OF THE IRK, LOCOMOTIVE ENGINE. 915 
Using the 21st Prob. in Sec. 3, of Emerson’s 
Fluxions. 
Let D BE be the F 
position, before im- p E 
pact, of the beam, 
supported at the 
two ends, D and E. 
Let B A be the A 
space, through which the beam is bent, before it breaks ; and, 
let the beam, from the position D B E, be put into the posi- 
tion D A E; and let a weight, c, be laid upon it, at A, which 
will just break it. Then the weight, w, impinging horizon- 
tally, in the direction F B, on the middle of the beam, at B, is 
to bend the beam through B A, to the point A, where it breaks. 
w=the impinging weight in pounds avoirdupois. 
c= the weight, which suspended at A, will just break the beam. 
b=BA=the space through which the beam is bent, when it 
breaks. 
Let DCE be the position of the beam, at the time, ¢. 
2=BC. 
v=the velocity with which the point, C, is moving at the time, ¢. 
and let u=the required velocity with which w must impinge 
upon the first beam. 
When the beam is bent into the position, D C E, it exerts a 
force, which is proportional to the distance B C; and, therefore, 
Osc .-e =the moving force of the point C, in the direc- 
tion B C A, in consequence of the impact given to the beam, 
