62 On Crank Motion. 



The effect of an alternate rectilinear force, applied to the 

 extremity of the crank to produce rotation, is exactly similar 

 to that of the force of gravitation on the pendulum during 

 its descending arc ; and, if there Avere a loss of power in this 

 case, the pendulum surely would not, in virtue of the force 

 acquired during its descent, remount to the same height on 

 the other side of the center. 



This problem admits of a variety of demonstrations, based 

 as well on the laws of dynamics, as on those of statics, and 

 all, as far as I know, confirmatory of the principles above laid 

 down, but I think enough has been said on the subject to es- 

 tablish the doctrine. 



Having submitted the foregoing to the inspection of one 

 of the ablest mathematicians of our country, he says, " It ap- 

 pears to me that Mr. Hogan has committed an error in not 

 having taken time into consideration, and in estimating the 

 space passed over as a measure of force, 11 &c. But I ap- 

 prehend, that this objection will fall, when it is considered, 

 that the measure of an effective force is found by multiplying 

 its intensity by its velocity — and that the velocity of two for- 

 ces passing over unequal spaces in equal times, is as the spa- 

 ces passed over respectively. — As in the above demonstra- 

 tion, the tangential force moves from c to d in the same time 

 in which the applied force passes from a to b ; and as it is 

 shown that the intensity of these two forces is in inverse ra- 

 tio to the distances through which they respectively act — it 

 will, I presume, be readily conceded that the cause and ef- 

 fect are equal. 



I am, sir, with high respect and esteem, your obedient ser- 

 vant. I. DOOLITTLE. 



