136 Transactions.— Miscellaneous. 
Reference to the formula will show that the centripetal force varies as 
the square of the velocity. It will be well to see very clearly what this 
means. Taking the particular example already given, if the velocity be 
doubled the acceleration is quadrupled ; that is, the acceleration would be 
474 feet, nearly. This means that the force necessary to retain the stone 
in its revolution round the hand, if it constantly acted on a mass in the 
same way that the force of gravity does, would add to the velocity of the 
mass moving freely, 474 feet per second, which is nearly fifteen times the 
effect produced by gravity, and the hand would experience a pull equal to 
that which it would feel in supporting fifteen pounds weight (nearly). If 
the velocity had been trebled, the acceleration would be nine times 118 feet, 
and the weight nine times 3lbs. 11 oz. (nearly). If the velocity were 
increased nearly twenty-five times,—that is, if the pound mass made twenty- 
five revolutions per second (471 feet per second),—the pull exerted by the 
stone would be equal to the pull which would be exerted by a ton weight 
suspended from, say, a stout beam. If the pound mass revolved one 
hundred times per second, it would exert a pull equal to that which would 
be exerted by a weight of 16 tons. This velocity, 1885 feet per second, is 
about 800 feet faster than a fast cannon ball, and the weight, 16 tons, is 
almost sufficient to break, by stretching, ordinary bar iron one inch square. 
These figures are remarkable, but science teaches remarkable things, and 
we are not much surprised at them. The principle itself will have to be 
looked at closely. 
Momentum is the measure of force. It is the measure of the force of 
gravity. The acceleration produced by gravity, namely, 82 feet per second, 
really means the momentum generated in a mass by gravity. Let us use 
the word momentum instead of acceleration, meaning, when applied to the 
effect produeed by the force of gravity, the velocity with which the mass 
was moving at the end of the time. This can easily be done by taking ® 
one pound mass. If the revolving pound mass have its velocity success 
ively increased by blows, its momentum may be represented by 2, av, 5; 
cv, mv, and in this case the corresponding accelerations may be repre- 
sented by v!, a®v!, b? v1, cy, n2 vt when v! stands for acceleration, ordinarily 
represented by f, and in the special case of gravity by g. Both these sets 
of measures are momentum measures of force. Does it not seem strange 
that if the momentum of the revolving pound mass be increased n times, 
the momentum to be generated by the centripetal force will be i 
creased the square of n times. It may be conceived possible to make ” 
indefinitely great, and still it is asserted that the momentum generated by 
the centripetal force will be as the square of n. Does not this seem very 
much like creating force out of nothing. It may be urged against this, that 
