276 On the Transverse Strain, 
ik,—double the content of a cone formed by 
the triangle AEn rev olving round En. 
And since a cylinder on AB is = = p(ik)? 
x AB = p(d—x)*b; and the cone on nE — 
a b 
5 p(ik)? x aE = Bede) x 2 (da) = 3 
(d—«)3, we have S'= p(d—2)b—2 (d—x)3 = 
( Coa ie ). 
But S: §’: n. 
Therefore PC. d)a? + = =): pb( (d—)*— 
c) ::m:n. Hence PE ((a- d)a? + “)- 
oe — 
mpb( (d— xv)? — 
have 3n(a—d)x* ++ ne 3dma(d—a)* — m(d—a2)3; 
) and dividing by 2 = we 
whence by involution, &c. we get 
3md md2 
x3 +3(a—d)x? + nome t= =a (3a—d) ; 
a cubic equation from which the value of x 
may be obtained: and which is independent 
of the breadth of the beam. 
Suppose for example a and d are 9 and 8 
inches respectively, and m to n is as 4 to 5; 
which is the mean ratio obtained from our 
experiments. 
Then the equation above becomes 
v3 4. 3x + 960 a = 4864. 
Whence x = 4. 872025 nearly. 
