278 A. BOYD. 
distance from the arms. In every case allowance is made ~ 
for the extension of the distance rod, so that actual deflec- 
tions are plotted. 
The curves in fig. 9 represent a comparison of the exten- 
sions of an arm of each of three wheels at various speeds, 
both the observed and calculated extensions being given. 
The wheels represented are the three- four- and six-armed 
wheels with straight arms and without joints. The exten- 
sions are calculated according to Professor Lanza’s' theory, 
whose expression for the extension of the arm is 
Deen ee B ; 
Hg Oa 
where F =} 2 Wa ee 
fey Ge eT: i (m2 2) 
and K = B ab 
1 (71 a v4) ae 1 
A, R 2 Aa 
In these equations 4 R=extension of the arm due to 
centrifugal effect of the rim and of the arm itself (in feet). 
k=distance from centre of hub to centre of rim in feet. 
a= one half the angle between two consecutive arms. 
v= linear velocity in feet per second of centre of rim. 
A= area in square feet of cross section of rim. 
G= weight of the metal in pounds per cubic foot. 
g= 32°16 feet per second per second. 
F= pull in pounds exerted by each arm on the rim so 
that shearing force in the rim close to the arm = F/2. 
r, =distance in feet from centre of hub to outer end of arm. 
r,= radius of hub in feet. 
EH = modulus of elasticity of cast iron in pounds per 
square foot. 
A,= area of cross section of arm in square feet when 
the arm is of uniform section throughout. 
* Lanza, Trans. Am. Soc. Mech. Engs., Vol. xv1., p. 208. 
