THE EQUILIBRIUM OF ELASTIC SOLIDS. 59 



To obtain an expression for the curvature of the plate at the vertex, let a 

 be the radius of curvature, then, as an approximation to the equation of the 

 plate, let 



= 



~' 



By substituting the value of x in the values of p and q, and in the equa- 

 tion of elasticity, the approximate value of a is found to be 





.9 



3m/ m 



t -18m/* 1 z - , . 



"- '" 



Since the focal distance of the mirror, or - , depends on the difference of 



Zi 



pressures, a telescope on Mr Nasmyth's principle would act as an aneroid baro- 

 meter, the focal distance varying inversely as the pressure of the atmosphere. 



CASE VII. 



To find the conditions of torsion of a cylinder composed of a great number 

 of parallel wires bound together without adhering to one another. 



Let x be the length of the cylinder, a its radius, r the radius at any point, 

 80 the angle of torsion, M the force producing torsion, 8x the change of length, 

 and P the longitudinal force. Each of the wires becomes a helix whose radius 

 is r, its angular rotation 80, and its length along the axis x Bx. 



I ( O;C 



Its length is therefore / (rodY + y? ( 1 ' 



V v \ x. 



{/ / O#*\ 2 

 1 1(1 )+i 

 V V / 



This force, resolved parallel to the axis, is 



^^t/Ff^'l' : 



82 



