10O 
Capt . Kater’s experiments for determining the 
will be x' and its fluxion dx, of which the fluent is 
a hl^. Now the height of the modulus of elasticity of 
steel is ten million feet, (Lect. Nat. Phil. II. 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 of an inch ; and 
supposing the angle a right one, a must be 424^000 ; and 
making x = 1, we have the whole compression of the edge 
within the depth of an inch ? - ? ‘- 0 - 6o - hl 4244001; and this 
logarithm 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 T — , supposing that they retained their elas- 
ticity, and underwent 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, demon- 
strated by M. Laplace, will prevent 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, 
Thomas Young. 
Welbeck Street, 5th Jan. 1818. 
P. S. It is easy to show that the determination of the 
length of the pendulum, by means of a weight sliding 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 employed. The 
