( 648 ) 
plied at each moment, is proportional to the quantity of fatigue- 
substance in store. As the latter has been originated by the trans- 
formation of transformable “energy-substance’’, the available quantity of 
“fatigue-substance” may be supposed to be eee to the whole of 
the hitherto operated effect, the final consequence being that the supply 
of fresh “energy-substance” at each moment is proportional to the 
hitherto transformed quantity. This may be represented by 6 f Pdt. 
Finally there exists still a third cause for the continual change 
undergone by P, i.e. the influence of the stimulus. This change may 
be considered to be a time-function, and represented by f(t). 
Thence we abtain: 
WP AB IPA Hfd - eee 
By transposing this value of W in the equation (1), we obtain: 
8 (GE +ePts'W)=aP+ ap Pd+af). - () 
which are after differentiating: 
ee ee ee 
or after a ae transposition : 
dP 
aE het Dr FaPP=afOHf"O -. . 
The solution of this equation is: 
— Ag—at —pt af (i) +f" @ 
uma) pers eee i 
A and B representing constants and D and ZD? the operators 
d ae 
ee and & |): 
The last term of the second member can be solved only when 
the numerator is known, viz. when we know what form of stimu- 
lation has been applied. 
I. In the very first place let us consider what will happen in 
the case of the stimulus having acted only for a very brief moment, 
and then ceasing. This implies the existence of a certain quantity 
of stimulation-substance no longer altered by a fresh supply; our 
f(t) thus being constant, whilst f(t) and /"(t)=0. In this case 
the last term may be omitted, the solution of the equation becoming 
consequently : 
P= Att Belts eine ee 
