Page:Scientific Memoirs, Vol. 1 (1837).djvu/626

hypothesis of the proportionality of the number of convolutions and of the electromotive power is confirmed in reality by the observation.—

The known formula for $\sin .{\frac {1}{2}}\xi$ is after the method of the least squares:

$\sin .{\frac {1}{2}}={\frac {\Sigma (n\cdot \sin .{\frac {1}{2}}\alpha )}{\Sigma (n^{2})}}$

and after having performed the calculation, we have from the foregoing table

$\xi =30^{\circ }\,9'\,{\mbox{or}}\,\log .\sin .{\frac {1}{2}}\xi =8\cdot 43989$

.

This value of $\xi$ gives for $\alpha$ the following values:

$\alpha$		DIFFERENCES.		$\alpha$		DIFFERENCES.
Calculated.	Observed.	In Degrees and Minutes.	In Degs.	Calculated.	Observed.	In Degrees and Minutes.	In Degs.
6° 18′	5° 39′	+ 0° 39′	+ 0°·6	45° 22′	45° 26′	− 0° 4′	− 0°·1
12 38	12 00	+ 0 38	+ 0·6	48 48	48 32	+ 0 16	+ 0·3
25 36	24 54	+ 0 32	+ 0·5	52 16	53 6	− 0 50	− 0·8
28 42	28 19	+ 0 23	+ 0·4	59 26	59 48	− 0 22	− 0·4
31 58	31 48	+ 0 10	+ 0·2	66 50	68 1	− 1 11	− 1·2
38 36	38 46	− 0 10	+ 0·2

the coincidence of the calculated with the observed deviations, confirming our presupposition that the electromotive power increases as the number of convolutions.

A second series of experiments on the same subject were made with the same wire, No. 3, except that the length of the wire through which the current had to pass, was no longer the same in each number of convolutions; we must therefore return to our general formula (B.). It was

$\sin .{\frac {1}{2}}\alpha =n\cdot {\frac {L+l+(\lambda )}{L+l+\lambda _{n}}}\cdot \sin .{\frac {1}{2}}\xi$.

The wire of the multiplier and of the conductors always remained the same, and was reduced to the diameter of the wire of the multiplier

$L+l=673\cdot 25\,{\mbox{inches}}$.

The lengths $\lambda ,\,\lambda _{i},\,\lambda _{ii}$ &c., were however changeable; I have therefore added these values, reduced also to the wire of the multiplier in the following table of the experiments.

$L+l+(\lambda )\,{\mbox{is}}=681\cdot 45$