Page:Scientific Memoirs, Vol. 2 (1841).djvu/90

We will add a few remarks on one or two circumstances.

 

"In speaking of the units to be employed in the measurements, mention was made only of a unit of distance and a unit of weight. But it should not be overlooked, that a certain weight, (a gramme, for instance,) does not mean, in this case, the quantity of ponderable matter which bears this name, and which is everywhere the same,—but the force which this quantity of matter exerts at the place of observation, under the influence of gravitation. It is well known that the force of gravity is not absolutely the same at different places; and if we chose the force of a gramme for our unit of weight, the intensity of the earth's magnetism would not be accurately measured by one standard at various places. The accuracy with which these measurements may now be made is such that this difference must not be neglected. The most simple way of meeting this difficulty is to reduce the force of gravity itself to an absolute quantity, by adopting as its measure the double height of descent in the unit of time, (for instance, a second,) and by expressing the force by the product of the mass into the number which measures the force of gravity. In this manner other numbers^[1] are obtained, both for the force of the magnetic needle employed, and for that of the earth's magnetism; which numbers are based on three units, i. e., a unit of distance, a unit of time, and a unit of mass —instead of resting on the two units before spoken of."

 

In calculating the numbers $M$ and $T$ according to equations (V.) and (VI.)

$M={\frac {1}{t}}{\sqrt {\frac {CR^{3}.\mathrm {tang} \,v}{2}}}\qquad T={\frac {1}{t}}{\sqrt {\frac {2C}{R^{3}\,\mathrm {tang} \,v}}},$

the value ascribed to the constant $C$ was

$C={\frac {\pi ^{2}}{g}}\cdot K,$

in which $\pi$ represented the known number 3·14159…; $g$, double the space of descent in the unit of time; $K$, the moment of inertia of the vibrating bar. The new numbers are obtained from the same equations, by ascribing to C the value

$C=\pi ^{2}K.$

1. They are to the previous numbers in the proportion of the square root of the number which measures the force of gravity to unity.