Page:Proceedings of the Royal Society of London Vol 60.djvu/357

330 Muskels,” in which he discusses the analyses of certain electrometer curves of muscle variation described by Professor Burdon Sanderson.*

His first statement demands an explanation on my part. He says, “ Bevor ich auf Sanderson’s Yersnche und Schliisse eingehe, mochte ich zeigen dass der von Burch und von Einthoven aufgestellte, das Capillar-Electrometer betreffende Satz, welcher der Construction zu Grunde liegt, auch aus meiner Theorie des Instruments unmittelbar folgt, was beide Autoren, obwohl sie meine Arbeit erwahnen, nicht bemerkt haben. Da beide ihren Satz empirisch gewonnen haben, so kann derselbe als eine schone Bestatigung meiner Theorie betrachtet werden.”

As a matter of fact, I did not know of Professor Hermann’s paper until after I had formed my own theory. In my second paperf on the subject I mentioned that it had also’ been treated by him, “ mainly from a mathematical standpoint,” and implied that, in my opinion, his data were insufficient. I still think so, and cannot admit that my experimental results' prove the correctness of his views.

That a mathematical formula, based upon a certain hypothesis, should agree with observed facts may be strong evidence in its favour, but is not necessarily a proof of the soundness of the hypothesis. For instance, the equation p = E. e~rt

may represent the discharge of a Leyden jar through a circuit of no inductance, or the swing of a pendulum in treacle. That it happens to be also the expression for the time-relations of the capillary electrometer does not of itself imply that the same causes are at work in all three cases, but simply that the forces concerned are so related that the movement is dead-beat. Professor Hermann, starting from Lippmann’s polarisation theory, assumes the simplest conceivable relation between the rate of polarisation and the acting P.D., namely, that they are proportional to one another. Putting i — the intensity of the current, and p = the amount of polarisation at the time t, he gets dp/dt = in which h is an instrumental constant.

Writing E for an electromotive force, which may be constant or variable, and w for the resistance of the circuit, he arrives at the differential equation dp dt h w (E - p ).

f “ Time-Relation3 of the Capillary Electrometer,’’ * Phil. Trans.,’ A, yol. 183, p. 81, 1892.
 * i Journal of P h ysiology yoL 18, p. 117.