Mr. Bevan's Experiments on the Modulus of Torsion. 421 



adopted, and as a cylindrical spindle or shaft of ith more in 

 diameter than the side of a square shaft, will possess nearly 

 the same stiffness in resisting a twisting force, it will, I pre- 

 sume, be sufficient in this place to give the rule for calculating 

 the deflection of a square prismatic shaft, to which I shall add 

 one example by way of illustration. 



Rule. — To find the deflection 8 of a prismatic shaft of a 

 given length I when strained by a given force ix> in pounds 

 avoirdupoise acting at right angles to the axis of the prism, 

 and by a leverage of given length = r; the side of the square 

 shaft = d. T, being the modulus of torsion from the follow- 

 ing table ; /, r, 8, and d, being in inches and decimals, 



j. e. for a numerator, the square of the radius of the wheel or 

 leverage multiplied into the length, and this product by the 

 weight in pounds : and for a divisor, multiply the fourth power 

 of the side of the square prism by the tabular modulus of tor- 

 sion : divide the former by the latter, and the quotient will be 

 the deflection or quantity of twisting in inches and decimals 

 when measured at the end of the radius /-. As an example, 

 let there be a square* shaft of English oak 50 inches long and 

 6 inches by 6 inches, subject to a strain of 3000 lbs. at the cir- 

 cumference of a wheel of 2 feet in diameter, or having a lever- 

 age of 12 inches f. 

 6 X 6 = .36 12 X 12 = 144. 



36 50 = length 



1296 7200 



20000 3000 = force 



"25920000 25920000)2 1 600000(0'83 = deflection, 



• If the transverse section of the prism or shaft be not a square, hut a 

 parallch)yrani, let h = the breadth, and d the deptli : the deflection will 

 be obtained by the following formula : 



{d-\-b)lr'\V _ . 



f If the measure of torsion should he required in degrees (A) 

 let e = 57-29o78 then ■^^.^- = A 



•1' , rlw 



or let — ^ = < then — ;i-- = A 



e 



dU 



thus for wrought iron and steel - = A 



r / t» 



