Page:Scientific Memoirs, Vol. 2 (1841).djvu/86

If we represent, according to this established unity, the magnetism of the needle by $m$, that of the bar by $M$, the distance (supposed considerable) between them by $R$, and the moment of rotation exerted by the bar on the needle by $f$, the reduced moment of rotation is

$mM=fR^{3}$

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The position of the bar relatively to the needle, assumed in this case, did not in fact exist in the Göttingen experiments, but a different position represented in the annexed figure. However, the same thing is true of the two positions, with this single difference, that $f$ has a different value, which we shall designate by $F$. In the Memoir "Intensitas" &c., it is proved that

$F=2f$

so that,

$mM={\frac {FR^{3}}{2}}$

(II.)

It is to this second case that the formulæ, hereafter to be mentioned, will refer, as applicable to the Göttingen observations.

 

"In this way therefore we have a complete and precise idea of the measure of the magnetic force of a magnetized needle. A needle of twofold power will impart to one equally magnetized a reduced moment of rotation = 4; and generally, when we know the number for the reduced moment of rotation which a needle imparts to another needle equally magnetized, we have the absolute measure of the power of magnetism in each needle; it being the square root of that number.

"There only remains then, in order to be able to reduce the force of terrestrial magnetism to absolute measures, to give some method by which the moment of rotation which a needle produces in a similar one at considerable distance, (and in the position represented in the figure) may be determined with precision. A great difficulty might at first appear, from a circumstance purposely omitted in what has been already said, viz. the impossibility of observing this very weak action of the needle $N\;S$ upon the needle $n\;s$, (which we will for a time suppose to be magnetized exactly as strongly as $N.S$); since it cannot be withdrawn from the omnipresent, and much more powerful ac-