i 
| 7 = 
“Tl c(u—4£%7 #22 | w,, 02) 
i 0 nN, 
Whence X a (u) is a o-product of n? factors whose residue sum, 
n?2 
S—awo, +n? —1o, and hence can be expressed as a linear homogeneous 
2 
function of x i defined in equation (4) 
By repetition of the argument made in case (a) it follows that X @ (u) can be 
2 
n 
expressed as a linear homogeneous function of ¢ (nu | ©, ©,). 
A bb 
peas 
a 0 
Hence our proposition is proved for all integral values of n. 
A ForMULA FOR THE DEFLECTION OF Car Boustrers.* By W. K. Harr. 
The body bolster of a car is a beam which carries the weight of the car and 
its loading and transfers this weight to the center of the truck bolster, which, in 
turn, transfers the weight to the wheels. 
The bolsters are either of trussed form or of beam form. In the latter case 
they are of I section or else with one flange and web plates. 
It is quite important to construct the body bolster so that it may be stiff 
enough to prevent contact at the side bearings. These side bearings are placed 
between the truck and body bolster to limit the oscillations of the car, Evidently 
if the side bearings come into contact the consequent friction will offer additional 
resistance when the car goes around curves. 
The problem is to compute the deflection of a beam of variable depth. 
In case of beam bolsters the moment of inertia of the cross section may be 
taken to be a linear function of the distance of the cross section from the free end 
of the beam. 
Referring to Fig. 1, let AB be one-half of a body bolster and OB the curve 
into which the half-bolster is bent. Any point of this curve is located with refer- 
ence to O by its co-ordinates x y; mn is a section of the bolster distant x from O; 
Fig. 4. Fig. 1. 
*The following is an abstract of a paper which is given in complete form in the Railroad 
Gazette for December 23, 1898. 
