Page:Scientific Memoirs, Vol. 1 (1837).djvu/624

metal could be perceived except at the ends which served for connecting them.

I now proceed to the experiments themselves.

I. On the Influence of the number of Convolutions upon the Electro-motive Power produced in them.

In these experiments I connected the wire No. 3 with the multiplier so that the conducting wire and the electromotive spirals were formed of one and the same piece ; the length of this wire was about fifty feet: here however this is of no consequence, as it remained the same in all the experiments. The experiments themselves are contained in the following table.

Number of the Convolutions	INDIVIDUAL DEVIATIONS.				Mean deviation, or $\alpha$.	$\alpha$ in minutes		${\frac {1}{2}}\,\alpha$.
	Side A of the Spiral to the north pole.		Side B of the Spiral to the north pole.
	End a of Index.	End b of Index.	End a of Index.	End b of Index.
	°	°	°	°	°
2	5·7	5·8	5·3	5·8	5·65	5°	39'	2°	49'
4	12·1	12·9	11·1	12·0	12·00	12	00	6	00
8	25·7	25·8	22·9	25·2	24·90	24	54	12	27
9	29·5	30·1	26·2	28·5	28·32	28	19	14	15
10	32·5	33·3	29·4	32·0	31·80	31	48	15	54
12	39·8	40·9	35·8	38·6	38·77	38	46	19	23
14	47·4	48·8	40·8	45·9	45·43	45	43	22	51
16	55·7	56·8	47·6	52·3	53·10	53	6	26	33
18	63·1	64·4	54·1	57·8	59·80	59	48	29	54
20	71·0	71·8	62·8	66·6	68·05	68	3	34	1

From this series of experiments we must now deduce the electromotive power of the spirals for each number of convolutions, for which purpose the following considerations will be of service.

The action of the electric current in the wire of the multiplier upon the magnet needle, is a momentary one, since the current itself exists only for a moment; we may therefore consider this action as an impulse given to the needle, and shall be able to measure its force by the velocity which it imparts. But the velocity of the needle at its exit is evidently as great as that which it acquires when it springs back to the point of exit; it may therefore be expressed ($f$ being constant) by

$A=f{\sqrt {(\sin .{\mbox{vers.}}\,\alpha )}}$

where $A$ represents the sought for velocity of the exit; or according to what has been above stated, the magnitude of the current in the wire of the multiplier, and $\alpha$ the angle of deviation of the needle produced by this force. This expression changes however by the substitution of $2\sin .^{2}{\frac {1}{2}}\alpha$, instead of $\sin .{\mbox{vers.}}\alpha$ into the following

$A=p\cdot \sin .{\frac {1}{2}}\alpha$

if we put $p=f{\sqrt {2}}$.