( 709 ) 
A FU) <0 GI OR Tey 
In this formula #(£) represents the total quantity of transformed 
energy and Z again the stimulus in physical units. The tran- 
sition of the system of the products of assimilation to that of the 
products of dissimilation does not depend on the intactness of the 
reflex-apparatus, but takes place as long as the tissue is alive. The 
given formula is therefore the representation of a general law of 
metabolism. 
The special forms under which this formula has been brought in 
physiology and experimental psychology, may be all derived from 
the more general formula by means of the same method. The function 
which occurs in the right-hand side of the equation must be very 
complicated and it is therefore improbable, that we shall soon be 
able to put an explicite function in its place. This function has 
been generally developed into a series by means of the theorem of 
MacrauriN. The term at which the series is interrupted in con- 
nection with the value of the coefficients determine the degree of 
approximation. The formula obtained in this way is naturally a 
formula of interpolation. 
The implicite function occurring in the left-hand side of the equation, 
cannot be treated in this way. This function is always decomposed 
in a sum of several terms agreeing with the number of forms into 
which the chemical energy of the system is transformed. 
If we apply this to formula (Za), it goes over in: 
Zo ua +2eRAR+3c,R?AR+ .. +3 (ce) 
BB oy Aar fly ne 20 be fete, dae eee ee ce pS 
In this formula the Gees which occur in = (cae are very 
small and have the property to approach to zero in the limit at 
the same time with AR. According to the first principal law =(4/) 
will always be equal to the total quantity of transformed energy. 
When we, as a first approximation, break off the series in which 
p(k) is developed at the first powers of ZL and put at the same 
time ¢)—=0, the general interpolation formula assumes the follo- 
wing form: 
ABP AM + Aly A sy. SG 
ARHe 
Rk 
The introduction of the special value ec, = 9 means physiologically 
that we neglect the existence of the threshold value. Under these 
circumstances the simplified interpolation formula will only apply 
to a perfectly isolated retlex-apparatus without passive resistances, 
Under these circumstances, however, the sign of inequality has no 
