( 650 ) 
fo YP Ge. 
IV. Lastly, if p(t)= C), the differential equation becomes: 
as 2 zE k? P ) 2 
dE + 1h +- == U, e 6 -%e ant % e ( a) 
of which the solution is: 
P=eVfjAsnat+ Besat}+C. .. . . (13) 
In the foregoing we have deduced a few relations, to the number 
of four, all of which may be maintained on theoretical grounds. 
We next intend trying to investigate whether there exist any facts, 
likely to lend some support to our views. To this purpose we will 
examine the facts concerning each formula separately. As a matter 
of course however, we ought to state beforehand, that in these brief 
and ,provisory” communications, opening a new and most extensive 
area. of research, it will be possible only to give superficial indications, 
complete proofs being wholly out of the question. 
Ad. I. The course of an isotonic muscle-contraction shows a 
striking resemblance to the curve represented by (7). Of course this 
does not imply that practically the course of an isotonic muscle- 
contraction may be expressed by our formula (7) as it stands bere. 
Still there do exist a few points indicating the possibility of deducing 
from our formula an appropriate expression. We know that a con- 
traction does not begin simultaneously at all parts of the muscle ; 
it begins at one point, whence it extends itself over the muscle like 
a wave. During this process some parts of the muscle are slightly 
stretched before contracting. Consequently a certain space of time 
shall necessarily elapse before the shortening commences, or at any 
rate before it may be observed at the end of the muscle. Starting 
now from the supposition that on a definite point of a muscle an 
effect appears in the form indicated by our formula, subsequently 
extending itself gradually over the whole of the muscle, we have 
got a few indications enabling us to proceed afterwards to a theore- 
tical treatment resulting in an expression, rendering with sufficient 
accuracy the course of the contraction, as observed practically : 
an expression therefore, in which the fact is taken into consideration 
of a certain space of time being required for putting into motion 
the mass of muscle and the writing-apparatus fastened to it. 
Literature offers much information on this subject which we 
might quote in corroboration of our theory. I have only to recall to 
mind the views on the nature of muscle-contraction, put forward by 
Fick, Herine, SCHENK, Gap and others, 
