614 LENZ ON ELECTRO-MAGNETISM. 
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. 3 § is after the method of the least squares: 
= (n° sin.$ a) 
= (n*) 
and after having performed the calculation, we have from the foregoing 
table 
sin.4 § = 
£ = 3° 9! or log. sin. } § = 843989. 
This value of € gives for « the following values: 
a DIFFERENCES. a 
DIFFERENCES, 
In Degrees and 
Observed. Minutes. In Degs. 
In Degrees and 
Calculated.| Observed. Miniter: In Degs.] Calculated. 
45° 22/ | 45° 26’| —0° 4 
48 48 | 48 32 | +0 16 
52 16 | 53 6 | —O 50 
6°18] 5° 39 | +.0° 39 6 
6 
5 
4| 59 26 | 59 48 | —O 22 
2 
a) 
+ 
12 38 | 12 00 | +0 38 |+ 
25 36 | 24 54 | 410 32 [t+ 
+ 
be 
28 42 | 28 19 | 40 23 
the coincidence of the calculated with the observed deviations, con- 
firming 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 
L+/+Q) 
L+l+ A, 
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 + 1 = 673°25 inches. 
The lengths A, A,, A,,, &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 + 12+ (d) is = 681-45 
= iain f in fi ee 
sin. fa = n° sin. 3 &. 
