334 Mr. G. J. Burcli. On Professor Hermanns 



Professor Hermann finds the complete primitive of this differential 

 equation, and then, introducing various values of r and the function 

 E = e/(0> draws, by a process which is indeed laborious, the curves 

 of the corresponding excursions. My own method gives a good deal 

 of the information so obtained in a much simpler manner. 



Adopting the letters used by him, when/ vanishes we have 



dp,'dt + rp = 0, 



that is to say, whenever the E.M.F. falls to zero the reduced values 

 of the subnormal and the radius vector are equal, but of opposite sign, 

 and the curve, therefore, can never come back to the zero line under 

 the action of a current which pulsates but does not alternate (see 

 figs. 2 and 4 in Hermann's paper). When the meniscus crosses the zero 

 line, rp = 0, and dp/dt = ref(t), i.e., the impressed E.M.F. is then 

 directly proportional to the subnormal. This involves the further 

 fact that the crossing of the zero line by the meniscus must always 

 lag behind the change of sign of the E.M.F. 



If dpjdt vanishes, as it does at the apex of a spike or the bottom of 

 a notch, the instantaneous value of the impressed E.M.F. is directly 

 proportional to the distance of the meniscus from zero. 



The curves drawn by Professor Hermann are for the most part, so 

 far as the eye cau judge, similar to those obtainable under like condi- 

 tions with the capillary electrometer. I have photographed and 

 analysed many such, using rheotomes and dynamos of various kinds, 

 both alternating and direct current, as sources of E.M.F. I have 

 proposed, in a paper which has been in the publisher's hands since 

 last November, that this method should be used to determine the 

 characteristic current curves of dynamos.* 



All the confusing influence of the lag vanishes when such curves 

 are analysed there is no need to trouble about the equation to the 

 curve, since each several term of its differential equation at any given 

 point is found at once by my mode of analysis. But I must point 

 out that an error has crept into Professor Hermann's rendering of 

 the curve given in fig. 6 or, rather, as it only pretends to be an 

 approximation, that it is not equally accurate throughout. The por- 

 tion c'd'f which corresponds to a diminishing negative (below zero) 

 potential is represented as rising with 'increasing velocity instead of 

 falling more slowly, as it should do. Yet, when this negative poten- 

 tial ceases, the curve commences to fall from d' to e' along the 

 logarithmic curve of discharge. This is impossible. When e f(t) is 

 negative, the algebraic sum of dp/dt and rp must be negative also if 

 the fundamental equation holds good. Probably the straight line cd 

 has been placed too far to the right. 



* ' The Electrician/ July 17, 1896, et sey. 



