THE LAW OF RESISTANCE IN PARALLEL CHANNELS. 973 
This method of treating such experimental results was introduced in m 3 7 paper on 
Thermal Transpiration (see Phil. Trans., Part II., 1879, p. 753). 
Instead of curves, of which i and v are the abscissae and ordinates, log i and log v 
are taken for the abscissae and ordinates, and the curve so obtained is the logarithmic 
homologue of the natural curve. 
The advantage of the logarithmic homologues is that the shape of the curve is made 
independent of any constant parameters, such parameters affecting the position of all 
points on the logarithmic homologue similarly. Any similarities in shape in the natural 
curves become identities in shape in the logarithmic homologues. How admirably 
adapted these logarithmic homologues are for the purpose in hand is at once seen from 
diagram II., Plate 73, which contains the logarithmic homologues of the curves for 
both pipes 4 and 5. 
A glance shows the similarity of these curves, and also their general character. 
But it is by tracing one of the curves, and shifting the paper rectangularl } 7 until the 
traced curve is superimposed on the other, that the exact similarity is brought out. 
It appears that, without turning the paper at all, the two curves almost absolutely fit. 
It also appears that the horizontal and vertical components of the shift are— 
Horizontal shift.'913 
Vertical shift f . ..*294 
which are within the accuracy of the work respectively identical with the differences 
D 3 I) 
of the logarithms of — and — for the two tubes. 
37. The general law of resistance in pipes .—The agreement of the logarithmic 
homologues shows that not only at the critical velocities but for all velocities in these 
D 3 . 
two pipes, pressure which renders —the same in both pipes corresponds to velocities 
D 
/*" 
which render — v the same in both pipes. This may be expressed in several ways. 
Thus if the tabular value of i for each pipe plotted in a scale be multiplied by a 
D 3 
number proportional to — for that particular pipe and the values of v by a number 
proportional to p, then the curves which have these reduced values of i and v for 
abscissse and ordinates will be identical. 
A still more general expression is that if 
i = F(/;) 
expresses the relation between i and v for a pipe in which D = 1 , T= 0 , P=l. 
™-f(— 
p~ \p 
expresses the relation for every pipe and every condition of the water. 
6 1 
MDCCCLXXXIII. 
