84 



C. V. L. Charlier 



According to Meddel. N;o 70 is 

 so that 



Äono = 0.239 X 10 -^8 



3v = 27.91 X 10-'8 



aud the time of relaxation — 



(202) 1 : 3v = a.ß83 X 10'« years. 



Curiously enough Jeans has obtained, using the repulsionlaw of Maxwell, a 

 value of the time of relaxation nearly of the same order of magnitude as that 

 deduced above from the law of Newton. This coincidence is probably due to a 

 mere chance. 



The time 10^'' years is an approximate measure of the time required for a 

 sensible alteration in the velocity ellipsoid of the stars on account of the passages. 



52. Molecules. If the law of Newton is applied to the kinetic theory of 

 the gases it proves necessary to use another value of the constant of attraction, 

 than that used for stars. Such a modification was, for different reasons, a priori 

 to be expected. The value of the constant of attraction for gases may be deduced 

 from the known results obtained in the classical theory. 



Maxwell has deduced the value of the time of relaxation for gases. Assuming 

 the number of Avogadro as known, we are able to compute q and hence the con- 

 stant of attraction for gases. 



The formula for v may be written in the form 



(203) , T|7^ ^000 « ^ , 



where the last factor {q-T : K^) depends only on q. From the known values of 

 3v (= 1 : time of relaxation), Jq^q (= the number of Avogadro), a {— mean component 

 velocity of the molecules) and D (= half the mean distance of the molecules) 



Q ^ ■ J^i 



may be computed and thence the value of q. It follows from the table at the end 

 of this memoir as well as of the fig. 8 that q^T.K^ is vanishiug for small values 

 of q and also for large values and has a single maximum. It follows that to a 

 given value of q^T : correspond either two values of q or no real value of this 

 quantity. We shall find that there are two real solutions. 



The numerical computation runs as follows, where all quantities are expressed 

 in the C. G. S. system. 



I put with Jeans * (P. 297) 



3v = 6 X 10^ 



* This refers to air. Hence some modifications in the following calculations (carried out for 

 hydrogen), which only aim at giving the order of magnitude of the constant of attraction. 



