June 21, 1900] 



NATURE 



189 



Pascoe, King, Macalister, Mitchell. Exhibitioners : Crocker, 

 Denham, Simpson, Balls. Hockin Prizeman (lor electricity) : 

 Browning. Engineering Scholar : Paton. 



The attention of teachers and others engaged in schools is 

 directed to the appeal made by Prof. Karl Pearson in our corre- 

 spondence columns. Observations of the physical and mental 

 characters of children are required, and measurements of the 

 head, in order to provide material for an investigation of heredity 

 upon which Prof. Pearson is engaged. There should be no difti- 

 culty in obtaining the co-operation of masters and mistresses in 

 schools in this work, for the observations and measurements can 

 be made with very little trouble, and they are of as much interest 

 from an educational point of view as they are to biological science. 



SCIENTIFIC SERIAL. 



Bulletin of the American Mathematical Society, May. — 

 The number opens with four papers read before the Society at 

 the dates annexed : On the geometry of the circle, by Dr. V. 

 Snyder (December 28, 1899) ; isomorphism between certain 

 systems of single linear groups, by Prof. L. E. Dickson 

 ^ February 24) ; the Hessian of the cubic surface ii. , by Dr. 

 ' I. Hutchinson (February 24); and note on the group of 



■ morphisms, by Dr. G. A. Miller (February 24). These 

 i^.ipers are short and, in the main, continuations of work pre- 

 viously published by the authors. — Prof. F. S. Woods con- 

 tributes an interesting sketch of a German translation, by F. 

 Engel, of two articles by Lobachevsky, with the titles " Ueber 

 die Anfangsgrtinde der Geometrie" and " Neue Anfangsgriinde 

 der Geometrie mit einer Vollstiindigen theorie der Parallel- 

 linien." The reviewer's conclusion is that, "while it is re- 

 markable that the solution of a two-thousand-year-old problem 

 should be given almost simultaneously by three men, it should be 

 .emembered that these three were not the only mathematicians 

 who had worked upon the problem. More than one had missed 

 the solution by a hair's breadth only ; Lobachevsky, Bolyai 

 and Gauss succeeded in finding it " — Other notices are Vogt's 

 "Algebraic solutions of equations," by J. Pierpont ; the elements 

 of the diflferential and integral calculus, based on the work by 

 Xernst and Schonflies (translated by W. A. Young and C. E. 

 Linebarger), by L. E. Dickson ; and E. Pascal's "Die Variations- 

 rechnung," by J. K. Whittemore. — University and general 

 mathematical information come into the "Notes" and "New 

 Publications." 



SOCIETIES AND ACADEMIES. 

 London. 



Royal Society, April 5. — " The Kinetic Theory of Planetary 

 Atmospheres." By Prof. G. H. Bryan, F.R.S. 



The application of the kinetic theory to the atmospheres of 

 planets dates from the paper of Waterston, who gave an in- 

 vestigation based on the then only possible assumption of equal 

 velocities for all molecules, an assumption since known as 

 Clausius' law. Of later papers reference is due in especial to 

 Dr. Johnstone Stoney's memoir "Of Atmospheres on Planets 

 and Satellites" (Trans. R Dublin Soc), in which the test of 

 permanence of a gas in the atmosphere of a planet is made to 

 depend on the ratio of its velocity of mean square to that rela- 

 tive velocity which would enable a suitably projected body to 

 escape from the planet's attraction. If it be admitted, as Dr. 

 '-^toney assumes, that helium cannot exist in our atmosphere, it 



Hows that vapour of water cannot exist on Mars. 



The author's object has been to investigate the logical con- 

 clusions obtained by applying the Boltzmann-Maxwell distribu- 

 tion to the atmospheres of planets. In 1893 calculations were 

 made, having special reference to the absence of atmosphere 

 from the moon, but these took no account of axial rotation. 

 When this cause is taken into account, the distribution of co- 

 ordinates and relative velocities of the molecules is found to be 

 the same as if the planet were at rest, and "centrifugal force" 

 applied to the system. The surfaces of equal density are of the 

 forms originally investigated by Edward Roche, of Montpellier, 

 and they cease to be closed surfaces when passing to the outside 

 of the point on the equatorial plane where centrifugal force just 

 balances the planet's attraction. Calling the surface through this 

 point the "critical surface," the density of molecular distribu- 

 tion over this surface must be very small to ensure permanence. 



NO. 1599, VOL. 62J 



The ratio of the density at the planet's surface to the density at 

 the critical surface has been called the "critical density ratio," 

 and the author calculates its logarithm for particular gases at 

 different temperatures on the various planets. The use of this 

 logarithm has the advantage that the calculation can at once be 

 extended to any gas at any temperature. 



The high value obtained in the case of helium, considered 

 in reference to the earth, appears to afford abundant proof that 

 if helium existed in our atmosphere it would possess a very 

 high degree of permanence at ordinary temperatures. To test 

 this point further, a calculation is made of the total rate at 

 which molecules would flow across the critical surface, this rate 

 being regarded as a superior limit to the rate at which the 

 planet would lose its atmosphere, since it takes no account of 

 molecules which describe free paths beyond the limit and fall 

 back again. To further exhibit the results in a tangible form, 

 the rate of flow is estimated by the number of years in which- 

 the total amount of gas escaping across the critical surface 

 would be equal to the amount of the gas in a layer covering 

 the surface of the planet to the depth of I cm. This measure 

 is independent of the actual quantity of the gas under consider- 

 ation existing in the atmosphere, since, if this quantity be in- 

 creased, the rate of flow across the critical surface and the 

 amount of gas present in the surface layer l cm. thick will be 

 increased in the same proportion. 



If a gas of molecular weight 2, such as helium, be supposed 

 to exist in the earth's atmosphere, the loss in question would 

 occupy 3-5 X lo^** years at - 73°C., 3 x lo^^ years at 27°, 

 84 X iqI** years at 127° C., 6 x 10'^ years at 227" C, and 222 

 years at 327° C. 



If we halve the absolute temperatures, we have the conditions 

 applicable to hydrogen, the losses in question therefore taking 

 place in 8-4 x lo^" years at - 73° C, 6 x io» years at -23°C.„ 

 and 222 years at 27° C. 



For water vapour on Mars, the corresponding results are 

 1-2 x io-'=* years at - 73°, 19 x iqI" years at 27°, 2-4 x 10" 

 years at 127", 4-3 x 10'* years at 227°, and 106 years at 327°. 



These figures indicate that helium cannot practically escape 

 from our atmosphere at existing temperatures, nor can vapour 

 of water escape from the atmosphere of Mars. A leakage 

 may, and undoubtedly does, take place, which may appear con- 

 siderable when estimated by the number of actual molecules 

 escaping, but it is wholly inappreciable relative to the mass of 

 gas left behind. 



At a future time it is proposed to examine the corresponding; 

 results, based on the hypothesis that the atmosphere of a plane* 

 is distributed according to the adiabatic instead of the isothermak 

 law. 



" On the Weight of Hydrogen desiccated by Liquid Air." 

 By Lord liayleigh, F.R.S. 



In recent experiments by myself and by others upon the 

 density of hydrogen, the gas has always been dried by means of 

 phosphoric anhydride ; and a doubt may remain whether, on 

 one hand, the removal of aqueous vapour is sufiiciently com- 

 plete, and on the other, whether some new impurity may not 

 be introduced. I thought that it would be interesting to weigh 

 hydrogen dried in an entirely different manner, and this I have 

 recently been able to effect with the aid of liquid air, acting as 

 a cooling agent, supplied by the kindness of Prof. Dewar from 

 the Royal Institution. The operations of filling and weighing 

 were carried out in the country as hitherto. I ought, perhaps, 

 to explain that the object was not so much to make a new deter- 

 mination of the highest possible accuracy, as to test whether 

 any serious error could be involved in the use of phosphoric 

 anhydride, such as might explain the departure of the ratio of 

 densities of oxygen and hydrogen from that of 16 : i. I may 

 say at once that the result was negative. 



Each supply consisted of about six litres of the liquid, con- 

 tained in two large vacuum-jacketed vessels of Prof. Dewar's 

 design, and it sufficed for two fillings with hydrogen at aa 

 interval of two days. The intermediate day was devoted to a 

 weighing of the globe empty. There were four fillings in all, but 

 one proved to be abortive owing to a discrepancy in the weights 

 when the globe was empty, before and after the filling. The 

 gas was exposed to the action of the liquid air during its passage 

 in a slow stream of about half a litre per hour through a tube of 

 thin glass. 



I have said that the result was negative. In point of fact the 

 actual weights found were iV to /^ milligrams heavier than in 

 the case of hydrogen dried by phosphoric anhydride. But I 



