on the Theory of Gradients in Railways. 53 
indeed one which is the extreme case of an inclined plane, viz. 
that of a perpendicular fall, you have arrived at a conclusion 
which certainly is totally at variance with the views which I 
have been accustomed to take of the theory of forces. In 
your First Report to the Directors of the London and Bir- 
mingham Railway Company, page 90, in speaking of the effect 
produced by the wheels of wagons passing over the joints of 
rails where one has sunk below the level of the other, so as to 
form a sort of slip, you say: 
_ «It has perhaps never occurred to such persons that a dif- 
ference of level at a joint-chair will, when the carriage is moving 
from the higher to the lower level at its greatest speed, cause 
the wheel to pass the distance of a foot without pressing on the 
rail, and consequently throwing the whole weight, which ought 
to be borne equally by the two rails, wholly upon one. Yet 
this is a fact resting upon a natural Jaw, and cannot be other- 
wise. To fall th of an inch by the action of gravity requires 
gzth part of a second, and in that time the carriage will have 
advanced a foot, and consequently in that space the whole 
weight has been borne by one rail only.” 
_ I freely confess that I am one of the persons you allude to, 
to whom such an idea never would have occurred. I am en- 
tirely ignorant of the natural law to which you allude, but I 
am not ignorant of a natural Jaw which is altogether incom- 
patible with your conclusion; and my conviction that the 
whole weight cannot press on the remaining wheel is quite as 
clear and strong as yours is that it will so press. It is quite 
true that the force of gravity will cause a body to fall freely 
jisth of an inch in J,th part of a second, but when the force 
of gravity is thus employed it cannot at the same time cause 
the whole weight of the same body to press upon a fixed point. 
The fact is, that when the wheel passes from the higher to the 
lower level, the centre of gravity being unsupported falls, and 
the only pressure exerted upon the remaining wheel depends 
on the moment of inertia of the load in receiving an incipient 
angular motion, and it is evident that this pressure must be 
extremely slight; but, whatever be its amount, it is totally dif- 
ferent both as to effect and cause from that which you allude 
to. If you consider that during the moment of a perpendicular 
fall, in the case of one rail being below the level of the other, 
the weight while it falls still presses with its whole force upon 
the rails, your view even of the most elementary principles of 
this part of mechanics is so essentially different from mine, 
that the wonder is, not that we should differ in one instance, 
but that we should agree in any. 
Referring again to your second Report, where you have 
