284 On the Transverse Strain, 
(7?—a?)? _ -785398 &e. x r3 
Bie Tee re 
(r?—a?)? 
Substituting then 2 P for EP + EP’, and 
the above value for EG, the strength will be 
== *785398 &e. X roa P. 
sx PRU KOA YA 4 -785398Ke. x 2r 
expressed by, (VAS hy pod ad 
aLC 
_ 1670796 &e. xX 16 gg. aud ) 
= 1ST AE agen e yen 
by reduction and substituting for b. 
Cor. Ifthe neutral line pass through the 
centre, then a = r, and the strength. 
§ . rm 3s 
=o * are of tension x + diameter. 
If it should be required to give rigorous 
solutions to the two last questions, it will be 
necessary to obtain in them the correct values 
of EP and EP’; and for that purpose we 
shall subjoin the following formule, omitting 
the investigations as too tedious :— 
If E, fig. 9, be supposed to be the point of 
suspension of any segment, ACB, of a circle 
vibrating flatways, or in a direction perpen- 
dicular to its plane, the distance EP of the 
cenire of percussion of that segment from E 
will be 
(a -2re He = r)yAp — > (a—r) (2ra—a* \3 
(a—r) A <u 3 = (2ra—a? je ah 
