520 ON THE EXPLOSION OF THE BOILER 
R=the radius of curvature of the curve aycb, at the 
point, y. 
I=the moment of inertia of all the fibres of the beam, 
about an axis passing through the centre of 
pressure of the beam, at the point, y, perpen- 
dicular to the plane of the lamina A A’ B' B. 
E=the weight, in pounds, which would be required 
to extend a beam, whose section is one square 
inch, to double its length. 
Then, substituting in equation (506) of Mr. Moseley’s 
Engineering, &c. 
i eigres ) O  Te 
eee 1) Sa ad 
But, ade ty dx d’y =5 z 
(+ dy’) 3 = 
tion of the beam being very small, dy’ is very small when com- 
, nearly ; because, the deflec- 
; 12° d? WwW 
pared with dz’ ; and, therefore, t= IEI sEr(g"— nde) 
; 1Pdy 
By Integration ee sat 
dent, that exd touches the curve, cya, at the point ¢; and, 
therefore, when x=o, the tangent of the angle yex=o, and, 
consequently, c=o. 
(ax—zx*)+c; but, it is evi- 
. 
3 
a a 
ay et ay 
Again, by Integration, 12*°y = TET ea “ } which 
needs no correction. 
