286 MEASUREMENT OF HIGH TEMPERATURES. [bull. 54 
logarithms. Unfortunately these values of zrj and 7t 2 themselves con 
tain vp, for which, however, the approximate value given by Poiseuille 
Meyer's law may usually be substituted with sufficient accuracy. 
In view of these difficulties Hoffmann investigates an empirical rela 
tion by observing that (ceteris paribus) the certain small length oil 
maximum efflux is subject to Navier's law, whereas as length increases 
the efflux obeys Poiseuille-Meyer's law. If, therefore, time of efflux 
(ceteris paribus) be studied as a function of length, Navier's law fixes 
a point, while Poiseuille-Meyer's law fixes an oblique line passing; 
through the origin. Hoffmann then supposes on the basis of his experi- 
mental results that the actual passage from the point to the line takes s 
place nearly along an hyperbola, of which the said point is the vertex, 
and the said line the asymptote. A suitable modification of this hy- 
pothesis leads Hoffmann to the equation 
i 
vp. 
AT" ~T~ 
where 
p _ R*7rdg (p^p* 2 ) 
1 IU77 1 
y B 2 7t {p l -\-p 2 ) I C . 2 Pl 
IVl 2 V 0.43429 g ivf] 
+P2 
and where &=(Z-j-4) (2 Z+4) and a has a tabulated value of nearly 1, but 
varying with the mean difference of pressure. 
Hoffmann's equation contains difficulties of calculation of a very 
tedious and impracticable kind, particularly in view of the involved 
occurrence of the factor 0, which represents the thermal variations 
of the transpiring gas. With full deference, therefore, for the accu- 
racy of application which Hoffmann has reached in his results, I shall 
nevertheless compute r/ by the formula (5) on page 253, above; i. e. ? 
directly by the Poiseuille-Meyer law. Having done this, it was my; 
further object to find from the known law of variation of 77 with tem- 
perature, what correction was to be applied to the Poiseuille-Meyer 
equation, to make the data for tubes not rigorously capillary conform 
with the data already in hand for truly capillary tubes. The plan 
which I have in mind is somewhat different from that of Hoffmann 
and more in harmony with the general tenor of my experiments. The 
form which I aim to give my correction is an exponential, in which 
the dimension of the capillary tube and the actual viscosity of the 
transpiring gas are the variables. I found, however, that to do this 
satisfactorily it would be necessary to repeat my experiments at greater 
length than I am now justified in doing; and observing that the data 
which I have in hand make up a diagram of the transpiration phe- 
(940) 
