Page:Electromagnetic phenomena.djvu/21

least squares, the coefficients k₁, and k₂ having been determined in such a way, that the values of η, calculated, for each observed ζ, from Kaufmann's equations (34), agree as closely as may be with the observed values of η.

I have determined by the same condition, likewise using the method of least squares, the constants a and b in the formula

$\eta ^{2}=a\zeta ^{2}+b\zeta ^{4}$

which may be deduced from my equations (36) and (37). Knowing a and b, I find β for each measurement by means of the relation

$\beta ={\sqrt {a}}{\frac {\zeta }{\eta }}$.

For two plates on which Kaufmann had measured the electric and magnetic deflexions, the results are as follows, the deflexions being given in centimeters.

I have not found time for calculating the other tables in Kaufmann's paper. As they begin, like the table for Plate 15, with a rather large negative difference between the values of η which have been deduced from the observations and calculated by Runge, we may expect a satisfactory agreement with my formulae.

Plate N°. 15.    a=0,06489,    b=0,3039.
ζ || colspan="5"| η || colspan="2"| β
	Observed	Calculated by R.	Diff.	Calculated by L.	Diff.	Calculated by
						R.	L.
0.1495 0.199 0.2475 0.296 0.3435 0.391 0.437 0.4825 0.5265	0.0388 0.0548 0.0716 0.0896 0.1080 0.1290 0.1524 0.1788 0.2033	0.0404 0.0550 0.0710 0.0887 0.1081 0.1297 0.1527 0.1777 0.2039	-16 -2 +6 +9 -1 -7 -3 +11 -6	0.0400 0.0552 0.0715 0.0895 0.1090 0.1305 0.1532 0.1777 0.2033	-12 -4 +1 +1 -10 -15 -8 +11 0	0.987 0.964 0.930 0.889 0.847 0.804 0.763 0.724 0.688	0.951 0.918 0.881 0.842 0.803 0.763 0.727 0.692 0.660

Plate N°. 19.    a=0,05867,    b=0,2591.
ζ || colspan="5"| η || colspan="2"| β
	Observed	Calculated by R.	Diff.	Calculated by L.	Diff.	Calculated by
						R.	L.
0.1495 0.199 0.247 0.296 0.3435 0.391 0.437 0.4825 0.5265	0.0404 0.0529 0.0678 0.0834 0.1019 0.1219 0.1429 0.1660 0.1916	0.0388 0.0527 0.0675 0.0842 0.1022 0.1222 0.1434 0.1665 0.1906	+16 +2 +3 -8 -3 -3 -5 -5 +10	0.0379 0.0522 0.0674 0.0844 0.1026 0.1226 0.1437 0.1664 0.1902	+25 +7 +4 -10 -7 -7 -8 -4 +14	0.990 0.969 0.939 0.902 0.862 0.822 0.782 0.744 0.709	0.954 0.923 0.888 0.849 0.811 0.773 0.736 0.702 0.671

§ 14. I take this opportunity for mentioning an experiment that