128 MR. BEVAN ON THE MODULUS OF TORSION. 



inches in length, and from three inches to three tenths of an inch in thickness. 

 Due care was observed to prevent any error in the apparent torsion or twist 

 arising from compression at the ends of the prisms, both at the clamp by which 

 they were fixed, and at the radial lever at which the successive weights were 

 applied ; two sources of error which have materially affected former experi- 

 ments on this subject, in other respects carefully made. 



To every specimen under experiment I attached two indexes ; one a few 

 inches from the end fixed in the clamp or vice, and the other at a small distance 

 from the attachment of the lever or wheel, where the weight or straining power 

 was applied ; and the distance between the two indexes was used as the length 

 for calculating. Another error of less magnitude I have been able to avoid 

 by fixing a pivot or small gudgeon at the supported end, in the line of the axis 

 of the prism, instead of making the lower side or angle of the prism at the 

 supported end the revolving point. 



My experiments were made upon prisms of very different proportions as to 

 breadth and depth, viz. from ^Vth to equality. 



In general practice, the square or cylindrical shaft is usually adopted, and 

 as a cylindrical spindle or shaft of |th more in diameter than the side of a 

 square shaft, will possess nearly the same stiffness in resisting a twisting 

 force, it will, I presume, be sufficient in this place to give the rule for calcu- 

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

 example by way of illustration. 



Rule. — To find the deflection 5 of a prismatic shaft of a given length I when 

 strained by a given force w 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 following table ; /, r, I, 

 and rf, being in inches and decimals, 



d*T — ° 

 i. 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 mo- 

 dulus of torsion : divide the former by the latter, and the quotient will be the 

 deflection or quantity of twisting in inches and decimals when measured at 



