330 Mr. G. J. Burch. On Professor Hermanns 



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 Versuche und Schliisse eingehe, mochte 

 ich zeigen dass der von Burch und von Einthoven aufgestellte, das 

 Capillar-Electrometer betreffende Satz, welcher der Construction zu 

 Grunde liegfc, 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 Bestiitigung 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, " mainl}- 

 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 hypo- 

 thesis. 



For instance, the equation 



p E . e~ rt 



may represent the discharge of a Ley den 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 = hi, 



in which li 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 



* ' Journal of Physiology,' vol. 18, p. 117. 



f "Time-Relations of the Capillary Electrometer," 'Phil. Trans.,' A, vol. 183, 

 p. 81, 1892. 



