LECTURES. 219 



light, and the bending of a rectangular prism of glass. Also illus- 

 trated by a diagram. 



(118.) Elasticity of Torsion. — Apparatus and experiments of Cou- 

 lomb exhibited. Double horizontal pendulum suspended by a fine 

 wire. ' 



The force of torsion is just in proportion to the angle of torsion, or 

 again we have ut tensio sic vis. 



All the vibrations are therefore in this case also performed in the 

 same time, whatever be tlie amplitude. 



Because the force of torsion varies as the angle of torsion, the vibra- 

 tions of a torsion pendulum are governed by the same laws as those 

 of the cycloidal pendulum; hence we shall have by mechanics 



/ 



In this expression, in which T is the time, / the elastic force, and L 

 the length of the radius of the double pendulum, the diameter of the 

 wire and the weight which stretches the wire are each supposed to be 

 equal to unity. 



If the weight be increased to W, then the velocity or the measure 

 of the force will evidently be diminished in the same ratio, and in- 

 stead of / we shall have-^. Hence by substitution, 

 •^ W 



7" 



1. The time of vihration is as the square root of the lueight luhich 

 stretches the ivire. 



If the length of the wire be increased to I, then for a given angle 

 of torsion the molecules will be separated inversely as the length ; 



therefore the force will be expressed by_, and by substitution, we 

 shall have 



T = .7 



LI 



y or 



2. The other quantities remaining the same, the time varies as the 

 square root of the length of the luire. 



Again, if the diameter of the wire becomes r, then r- will represent 

 the increased number of molecules, and since the mean distance of 

 separation of these for a given torsion will vary as r, and also the 

 distance from the centre to the point of application at r, it follows 

 that the whole force will be expressed by r^, and therefore by substi- 

 tuting again, we shall have 



L 



7 '' 



The time varies inversely as the square of the radius of the ivire, the 

 other quantities being constant. 



All these inferences are in strict accordance with the results of ac- 

 curate experiments. 





