430 | On the Pendulum. 
——dz, of which the fluent is @HL —, Now the height of 
the modulus of elasticity of steel is ten million feet, (Lect. Nat. 
Phil. IT. p. 509) and the weight of a bar, an inch square, and of 
this height, would be about 30 millions of pounds ; so that if the 
weight be 10 pounds, and the line of bearing an inch long, the 
thickness at the ‘distance a must be one three-millionth ot an 
inch; and supposing the angle a right one, @ must be -.4455353 
and making x=1, we have the whole compression of the edge 
within the depth of an inch zrato0 HL 4244001 ;. and this lo- 
garithm being 15°26, the correction becomes equal to the 360 
thousandth of an inch. If the bearing were one-tenth of an inch 
only, the compression for both the opposite edges would become 
~siss supposing that they retained their elasticity, and under- 
went no permanent alteration of form. In fact, however, the 
edge must be considered as a portion of a minute cylinder, which 
will be still less compressible than an angle contained by planes ; 
and the happy property, demonstrated by M. Laplace, will pre- 
vent any sensible inaccuracy from this cause, however blunt the 
edges may be, supposing that the steel is of uniform hardness in 
both. 
Believe me, my dear sir, very sincerely yours, 
Welbeck-street, Jan. 5, 1818. Tuomas Younac.” 
«°P.S. It is easy to show that the determination of the length 
of the pendulum, by means of a weight stiding on a rod or bar, 
which is the method that I have proposed as the most convenient 
for obtaining a correct standard, is equally independent of the 
magnitude of the cylinder emploved. The reduced inertia 2*P 
here consists of two portions: for the rod we may take the equi- 
valent. expression d/Q, which we may call axy, a being the 
weight of the bar (Q), x the distance (d) of the centre of gravity, 
and y the equivalent length (/): for the ball we must employ 
the formula 2x*P = Zy?P +d’Q, and call Zy?P, wu, and d?Q, bz?, 
b being the weight of the bail, and x the distance of its centre 
of gravity from the point of suspension: and in the same man- 
ner the force =(x+7)P=(d+r)Q must be composed of the two 
portions a(7+r) and )(x+7), so that the equivalent length be- 
24 axry+tu 
ary+u+t bez b : 22+ 
comes —————_-__ = —-__——__-; which we may call —— 
a(e+r)+b(z+r) ax + ar + br Zz 
Matra, 
=t, The experiment being then performed in four different 
positions of the weight, at the distances d’, d”, and d”, so that 
the second value of z may be z—d'=z’, the third ada! 7 
and the fourth s—d’”’=x”, we must observe the times of vibra- 
tion, 
