July 22, 1922] 



NA TURE 



113 



The effect, if there were one, should be proportional 

 to the number of molecules striking the funnel per 

 second, i.e. to the total pressure. 



R. d'E. Atkinson. 

 Clarendon Laboratory, Oxford, June i. 



In reply to Mr. R. d'E. Atkinson's letter, I should 

 like to point out that, while his conclusion is un- 

 doubtedly true with regard to light, it is by no means 

 clear that analogy justifies his extension of this 

 conclusion to the molecular problem under con- 

 sideration in my paper. The fundamental conception 

 of unchanging uniform concentration would appear 

 incorrect when applied to particles proceeding 

 between collision centres and entering a minute vessel, 

 the diameter of which is considerably less than the 

 mean free path of the gas concerned. This confusion 

 of issue, introduced by regarding the problem of 

 light as identical with that I was considering, may 

 perhaps be brought out most clearly by the following 

 calculation, which is almost identical with the one 

 Mr. Atkinson suggests would be possible. 



If ABCD (Fig. 1) is the figure dealt with in the 

 paper, and DH, AF, PE all be inclined at angle a to 

 BC, while DI is perpendicular to BC, and D' is the 



D" 



mirrored image of D with respect to BZ, P being 

 the point on BZ such that angle EPB is equal to 

 angle DPA, then the following relationships may be 

 calculated. 



Case 1, where a is not less than angle D'BC. By 

 the usual laws of reflection, light approaching BC 

 from below, approximately at angle a, must pass out 

 at AD if it enters between E and H, but will be 

 returned through BC if it enters either between B 

 and E or between H and C. 



EH = EF + FH = PG + a = acota + «. 



Case 2, where a is not less than angle DBC, and is 

 not more than angle D'BC. In this case only light 

 entering between B and H will escape through AD. 



BH = BI-HI = ^«- r ^l=, 

 2 tana 



= a(i£-Jcota). 



Case 3, where a is less than angle DBC. In this 

 case all the light will necessarily be returned through 

 BC. Where a is greater than a right angle these three 

 cases are merely duplicated. 



Hence, if equal light intensity in all directions be 

 assumed, and if A be taken as a constant represent- 

 ing its uniform concentration, then the ratio of the 



NO. 2751, VOL. I io] 



amount of light which passes from AD to BC to that 

 which passes from BC to AD in unit time must be 



a = 90° 

 A / a sin a . da. 

 .' a = o° 



( ,-a = 90° -a = /_D'BC \ 



: - A / {a + a cot a) sin a . da + A la(i& -1 cot a) sin a. da y 

 [ .'a = /.D'BC .'a = lDBC ' J 



I ra=9r>° a=_D'BC ) 



= Aa: - Aa I (sin a + cos a) ia + Aa I (iisin a -A cosaWa - 

 [ J o. = lD'BC .' a = _DBC" J 



= Aa : Aa (0-643 + 0-357), approximately, 

 = Aa : Aa. 

 The above integration to equality is essentially 

 dependent upon the axiomatic acceptance of the 

 unchanging existence of equal concentrations or 



6 



6 



b 



intensities in all directions, uniformly throughout the 

 medium in which the cone is placed. Such unchanging 

 uniformity of concentration might be presumed to 

 exist in perfectly diffused light, but it cannot exist 

 in gases, since changes of concentration occur as 

 mtermolecular collisions, and must be important in 

 relation to the entering of vessels considerably smaller 

 than the mean free path of the gas. The light 

 problem is one of flow; the molecular problem may 

 be regarded as one of (interrupted) oscillation, at 

 least to a large extent. 



If each of the little circles in Fig. 2 be taken to 

 represent equal areas (or spheres if three dimensions are 

 being considered), the probability of molecules pro- 

 ceeding outwards, from collision in one of these 

 circles, along a path X, is equal to that of their 

 proceeding from collision, in that same or any other 

 equal circle, along a path Y, this being true however 

 many circles are under consideration, even in the 

 limit of their occupying the whole space within free 

 path distances from the cone. If two directions, X and 

 Y, are considered for a large number of such circles, 

 regularly placed so as to be representative of the 

 equal probability of collision in all parts, it is obvious 

 that molecules approaching BC along directions X 



and Y, and starting from collision sources, do not 

 cross BC in numbers proportional to the sines of the 

 angles of these paths with BC, as has to be assumed 

 in light calculations such as the one above, which 

 may be illustrated by Fig. 3 where no collisions occur, 



D 2 



