244 Mr.W. S. B.Woolhouse on the Theory of 
According to Dr. Lardner, the subject is “totally distinct 
from the consideration of accelerating forces”; he considers 
it to be essential that the velocities be continued uniform, and 
therefore discards everything in the shape of an accelerating 
force. Now, in order that such a theory may be sustained, 
it is a well known elementary principle of forces, that the power 
employed must be always precisely equal to the resistance, or 
the amount of friction combined with the proper resolved effect 
of gravity along the railway, observing, however, that in the 
term friction, we must include the resistance to the motion ex- 
perienced by the carriages, &c., in passing through the atmo- 
sphere. We shall not here discuss the practicability of pre- 
serving this exact balance between the forces at the various 
changes of inclination ; nor shall we offer any serious objec- 
tion to the principle that the friction is the same for all veloci- 
ties, which has received the sanction of general practice, 
though doubtless inaccurate, as far as regards the effect of the 
atmosphere. 
Continuing the notation of the preceding letters, we have ¢ 
for the moving power that will keep the load moving at a 
uniform speed V along the level plane; ¢ + sin < for the moving 
power to keep the load moving at the same uniform speed up 
the inclined plane; and ¢ —sine for the moving power to sus- 
tain the same uniform speed down the inclined plane. To 
the truth of this there cannot be any doubt, if we assume, as 
Dr. Lardner has done, that the friction ¢ is not altered by the 
slight inclination of the plane. By following Dr. Lardner’s 
reasoning, we are hence fairly led to the result that the same 
amount of mechanical force will be expended in ascending 
and descending the inclined plane, as in drawing the same 
load backwards and forwards along the level plane of the same 
length L. 
Though Dr. Lardner is certainly justified in stating this 
conclusion to be a plain result of first principles, it should at 
the same time be remembered, that it rests solely on the hypo- 
thesis that the power in each case is to be precisely adapted 
to the amount of resistance, so as to preserve throughout the 
the same uniform velocity V. This hypothesis has not been 
admitted by Mr. Barlow, and it must necessarily fail in deter- 
mining the effect produced by the deflection of a rail during 
the transitory passage of the carriages. In this way, it appears 
to me that the principle advocated by Dr. Lardner carries 
with it a restriction that entirely unfits it for an objection to 
what has been advanced by Mr. Barlow, in his Second Re- 
port, addressed to the directors of the London and Birming- 
ham Railway Company. On the other hand, * however, I can 
