G. F. Firzazratp—On the Superficoal Tension of Fluids. 97 
to be composed of a number of circular fibres, each the zi jth of a centimeter 
in diameter, and each of these to consist of closely-packed fibrillaw, and to facilitate 
computation, if we assume each fibrilla to be of a triangular section, and the side of 
each triangle to be the ggypth of a centimeter in length, these quantities being 
about the amounts observed in mammalian muscles, it is easy to calculate that there 
will be about 500 meters of circumference of fibrillee per square centimeter of muscle 
which, with a superficial tension equal to that of water, gives a disposable force of 
four kilograms per square centimeter. The amount observed is about 7 kilograms 
per square centimeter,* and I think that what I have obtained comes sufficiently 
close to that observed for a more advantageous mode of distribution of the fibrille 
or a slight diminution of their size to account for the difference. Taking the thick- 
ness of the active superficial layer to be that obtained in the first part of this 
paper, the maximum force which could be obtained by making the structure as fine 
as possible, and the superficial tension that of water, would be nearly 1,000 kilograms 
per square centimeter, so that there is plenty of margin for compensating diminished 
superticial tensions by increased fineness of structure. It is remarkable in this 
connexion that in frogs, whose muscles are more coarsely made, the maximunt 
contractile force falls very much below that of the mammalia. A system of 
elongated cylindrical fibrillee would not be in stable equilibrium, but would break up 
into short lengths of less than three times their diameter, and this is just what is 
observed to be the case in all striated muscles. It has been questioned whether 
the fibrillar divisions and transverse strize to be found in dead muscles, have am 
actual existence in life. Yet I think there can be little doubt but that some structural 
peculiarity in life corresponds to these sub-divisions, and any such would produce a 
superficies capable of developing superficial tension. It may seem improbable that 
as high a superficial tension as that of water can exist in this case, but the undoubted 
fact of considerable electrical disturbance accompanying muscular contraction taken 
in connexion with M. Lippmann’s experiments proving the connexion between 
differences of electrical potential and superficial tensions, very much diminishes the 
force of this objection. If we suppose a structure to consist of a series of ellipsoids 
of revolution of ellipticity =sin @ and if r be the radius of the sphere whose volume 
is equal to that of each cell, then the force each would exert in the direction of its 
axis for surface tension=T is given by the equation, 
F incest 8 si 1 + 2cos2 5 ! 
= gig via cos (1 + 2cos? @)— 8(4cos? @—1)t, 
and it is easy to see that there is some given form of ellipsoid of revolution of giver 
volume for which this force will be a maximum, as it vanishes in the two extreme 
cases of a sphere and an infinite cylinder. If we calculate the pressure in x 
eylinder of radius 7, whose sides are formed of a series of rings like anchor rings, 
we find that the pressure is given by the equation, 
rol W 
Pz; 
and is independent of the section of each ring, so that by piling a great number of 
* See Haughton’s Animal Mechanics, pp. 63-71. 
