. The London, Edinburgh and Dublin philosophical magazine and journal of science . and draw acurve 0 Y through the extremities of the increased a portion =c to the tops of the ordinates of OB, anddraw the curve D C through the extremities of the lengthenedordinates. Then the problem is reduced to drawing a line NPRparallel to 0 L, such that N R : N P : : x2: x\. This may bedone by trial with proportional compasses. The ordinates M1Q1 = M1, and M2Q2 = M2 will then satisfythe conditions: for Criterion for the Oscillatory Discharge of a Condenser. 143 while 0 Q2 = L2 and 0 Qi = Lx a
. The London, Edinburgh and Dublin philosophical magazine and journal of science . and draw acurve 0 Y through the extremities of the increased a portion =c to the tops of the ordinates of OB, anddraw the curve D C through the extremities of the lengthenedordinates. Then the problem is reduced to drawing a line NPRparallel to 0 L, such that N R : N P : : x2: x\. This may bedone by trial with proportional compasses. The ordinates M1Q1 = M1, and M2Q2 = M2 will then satisfythe conditions: for Criterion for the Oscillatory Discharge of a Condenser. 143 while 0 Q2 = L2 and 0 Qi = Lx are in the ratio of x2 *k«. Then on the scale used 0 QL would give a numericalvalue for —=, and 0 Q2 for —J=^, from either of which / \/\Kt *J\Kt might be found. IX. On the Criterion for the Oscillatory Discharge of a Con-denser. By E. H. Barton, , , and W. , * THE ordinary condition for the oscillatory discharge of acondenser of capacity C through a wire of resistance Rand inductance L, namely <R2 is obtained from the differential equation 0=C +U^t+LW (1) by making Q proportional to ext and expressing the condition* Communicated by the Physical Society: read March 24, 1899. 144 Dr. Barton and Mr. Morton on the Criterion for that the resulting quadratic has imaginary roots. Now ifaccount be taken of the distribution of the current in thewire, the well-known work of Maxwell and Lord Rayleigh*shows that the above differential equation must, for a straightwire, be supplemented by terms on the right, ~^R«V^+A^V^-rloRV^&c., . (2) where a is the length of the wire divided by its re
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