Page:Scientific Memoirs, Vol. 1 (1837).djvu/627

Number of the Convolutions.	DEVIATIONS.				Individual Means.	Complete Means or $\alpha$.	$\lambda$	$L+l+\lambda$
	Side A of Spiral to the north pole.		Side B of Spiral to the north pole.
	End a of Index.	End b of Index.	End a of Index.	End b of Index.
5	18.5	18.5	19.8	20.5	19.33	19.40	17	690.25
	18.6	18.8	20.2	20.3	19.47
10	37.3	37.6	39.6	39.3	38.45	38.41	28	701.25
	37.3	37.5	39.4	39.3	38.37
15	57.8	58.7	58.6	58.2	58.32	58.15	39	712.25
	57.4	58.2	58.6	57.6	57.95
20	81.4	82.3	80.7	79.8	81.05	80.91	50	723.25
	81.3	82.3	79.7	79.8	80.77
25	110.0	112.7	103.1	101.9	106.67	106.67	61	734.25
	110.0	112.8	103.7	102.2	106.67

If we now apply the method of the least squares to this table, as we did to the first, we obtain

$\xi =3^{\circ }.97\,{\mbox{and}}\,\log .\sin .{\frac {1}{2}}\xi =8.53944$

and with this value we obtain from formula (B.) the following deviations:

Number of Convolutions.	DEVIATIONS.		Difference.
	Calculated.	Observed.
5	19.53	19.40	+ 0.13
10	39.00	38.41	+ 0.59
15	59.07	58.13	+ 0.94
20	80.67	80.91	− 0.24
25	105.67	106.67	− 1.00

In this place also the calculation coincides well with the observation; as I expected however to attain this coincidence still more completely, if I allowed the length of the conductors to remain the same for all the experiments, I made a second series of experiments similar to the above with another multiplier, where $\lambda ,\,\lambda '$, &c., remained always equal to one another; this series has also been performed with more care than the others above-mentioned, since each of the numbers contained in the following table is the mean deduced from three observations, in which mean however I retained only one decimal place. The columns designated by 1, 2, 3, 4 are intended for the same purpose as the four columns in the former tables.