June 24, 1909J 



NA TURE 



491 



trating than the a particles, and so would escape detec- 

 tion in absorption experiments in gases at ordinary 

 pressures. 



If this new radiation consists of the " rest-atom " of 

 radium G, we have in the property that it is projected 

 with high velocity and in that that it carries an electrical 

 charge the means of ascertaining its mass. Such a know- 

 ledge would give very definite information regarding the 

 constitution of the final radio-active product of radium, 

 and would also, in addition, furnish a means of checking 

 the accuracy of the now highly authenticated theory by 

 which the various known radio-active products of radium 

 are connected and related. 



The existence of this radiation, moreover, would afford 

 a means of ascertaining whether the rest-atoms of 

 radium G are the final products of radium or not, for it 

 should be possible to obtain, through bombardment, a 

 coating of these rest-atoms on a body such as the plate B 

 in the experiments described above. This plate could then 

 be placed in a high vacuum and investigated for the 

 acquisition of an electrical charge. Any gain of charge 

 which it might experience could be taken as proof of the 

 formation of a new product, while the absence of such 

 gain might be taken as evidence that radio-activity had 

 ceased, and that in the rest-atoms of radium G stability 

 is finally attained. J. C. McLennan. 



Physical Laboratory, University of Toronto, June 7. 



Molecular Effusion and Transpiration. 



One of Maxwell's most famous laws is his law on the 

 distribution of velocities, to the effect that all the mole- 

 cules of a gas do not possess the same velocity, but that 

 the various velocities of the molecules group about a 

 certain average velocity n in a definite way, which was 

 further theoretically determined by Maxwell. This law 

 has not, however, hitherto been directly proved by experi- 

 ment, and I am therefore of opinion that the following 

 may be of some interest to English readers. 



The flow of the gases through very small apertures and 

 narrow tubes at ordinary pressure has been investigated 

 bv Graham and several others, and definite laws (the 

 effusion and transpiration laws) which apply to these flows 

 have been found. My experiments now show that if the 

 area of the aperture or the transverse section of the tube 

 are small compared with the mean free path of the gas 

 molecules, then other and still simpler laws than those 

 mentioned will apply, and that these laws are easily 

 dcducible from the kinetic gas theory and Maxwell's law 

 on the distribution of velocities. Detailed reports of the 

 experiments have been published in Annalcn der Physik, 

 Bd. xxviii., igoq. 



Molecular Effusion.— According to the kinetic gas 

 theory, the number of molecular shocks which the surface- 

 area A of a wall receives during a second from the 

 surrounding gas is equal to ^NAn, where N is the number 

 of gas molecules in each cm.' and n the average velocity 

 of the molecules. If there is an aperture in the wall 

 having an area A, and if N' and N" are the numbers of 

 gas molecules at each side of the wall respectively, 

 J.A.n(N' — N"1 more molecules are flying through the aper- 

 ture in the course of a second in one direction than in the 

 other. Taking m as the weight of each molecule, the 

 weight G of the gas flowing through the aperture during 

 a second would be 



G = JAn(N'«;-N"«/) = lAn(p'-p") = lAnp,(/-/'). 

 where p is specific gravity, p the pressure, and p, the 

 specific gravity of the gas at the pressure i dyn./cm.° and 

 the temperature of the gas. According to Maxwell's law 



on the distribution of velocities we get n = » / — > 



* Trpi 

 which gives 



The fact that the weight found is proportional to, and 

 therefore the volume of gas is inversely proportional to, 

 the square root of the specific gravity has been shown 

 by numbers of experiments made by different investigators ; 



NO. 2069, VOL. 80] 



but the factor ', — ; and the proportionality with the differ- 



V2ir 

 ence of pressure have not been experimentally found 

 earlier, and they prove to apply only when the mean free 

 path is more than about ten times greater than the 

 diameter of the aperture. By a series of experiments with 

 an aperture in a plate of platinum 0-0025 mm. thick, where 

 the area of the aperture was found by means of the micro- 

 scope to measure 5.2i + o-i6 millionth square centimetres, 

 I found the following proportions between the observed 

 quantity and that computed from the above formula : — 

 hydrogen, 0-978; oxygen, 0-981. 



From another aperture, the area of which was 

 66.0X10-'' cm.^, the following proportions were found: — 

 hydrogen, 1-021 ; oxygen, 1-038. 



Consequently, the difference between theory and observa- 

 tion is 2 per cent, to 3 per cent., which is considered 

 chiefly to be due to the difficulty of making an exact 

 determination of the areas of such small apertures. If 

 by computation of the above formula no attention had 

 been paid to Maxwell's law on the distribution of veloci- 

 ties, and all the molecules had been considered as moving 



with the same velocity, we should have taken n= ./ -' 



the effect of which would be that the computed values 

 would become 8-6 per cent, greater than if we used Max- 

 well's formula, and the difference between theory and, 

 experiment caused thereby could scarcely be explained as 

 an error of observation. 



By the above-mentioned experiments the pressures were 

 measured with McLeod's manometer, and the determina- 

 tions of pressures checked each other, so that there was 

 not found the slightest indication of a real or apparent 

 deviation from the laws of Mariotte and Gay-Lussac. 



The formula may be used for determination of p'—p" 

 if A and G are measured for some gas. In this way I 

 have made an experimental determination of the maximum 

 pressure of mercury vapour at 0°, and a series of higher 

 temperatures up to 46°. By 0° the pressure was found 

 to be 0-0001846 mm. mercury pressure. From the 

 measurements I have obtained the following formula fof 

 the vapour-pressure p, given in mm. mercury (common 

 system of logarithms, T = absolute temperature^ : — - 

 log /I = 10-5724- o-847log T-3342-26/T. 



The mean deviation between the values derived from 

 this formula and those observed amounts to 0-003 of the 

 value, which shows that the constants of the formula are 

 determined with fairly great accuracy. It is seen that if 

 the formula is used for extrapolation to pressures at higher 

 temperatures we get now positive, now negative devia- 

 tions from the determinations made by other experi- 

 mentalists, so that the formula in reality expresses the 

 vapour-pressure of the mercury up to 880°, which is the 

 highest temperature at which Cailletet and his collabora- 

 tors have determined the pressure. At this temperature he 

 found a pressure of 162 atmospheres where my formula 

 gives 15S atmospheres. 



Molecular Transpiration. — A series of experiments I 

 have made with relation to the flow of gases through 

 narrow tubes at low pressures has also confirmed Max- 

 well's law on the distribution of velocities. The calcula- 

 tion of the quantity of gas flowing through the tubes can- 

 not, however, be made without using a new theory for 

 the reflection of gas molecules from a wall. My theory 

 for this reflection of gas molecules, which has been fully 

 confirmed by the experiments, is as follows : — 



A gas molecule meeting a wall is reflected in a direc- 

 tion which is absolutely independent of the direction in 

 which it is moving against the wall, and a great number 

 of molecules, meeting a wall, are reflected in every direc- 

 tion according to Lambert's law (the cos. law on the 

 emission of light from a hot body). Consequently, the 

 gas molecules may be considered as having strayed into 

 the wall or as having been absorbed by it, to be emitted 

 afterwards therefrom, provided that the gas and the wall 

 have the same temperature. The calculation of the 

 quantity of gas streaming through the tube is quite simple, 

 though, however, too extensive to be given here. For the 

 weight of gas flowing through the tube in each second 

 we get the following expression : — 



