THE LAW OF RESISTANCE IN PARALLEL CHANNELS. 
975 
this law was independent of the diameter of the tube. This point has been very 
carefully examined, for it is found that the inclination of these lines differs decidedly 
from that of 2 to 1, being 1*723 to 1, and so giving a law of pressures through a range 
1 to 50 of 
l a V 
,1-723 
This is different from the law propounded by any of the previous experimenters, 
who have adhered to the laws 
i = tr 
or 
i = Av+Br 2 
That neither of these laws would answer in case of the present experiments was 
definitely shown, for the first of these would have a logarithmic homologue inclined 
at 2 to 1, and the second would have a curved line. A straight logarithmic homo¬ 
logue inclined at a slope 1*723 to 1 means no other law than 
% oc v 
1-723 
I have therefore been at some pains to express the law deduced from my experiments 
on the uniform pipes so that it may be convenient for application. This law as already 
expressed is simply 
D*. - 
n l =f 
1 
Dr 
P 
where f is such that 
x =f ( y) 
is the equation to the curve which would result from plotting the resistance and 
velocities in a pipe of diameter 1 at a temperature zero. 
The exact form of f is complex, this complexity is however confined to the region 
immediately after the critical point is passed. 
Up to the critical point 
.DU Dr 
po 2 B t . p 
After the critical point is passed the law is complex until a velocity which is 
1*325 v c is reached. Then as shown in the homologues the curve assumes a simple 
character again 
A D 3 ._ 
^ P 2 1 “ 
B 
DU 1-723 
that is, the logarithmic homologue becomes a straight line inclined at 1‘7*23 to 1. 
Beferring to the logarithmic homologues (Plate 73, diagram II.), it will be seen that 
although the directions of the two straight extremities of the curve do not meet in the 
6 I 2 
