let V=velocity, and F=accelerating force, we always have, by 
2 
the laws of descent, ¢? =f hence the equation above, t?= aay 
b < a ree fates 
ee Gat ge from which 2=g’— 95, and substituting 
for g” its value, a=——2— 
This equation may be used when the height of a plane of a given 
length is required, such that a car, descending by its own gravity, 
may acquire a given velocity at the foot of the plane; or when the - 
height is given, the length s may be found. The value of « is found 
from equation A by experiment. According to the experiments of 
Mr. Wood, x=.15, where the friction is equal to about the 220th 
part of the weight. When the friction is taken as the 300th part of 
the weight, as is sometimes done, e=.107. In general, if the fric- 
tion is equal to the mth part of the weight, we always have a=8 wit 
: The friction f of the wheels being found, it is to be used asa __ 
given quantity in the case where a train of cars, descending an in- 
clined plane, draws up another train at the same time, the trains be- 
ing connected by a rope passing over a wheel at the top of the plane, — 
a te by small wheels or sheaves along the rail track. In 
s case it is nec 40 Gled Ai fn ae 
wtiedl a se ee wes fe feo friction of the rope, sheaves, and’ 
