678 Prof. M. Smoluchowski-Smolan on the 
obtained inexplicable contradictory results by careful expe- 
riments on both methods. 
§ 11. The theory of motion of gases in wider tubes, such 
as used for gas-pipes, is quite obscure as yet; the formula 
most used in practice is 
(Po— pid 
ae 
where a is a constant, d the diameter of the pipe, / its 
length, uw the mean velocity. Its form, indeed, satisfies the 
conditions of similarity, even for different gases, if by p be 
understood their density p= = Some other empirical 
forms, on the contrary, as, for instance, Stockalper’s, 
u=a 5 
( Pe— prjd 
r il 
lp (5 7 
p (5+ 5 
derived from experiments at the Gotthard tunnel, must be 
rejected, as incongruous. For any law of the general form 
Uu=(p1, Px |, d) 
must remain unchanged by substitution of the corresponding 

\ 
Dae 5 
values (2 fs , nl, nd ). 
n 
But it is sufficient to know the experimental relation between 
u and 7, >, / for a certain value of diameter and temperature 
in air; then we get the most general form for any gas and 
any d, 0, by similarity, in the form 
WM. l 
ys vee ) (sp» Spo, 12), . joe 
pod M (3): 
where s is an abbreviation for — (> 
: bd M, 0 
For the opposite extreme to transpiration, viz. the effusion 
through a fine aperture in a thin wall, commonly Bunsen’s 
law, maintaining proportionality of the passing volume to 
Fi for different gases, is accepted, at least for small 
difference of pressure, although recent researches (for example, 
Donnan, Phil. Mag. xlix. p. 423, 1900) have shown the 
agreement to be by no means satisfactory; the rule would 
apply with exactness, on the contrary, under the same suppo- 
sition as in the analogous case above, supposing pressures to 
be chosen in proportion of Tit 
