Induction-Coil Potentials Page 580

with correction for permeability, was 1·132 amperes. The observed least current giving a 1-cm. spark was 1·13 amperes, but generally a little more current was required. In Case III. the values were ·815 ampere calculated, and ·86 ampere observed. The difference is much greater in this case, but the correction for permeability is also greater and probably not so reliable.

Of the three cases Case I. gives the most definite value for the least sparking current, and is the most suitable to adopt as a standard, while the numbers in Table VII. show that the potentials in the other two cases are fairly closely proportional to the calculated values. The above results show therefore that, so far as the 1-cm. spark potential may be taken as a guide, the theoretical expression (1) leads to approximately correct values (within about 2·5 per cent.) of the maximum secondary potential over the range of current and primary capacity covered in the present experiments.

Further support of the theory is afforded by the similarity in the forms of the calculated and experimental curves (figs. 1, 2, 3, and Plate VIII. figs. 7, 8, 9), and by the agreement between the observed and calculated values of the frequency of the longer wave in each case. Thus the calculated frequencies are (from Table V.) 194·3, 232·8, 304·4; the observed values, obtained by measurement of the photographs, 193·9, 232·3, 301·6.

Possibly still closer agreement between the calculated and observed results would have been found if second-order quantities (e.g. \(\theta_1^2\), \(\theta_2^2\)) had been retained throughout, but the additional labour involved in the calculations would make the method too cumbersome to be of much value. What is more required at present is a simplified expression which will give approximately the maximum secondary potential, or an upper limit to its value which is not very greatly in excess of the actual value.

Such an upper limit may be arrived at by neglecting the resistances of the circuits so that \(k_1\), \(k_2\), \(\delta_1\), and \(\delta_2\) all become zero. If we further assume that the maxima of the two potential waves in the secondary occur simultaneously, the expression for the maximum potential becomes

\[ 2\pi L_{21} i_0 \frac{n_1 n_2^2 + n_1^2 n_2}{n_2^2 - n_1^2}, \]

i.e.

\[ 2\pi L_{21} i_0 \frac{n_1 n_2}{n_2 - n_1}. \]

This may also be expressed in terms of the ratio \(L_2 C_2 / L_1 C_1\).