380 PRINCIPLES OF GENERAL PHYSIOLOGY 



of only the first half, as it were, of the diphasic response ; it is, in fact, 

 " monophasic." 



We know, then, that a propagated disturbance can be set up in a nerve fibre 

 and we have next to inquire how such a " nerve impulse " is excited for. experi- 

 mental purposes. The agents which do this are known as " stimuli " and, for 

 practical purposes, electricity is the most useful, since its strength can be 

 accurately and conveniently graduated and measured. In the application of a single 

 stimulus, consisting of a definite quantity of electrical energy, we must remember 

 that energy is made up of two factors, quantity and intensity, so that we can 

 make up the same amount of electrical energy by varying the two inversely. 

 Now it was found by Waller (1899) that this is not a matter of indifference. 

 There is a certain definite ratio, different for different excitable structures, and 

 different conditions, such as temperature, at which a smaller quantity of energy 

 will excite than at another ratio, in which either the quantity or the potential is 

 higher or lower. This is called by Waller the " characteristic " number. How 

 is it to be explained ? Investigations of this kind can be best made by the use 

 of condenser discharges. When two metallic plates, separated by a non-conductor, 

 are charged to a different potential by connection to a source of electricity, the 

 quantity required to produce a given potential difference between them depends 

 on their size, distance apart and the dielectric constant of the medium between 

 them, as we saw on page 180. This is known as the "capacity" of the condenser. 

 By taking condensers of different capacities and charging them to different 

 potentials, we can obtain all the varieties required. The energy in ergs of the 

 discharge of a condenser is given by the formula, 1/2 U 2 C, where U is the 

 potential difference between the plates in volts and C the capacity in 

 microfarads. The expression, it will be noted, is analogous to the ordinary 

 one for kinetic energy. 



When a certain quantity of electricity is discharged through a high resistance, 

 such as a nerve, there is a perceptible difference in the time taken for the 

 discharge, according to the potential at which it commences. The formula 



expressing this fact is : 



t_ 



Ej = E x e <:, 



when there is no considerable self-induction in the circuit. 



E is the potential difference between the plates before commencement of 



discharge. 

 Ej is that after the lapse of time, t, during which the condenser has 



discharged through the resistance, R. 

 C is the capacity, 



and e, the base of natural logarithms. 



From this formula it will be seen that, other things being constant, the time taken 

 for discharge is proportional to R or to C. 



In the paper by Hermann (1906, p. 554), a series of curves will be found, showing the 

 different steepness of the curves of discharge of condensers of different capacity. 



The reader may be reminded that the capillary electrometer, used so frequently 

 in the investigation of the electrical changes of tissues, behaves as a condenser 

 in its time curves of charge and discharge. In the determination of the constants 

 in these cases, as in general, where the process starts rapidly and becomes slower 

 and slower as the final state is approached (Newton's " law of cooling," see above, 

 page 157), it is customary to make use of the time taken for half the process to be 

 completed, since the curve is changing its shape most rapidly at this period. 

 Towards the end, measurements are difficult and inaccurate on account of the 

 slow change. In the case of a condenser charged to a potential of 1 volt, the 

 character of the discharge is given by the time taken to fall to half a 

 volt. In the excitation of nerve, in fact, the steep and only active part 

 of the discharge is well over before this time ; slowly changing currents have no 

 exciting effect, as will be seen later. 



It appears from Waller's experiments, that there is a particular steepness 

 of curve which produces its effect with least expenditure of energy, and it seems 



