252 MEASUREMENT OF HIGH TEMPERATURES. [bull. 54. 
ber. Here $ is the density of the mercury column and g the accelera- 
tion of gravity at the place of observation. With this introduction 
the dimensions of ?/, computed from equation (2), are [m^T -1 ], which 
are identical, of course, with the dimensions required by the funda- 
mental formula of viscosity, or by the well-known equation of Maxwell. 
7]=0.318p{2L, deduced in the kinetic theory of gases. Equation (2) 
shows, moreover, that the dimensions of Z are linear, agreeing with the 
thermo dynamic interpretation of C, which is proportional to the mean 
free path of the molecule of a gas. C has been called " Gleitung's co- 
efficient" by Helmholtz, a name, the appropriateness of which appears, 
inasmuch as C=^ where e is the coefficient of external friction of the 
8 
gas. 
Neither formula (I) nor formula (2) contain direct reference to the 
temperature at which transpiration takes place. Such reference is, 
however, implied in the p occurring in the denominators of ^1) and (2); 
for the value of X) is given by Boyle-Charles's law as 
p=Jcp(l+ad) (3) 
where p and 6 are the density and temperature corresponding to the 
pressure p, and where Tc is constant. 
Regarding the general applications of (1) and (2) I will say that the 
derivation of these equations presupposes that p and p are independent 
of r, or that for the points of any given right section of the tube_^ and 
p are constant. Again it presupposes a nearly steady How, such that the 
differential coefficients of it 2 and - , i. e., 
dx 
du <Pu d 2 u 
dx 1 dx 2 * dxdr' 
• 
where x is measured along the axis of the tube are practically zero. 
Finally equations (1) and (2) are true only for circular sections. In the 
case of elliptic sections, 1 with semi-axes a and b y the equation (2) be- 
comes (supposing C=0) 
r i= ,ti^t i **» (3) 
1 pi S??La 2 +b 2 ' v ; 
so that the equation, when a aud b are not known, can only be used for 
the interpretation of relative measurements. 
Case of two cold ends, absolute apparatus. — Equation (2) is available 
for experimental measurement in a variety of ways. It presupposes, 
however, that the temperature of the capillary tube be the same through- 
out its length. This is, of course, a feasible precaution, for it is only 
necessary to weld the platinum capillary to platinum terminal tubes 
1 Meyer: Ibid., p. 364 ; Mattliieu : C. R., vol. 57, 1863, p. 320. 
(906) 
