60 On Crank Motion. 



Art. XI. — On Crank Motion; by Isaac Doolittle, 

 Bennington Iron Works, Sept. 22, 1827. 



My Dear Sir — I had hoped to live long enough to see the 

 discussion about the crank problem settled and dropped ; but 

 the dispute seems to be interminable. 



The problem itself is as simple as any other in mechanics, 

 and may safely be referred to the general principle adopted 

 and laid down by all modern French mathematicians, when 

 treating of the "principe de la conservation des forces vires" — 

 That there can be no loss of power in any machine except 

 what arises from one or more of the three following causes : 

 friction, shocks, or a sudden change in the direction of motion,'''' 

 (the resistance of media and the stiffness of cords being in- 

 cluded under the general term of friction.) 



Now in considering the action of the crank, the two latter 

 causes cannot operate ; there can, therefore, be no loss of 

 power, except what arises from friction, and in all the dis- 

 cussions which I have seen upon the subject, I do not now 

 remember any in which this cause was taken into account. 



If there be, as is contended by one of your correspondents, 

 a loss of more than one third of the power, in transforming 

 an alternate rectilinear movement into a continued circular 

 one by means of the crank, I should like to be informed 

 what would be the effect if the proposition were reversed, as 

 in the case of the common saw mill, and in many other in- 

 stances in practical mechanics. 



Your correspondent has, in the last number of your Jour- 

 nal, p. 77, no doubt through inadvertency, attributed to me 

 the following equation: 



"PX.6366X semi circumference ==*X diameter." 



This is not my equation, nor is it true ; for according to 

 his own assumption, Px.6366=t; and therefore the equa- 

 tion attributed to me cannot be true, since the semi circum- 

 ference is greater than the diameter, (in the ratio of 1 to 

 .6366) and since it has been known, from the days of Euclid, 

 that equal quantities, multiplied by unequal quuntities, can- 

 not produce equal quantities. 



The equation I gave, (see Vol. 12, page 367.) 



Px.6366= demi-circumference=Px diameter, is true, 

 and shows that there is no loss of power. 



