Page:Scientific Memoirs, Vol. 1 (1837).djvu/630

By means of formula (A.) we shall therefore obtain for the narrow spirals

$x=(L+l+\lambda )p\cdot \sin .{\frac {1}{2}}\alpha =701.25\cdot p\cdot \sin .(13^{\circ }\,7')$

for the wide spirals

$x'=(L+l+\lambda ')p\cdot \sin .{\frac {1}{2}}\alpha '=876.25\cdot p\cdot \sin .(11^{\circ }\,21')$,

therefore the relation of the electromotive powers, or

${\frac {x'}{x}}={\frac {876.25\cdot \sin .(11^{\circ }\,21')}{701.25\cdot \sin .(13^{\circ }\,7')}}=1.0838$,

}therefore not deviating much from 1, that is, the electromotive power is in both spirals the same.

I endeavoured in a more striking manner to confirm this position by the following experiment: I wound the wire No. 2 in six convolutions round a great wooden wheel of 28 inches in diameter, and placed the wheel on the iron cylinder. After having completed, as in the former cases, the experiment, I wound also six convolutions of the same wire immediately round the same iron cylinder, where also, as above, the convolutions again were 0·73 inch in diameter. The experiment gave

	Angle of deviation.				Mean or $\alpha$	$\lambda$	$L+l+\lambda$
	1	2	3	4
Narrower convolutions.	13·1	15·8	12·8	12·4	13·52	19·2	692·45
Wider convolutions.	7·1	8·7	7·1	8·7	7·90	549·2	1222·75

therefore

${\frac {x'}{x}}={\frac {1222.75\cdot \sin .(3^{\circ }\,52')}{692.45\cdot \sin .(6^{\circ }\,45'.5)}}=1.0107$.

Here the proportion of both electromotive powers approaches still more nearly to unity than in the former case, although the proportion of the diameter of the spirals is $=1:38.3$. We may therefore regard as a tiling proved by experiment, the position, that

"the electromotive power which the magnetism produces in the surrounding spirals is the same for every magnitude of the convolutions."

Since however a spiral wire inclosing the armature presents to the action of the magnetism in the armature a length greater in proportion as its diameter or its distance from the armature is greater, it follows from the law just discovered that the electromotive action of the magnet upon one and the same particle of the wire decreases in the simple ratio of the distance. This is as it were the reversal of the law demonstrated by Biot in the field of electro-magnetism, which, as is known, states that the action of an electric closing wire upon a magnetic needle decreases in the simple ratio of the distance; and it follows from our ex-