76 Answer to Mr. Quinby. 



and corrected : he knew that the terms of the proportions 

 were intended to have been written alternately and not in 

 the form in which they appeared, and should not have taken 

 advantage of such a mistake to have avoided the acknowl- 

 edgment, that his error was pointed out : had he received no 

 correction of these proportions, the remarks which followed 

 them would have been of themselves sufficient to have shown 

 the intention of the writer of the examination. No credit 

 was claimed by me for the discovery of an error which re- 

 quired but a slight knowledge of Plane Geometry to detect. 



The next paragraph of Mr. Quinby's reply contains a de- 

 monstration of the incorrectness of Mr. Ward's proposition : 

 the paragraph closes in this way, " therefore the principle 

 assumed by Mr. Ward is not correct, and my proposition, 

 which the writer of this examination asserts is incorrect, is 

 true :" no such assertion is contained in my examination, the 

 words used in relation to this proposition are these, " but first 

 let me remark upon the manner in which Mr. Ward's propo- 

 sition, relative to the crank, is treated by Mr. Quinby" — the 

 manner, — it did not enter into my plan to touch upon Mr. 

 Ward's proposition further than to expose Mr. Quinby's er- 

 ror in his manner of treating it. 



Mr. Quinby then takes the equation $R=P;r, (in which <£> 

 represents the effective force, R the radius of the crank wheel, 

 P the power applied to the crank, x the perpendicular from 

 the point of application of the force to the vertical diameter 

 of the crank,) given in my examination of the crank problem, 

 to the mode of solving which, he objects ; he observes, " In 

 the equation *R=Pa:, he, (the author of the examination,) 

 has two variable quantities ; and he supposes one of them to 

 be equal to a constant quantity," — not so, — in the equation 

 <$R=P.r, $ and x are variables, R the radius of the crank is 

 a constant, and P, by the terms of the question, is considered 

 as a constant force applied to the extremity of the radius of 

 the crank wheel ; then * must vary with x, and must have its 

 mean value when x is a mean : this was the mode used to 

 solve the equation and to find the mean value of *, and to this 

 mode I can see no objection. Mr. Quinby further says : 

 " The equation, however, which he," (the author of the ex- 

 amination,) " has given, will solve the problem ; and gives 

 the same result as that which I gave in my demonstration ; 

 for since <£>R=P;r, and this for any position whatever of the 

 crank, it is plain that there can be no loss of power, for if 



