110 MR JAMES CLERK MAXWELL ON THE 
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 
ie 
= 5; 
By substituting the value of x in the values of p and g, and in the equation 
of elasticity, the approximate value of @ is found to be 
1 
t (hy + he) (s5 p 3 5a) 7 


Lae 1 9 
zp (a 3 su) mn 
t —18 mp , hth, m—dp (53,) 
as —h, 10m+51p a h,—h, poe 
Since the focal distance of the mirror, or 5 “, depends on the difference of 
pressures, a telescope on Mr Nasmytu’s principle nae 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 2 be the length of the cylinder, a its radius, 7 the radius at any point, 
66 the angle of torsion, M the force producing torsion, dz the change of length, 
and P the longitudinal force. Each of the wires becomes a helix whose radius is 
r,, its angular rotation 6 6, and its length along the axis x—0 @. 

Its length is therefore at (rd 0)? +2 (1- ue as 
and the tension is es (a—J (ay are @)’) 
This force, roe ame: to the axis, : 
ey) 
Om we 
and since — and r — are small, we ue assume 
d d Ox 00 
d0 dr pot (2-5 a s) ) 
= TE (7 22/4 *)") Tears 
The force, when resolved in the tangential direction, is approximately 
aoa BCS Fate) ) 
MW=rk Gs O00 Sas. 78 ae (55.) 




