394 PROFESSOR A. H. GIBSON ON 
formed to a radius of 10°10 inches. The values of — and of 2 were obtained directly 
El CJ 
by loading a straight piece of the same wire as a cantilever 16 inches long and measuring 
its deflection under an end load, and by measuring its angle of twist in a torsion-meter 
under a known torque. As a result the mean values a= 00116; => ‘001438, in 
inch-lb. units, were obtained. This makes 
Tr —s . . re =— . 
a es iy sw 
and these values have been adopted in the various calculations. The following are 
experimental and calculated values of the deflection at the weight, for an applied load 
of 1 lb. at the free end. 
Deflection (ins.). 
a Calculated. Measured. 
90° 1:469 1-475 
135° 44.75 4-475 
§ 3. CrrcuLar-Arc CANTILEVER witH Unirorm Loapinc—w Les. PER Unir Leners. 
Taking the origin at the free end, we have, at any point @ (fig. 3), 
6 
Mo -[ wr? sin ddd = wr2(1 — cos 8), 
8 
Te -| wr>(1 — cos $)dd = wr?(6 — sin 6), 
0 
Hire, 3: 
as the moments produced at T by the loading on that portion of the beam between 
T and the free end. 
