DISCONTINUOUS AND INDETERMINATE FUNCTIONS. 71 
The equation 
w =ooo 
+ 0 ooiv-{(f)"+(T)”+(f)”+( i — sr 
(15) 
2£Z\°° | 
12 a) ) 
represents a ladder, assumed vertical, the origin being at the 
center of the middle rung. The first term gives the sides, of 
length 2 L and diameter 2 R. The second term gives the 
rungs, which have a length 2 l , breadth 2 b, and height 2 a. 
The distance between their centers is 6 x 2 a, and they are 
inserted half way through the sides. 
Application to Physical Problems .—We give two illustra¬ 
tions, as follows: 
The equation 
J F=^[l-iV-(i)"] (16) 
represents the attraction between a homogeneous spherical 
shell, infinitely thin, having radius R upon a mass at a dis¬ 
tance r from the center. When r < R the force becomes zero. 
The equation 
v= k [l — N~ (1)“] + k (3 B? — r 2 ) N - (-rT (17) 
represents the potential of a particle at a distance r from the 
center of a spherical homogeneous mass of radius R. The 
first term is finite for points outside the sphere, the second 
term for points inside. 
