Page:Die elektromagnetische Masse des Elektrons.djvu/2

can be represented by correction-terms depending on the apparatus dimensions, so that even considerable errors in the determination of the latter ones, are of little influence on the results.^[1]

Table I
z cm	y cm	β	ψ(β)	k2	δ perc.
0,348 0,461 0,576 0,688	0,0839 0,1175 0,1565 0,198	0,957 0,907 0,847 0,799	3,08 2,49 2,13 1,96	2,16 2,165 2,20 2,165 Mean: 2,173	-0,6 -0,4 +1,2 -0,4	k1=0,532 $\epsilon ={\sqrt {\frac {\Sigma \delta ^{2}}{3}}}=\pm \ 0,8$ perc.

Table II
z cm	y cm	β	ψ(β)	k2	δ perc.
0,200 0,250 0,300 0,350 0,400 0,450 0,525	0,0241 0,0305 0,0382 0,0469 0,0574 0,0688 0,0856	0,930 0,917 0,875 0,831 0,777 0,730 0,684	2,69 2,56 2,26 2,065 1,89 1,78 1,695	[2,19][2] 1,87 1,855 1,845 1,895 1,864 1,850 Mean: 1,863	[+17,5] +0,4 -0,4 -1,0 +1,7 0,05 -0,7	k1=0,260 ε = $\pm$ 1,0 perc.

Table III
z cm	y cm	β	ψ(β)	k2	δ perc.
0,35 0,45 0,50 0,60 0,70	0,0455 0,0651 0,0760 0,1000 0,1230	0,851 0,766 0,727 0,6615 0,6075	2,147 1,86 1,78 1,66 1,595	1,721 1,736 1,725 1,727 1,655[3] Mean: 1,723	-0,1 +0,7 +0,1 +0,2 -3,9[3]	k1=0,258 ε = $\pm$ 1,2 perc.

Table IV
z cm	y cm	β	ψ(β)	k2	δ perc.
0,150 0,175 0,200 0,225 0,250 0,275 0,300 0,325 0,350 0,375	0,0607 0,0720 0,0835 0,0991 0,1132 0,1290 0,1455 0,1630 0,1813 0,1988	0,963 0,949 0,933 0,883 0,860 0,830 0,801 0,777 0,752 0,732	3,23 2,86 2,73 2,31 2,195 2,06 1,96 1,89 1,83 1,785	8,12 7,99 (?) 7,46 8,32 8,09 8,13 8,13 8,04 8,02 7,97 Mean: 8,09	+0,4 -1,2 [-7,8] +2,8 +0 +0,5 +0,5 -0,6 -0,9 -1,5	k1=0,905 ε = $\pm$ 1,4 perc.

Le $F$ be the intensity of the electric field, $H$½ the intensity of the magnetic field, $k_{1}$ and $k_{2}$ two constants; then:

4)	$q=c\beta ={\frac {F}{H}}{\frac {\eta }{\zeta }}=k_{1}c{\frac {\zeta }{\eta }},$

5)	$\beta =k_{1}{\frac {\zeta }{\eta }},$

6)	${\frac {\epsilon }{\mu }}={\frac {\zeta ^{2}}{\eta }}{\frac {F}{H^{2}}},$

so that under consideration of 1):

7)	${\frac {\eta }{\zeta ^{2}\psi (\beta )}}={\frac {k_{1}c}{H}}{\frac {3}{4}}{\frac {\mu _{0}}{\epsilon }}=k_{2}$

or

8)	${\frac {\eta }{\zeta ^{2}\psi (k_{1}{\frac {\zeta }{\eta }})}}=k_{2}.$

Equation 8) thus represents the equation of the $(\eta ,\zeta )$-curve,

1. For details of the calculation, see W. Kaufmann, Gött. Nachr. 1902. H. 5. (Although the calculation is carried out in a somewhat different way.)
2. Not used for the determination of the average, since it was obviously distorted by plate errors or other disturbances.
3. Due to the larger inccuracy of the individual adjustment, it was introduced with ¼ weight when calculating the average; the point lies at the outermost viewable end of the curve.