274 MEASUREMENT OF HIGH TEMPERATURES. bull, si 
cepting the given function, it is, at the present stage of investigation^ 
a justifiable inference that the viscosity of a perfect gas varies as the 
§ power of absolute temperature. Now, inasmuch as by the relation, 
of Maxwell 
7/=0.318 pLfl, 
where p is the density, D, the velocity of the mean square, and L the 
mean free path of the molecule of gas, and inasmuch &$n=n, Vl + ad i \ 
and L are the only variables in this equation whose values change witH 
6", it follows that 
L=Lo VY+ad" 
In other words, the mean free path of the molecule of a perfect gas 
varies as the sixth root of absolute temperature. Moreover, in view 01 
the equation D,=£1 Q Vl+ad", it furthermore follows that the mean fret 
path of the molecule of a perfect gas varies as the cube root of the 
velocity of the mean square. This result is suggestive, perhaps ; foi 
if there be given a gas consisting of a fixed number of molecules in i 
fixed volume, or, in other words, if p be constant, then the only effeel 
produced by varying the temperature 6" is a mean increase of £1 dis] 
tributed uniformly throughout the volume of the gas. If the change 
of D, due to temperature be taken as a measure of the effect produced 
by temperature, as it were equally in all directions, then the part oj 
this thermal effect apportioned to the linear magnitude L is plausibly 
represented by the cube root of O,. 
Again, if the equation of Clausius be considered, viz, 
V2 as 2 
where X 3 is the mean volume per molecule and s the radius of Clausius'a 
" Wirkungssphare," then it appears that the volume inclosed withid 
the " Wirkungsphare" is diminished in magnitude by temperature i 
and that the diminution takes place proportionally to the square roon 
of the velocity of the mean square ■(£!). 
^ 
Sources of error. — Having thus stated the general character of thej 
results of the above tables, it is necessary to find the conditions upon 
which their validity depends, and to inquire as fully as the present reJ 
searches permit into the facts which militate against the inferences! 
drawn. This is by no means easy, nor even fully possible on the basisi 
of the experimental material in hand. 
The principal cause of discrepancy in the present work is this, that even 
in the most carefully adjusted forms of the present apparatus the mean 
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