Crank Motion. 364 
iJ. Crank Motion. Extract of a letter to > Editor, 
—— eae Iron Works, March 21, 
Dear Sir—Your correspondent, in his “ Exicences of 
Mr. Guinby s Principle of Crank Motion,” (Vol. 12, p. 124,) 
has arrived at a just conclusion, as far as his last equation, ’ 
but his deduction from that equation is incorrect, as he will 
doubtless agree, when he considers that ‘ the mean ‘tendency to 
rotation” = P x .6366 acts throughout the demi-circum ference 
of the circle described by the crank; while the applied pow- 
er=P, only acts through a distance =the diameter of that 
circle. Now it is very easy to demonstrate that : 
P x .6366 x ip De tates =P diameter, and your 
correspondent evinces too correct a knowledge of mechanics 
to contend that there is an disokite loss of power in its appli- 
cation to the crank where this equation exists. The prob- 
lem is reduced to the principle of the lever with unequal arms. 
Lam, Sir, &e. I. DooLirtT_Le. 
a 
April 4th, 1827.—My letter having lain over, I beg leave, 
before closing it, to point out an error which has crept into 
that deservedly popular work, ‘* N icholson’ s Operative Me- 
chanic and British Machinist’’—in page 12. Lond. Ed. in 
treating of the inclined plane, he says, “ the manner of using 
it for the raising of weights, is to cause the applied force sd 
act in a direction parallel to the line * * * 8 
the power gained is in proportion to the length of the se 
compared to the perpendicular.” 
Now if we suppose the angle formed by the inclined plane 
with the horizon to exceed 459, the perpendicular wou 
than the base, and, therefore, according to the above 
theorem, it would require a greater power to raise a body 
along the plane, than to raise the same body vertically ; 
hence the error is evident. 
The true statement is, as laid down 1 by most writers on me- 
chanics, and confirmed by that the power regal: 
ed to raise a body up an inclined, is to the weight 
raised, as the perpendicular is to the length of. the plane, 
when the power is applied i in a direction parallel to the pate: 
and as the. perpendicular is to the base, only when the power 
is applied i in a direction parallel to the base. — 
This is a principle now so generally known, tha A repeti- 
tion of it might be de su rfluou were it ace at sous 
persons might be inadvertently led into error by taking Nic 
