of experiments on the pendulum. 85 
Hence, by comparing the corresponding terms, we obtain 
C — 
— n; 
a = 
— .1 666667ft— 1 Logarithm, 
9.2218487 
b = 
.22222222 ft— 2 
8 . 34 6 7 8 75 
c = 
— .00268960/1—3 
7.4296867 
d = 
.00030815472—4 
6.4887650 
e = 
— ,0000340743ft — 5 
5.5324269 
/ = 
.00000367495ft— 6 
45652514 
g = 
— .000000389086/2 — 7 
3 - 59 11 459 
Zh = 
.00000004062/2— 8 
2.60873 
u = 
— .00000000420 ^— 9 
1.62323 
Z k = 
— .00000000043ft— 10 
0-63353 
After the exact determination of the first seven coefficients, 
the next three are obtained with sufficient accuracy by means 
of the successive differences of the logarithms, compared 
with those of the natural numbers. 
It happens very conveniently, that the conditions of the 
problem are such, as to afford a remarkable facility in deriving 
from this series another, which is much more convergent, and 
which gives us the hyperbolic logarithm of y; for since 
-/' = d*-^, and-fei*= 4 * + 4 ax 3 + i bx’ + . . 
if we multiply this by dx, and take the fluent, we shall have 
HLy = - i 4* + ^ + 67 W + • • •)•- 
We may determine the degree of compressibility corres- 
ponding to a given value of n, by comparing the equation 
— n ~ = dx or = dxp, with the properties of the 
modulus of elasticity M, which is the height of such a column 
of the given substance, that the increment of density y' , occa- 
sioned by the additional weight of the increment x', is always 
