674 Prof. M. Smoluchowski-Smolan on the 
Now let us see what information we can get about these 
points by our method. Suppose, first, our having found the 
empirical relation between resistance B and linear dimensions « 
of similar bodies, moving all with the same velocity in air of 
pressure , and temperature 0): B=(2). 
If we wish to know the resistance in air of other pressure p, 
symbolized by B=/(#, p), we have only to find out the similar 
case among those known already. This is the case 
(by: a= B=h=n=lan= i) 
belonging to the linear dimensions - with resistance o(™). 
0 0 
Now, as the dimension of resistance requires proportionality in 
the two cases to bn?= - it follows that the required law of 
resistance is given by 
sateen 00 22), 
H(2, p) 5 o( A 
Thus, if supposing (a) resistance to be proportional to linear 
dimensions, $(«)=az, we must infer its being independent 
of the pressure altogether, whilst (@) proportionality to super- 
ficial dimensions necessarily must be connected with propor- 
tionality to pressure. 
If the influence of velocity, too, has been found experi- 
mentally (for a given pressure and temperature)—@(u, ~) 
denoting this relation now—the range of these results can 
be extended, by similar reasoning («e=@=b=1; m=,/4; 
n=h«t®), to include the effect of variation of temperature. 
We shall have for the resistance at temperature 0 
Opty ee -[! M4 ( e r oe 
Moreover, if the gas be other than air, the influence of its 
molecular weight and viscosity can be inferred from the same 
experimental results, and in the same way, by similarity 
(250 ni Aes n= £), 
ie Va 
For the most general case, thus, resistance is determined by 
B=/(u, 2, 0, p, h, a, pw) 
ee 2 G] 2e+1 M0 ( 6)M ar Oy\et#) ; 
ale) Mp ON oi a ee ). ©) 
0 


