444 MR. S. CHAPMAN ON THE KINETIC THEORY OF A GAS 



shall quote the results forthwith. After simplification by means of the equations 

 (23) and (24), we obtain the formulae 



' 2 



/ 0( -\ A 2 

 (25) A,,n - 



/_- x 3/2 1/3 



(26) 



/. ' ^P' , 3 Aram' 2 /On CT' U \ p,, 1 



- a ) P + -.- ^^ (- + ^r) B J 



(m'^-m""^)} F u ] 

 where for convenience we have written k^ and k a for the quantities given by 



7, 2 jTOm i2 z, _ 2 vmmf\ 2 S' 18 



"1 5" ~ / TV ' 2 \ 5 ~~ rl TV~ ' 



/ T^/ ) /l/ 2 \ 5 I ] 



m + m Jr 12 \ m+m ] 



By putting m = m', v = v, a = a' in the above equations we get also the 

 following : 

 (28) ' Antt 2 = _4^(^) 3/2 ^a 11 Il" 1 , 



/ f) f\\ * / 2 i 2 i 2\ 4 ' 



By transformation of co-ordinates we obtain the following equations from (25) 

 and (28) : 



(30) A 18 wt 



_w, / mm' 2 /Amm'\ 3/3 ro/ /\/ , \-nt ... o hmm' 2 



= 47T ' VV -, 



T -*TVS- -u u- -- - 



(m+m') 3 \m + mV L m + m'\m m' 



M'2 / 

 mm 



(3D* ' A llW = 



* All the formulae (25)-(31) were in the present form before the paper was revised, with the exception 

 of (26). Their calculation was given almost in full, and was performed by essentially the same methods 

 as those explained above. The work was made rather more lengthy than necessary by the use of an 

 unBymmetrical transformation of the integrals in place of that given in equations (13)-(17), to which Pwas 

 led while endeavouring to simplify the calculation of A 12 w(w 2 + ip + w 2 ) . The calculation of Aw(w 2 + v z + w 2 ) 

 was also complicated by the fact that the gas was not assumed to be at rest ; but on revision, despite these 

 simplifications, I decided to omit the routine calculations altogether. 



Equation (26) was not given in the paper as originally written because it is connected with the 

 conductivity of mixed gases, and I was then unaware of any experiments on the subject which would 

 make so tedious a calculation worth the while. I have since found such experimental data, and have 

 therefore worked out the formula (26), the results of which (as will be seen in Part III.) show very 

 satisfactory agreement with the observations. Note added October, 1911. 



