99 
length of the pendulum vibrating seconds. 
to dl — d*. If now we suppose d to be increased by the small 
quantity s, the reciprocal, instead of l — d t will become 
+ which 
adding d~\-s, we have /— /|-j- 2 s, the increase of the length 
being 2(1 f l s ; and making this equal to — ~r, we have s—^~. 
and when the pendulum is inverted, substituting l — d for d , 
the expression becomes which, added to the 
former negative value of the same quantity, must always 
destroy it : so that the length of the equivalent pendulum 
will be truly measured by the simple distance of the surfaces 
of the cylinders, as M. Laplace has demonstrated. 
There is however another correction, of which it becomes 
necessary to determine the value, when a very sharp edge is 
used for the axis of motion, as in the pendulum which you 
have employed : since it appears very possible, that in this 
case the temporary compression of the edge may produce a 
sensible elongation of the pendulum. But it will be found, by 
calculating the magnitude of this change, that when the edge 
is not extremely short, and when its bearing is perfectly 
equable, this correction may be safely neglected. 
Supposing a to be the distance from the edge, in the plane 
bisecting its angle, at which the thickness is such, that the 
weight of the modulus of elasticity corresponding to the sec- 
tion shall become equal to the weight of the pendulum, the 
elasticity at any other distance x from the edge will be mea- 
sured by dc, while the weight is represented by a; so that 
the elementary increment x' will be reduced by the pressure 
of the weight to x' . and the element of the compression 
a a -f» x L 
