Nov. 22, 1888] 



NATURE 



83 



of agitation is found to be such that the mean square of 

 velocity of the meteorites is ahnost exactly % of the square 

 of the velocity of a satellite g;arin;j the surface of the 

 sphere in a circular orbit. 



As indicated above, it is supposed that in the meteor- 

 swarm the rigid envelope, bounding the isothermal sphere, 

 j is replaced by a layer or atmosphere in convective equili- 

 I brium. The law of density in the adiabatic layer is 

 determined in the paper, and it appears that when the 

 isothermal sphere has minimum temperature the mass 

 of the adiabatic atmosphere is a minimum relatively to 



I at of the isothermal sphere. Numerical calculation 

 ows, in fact, that the isothermal sphere cannot amount 

 mass to more than 46 per cent, of the mass of the whole 

 )thermal-adiabatic sphere, and that the limit of the 

 iiabatic atmosphere is at a distance equal to 2786 

 nes the radius of the isothermal sphere. ^ 

 It is also proved that the total energy, existing in the 

 rm of energy of agitation, is exactly one-half of the 

 (tential energy lost in the concentration of the matter 

 >m a condition of infinite dispersion. This result is 

 ought about by a continual transfer of energy from a 

 molar to a molecular form, for a portion of the kinetic 

 I energy of a meteorite is constantly being transferred 

 pto the form of thermal energy in the volatilized gases 

 fenerated on collision. The thermal energy is then lost 

 ^ radiation. 

 [It is impossible as yet to sum up all the considerations 

 ■hich go to justify the assumption of the isothermal- 

 Hiabatic arrangement, but it is clear that uniformity of 

 ■netic energy must be principally brought about by a 

 p-ocess of ditifusion. It is therefore interesting to consider 

 what amount of inequality in the kinetic energy would 

 have to be smoothed away. 



The arrangement of density in the isothermal-adiabatic 

 here being given, it is easy to compute what the kinetic 

 ergy would be at any part of the swarm, if each meteor- 

 e fell from infinity to the neighbourhood where we find 

 it, and there retained all the velocity due to such fall. 

 The variation of the square of this velocity gives an in- 

 dication of the amount of kinetic energy which has to be 

 degraded by conversion into heat and distributed by dif- 

 fusion, in the attainment of uniformity. This may be 

 called " the theoretical value of the kinetic energy." 

 It appears that in the swarm, this square of velocity 

 rises from zero at the centre of the swarm to a maximum 

 which is attained nearly half-way through the adiabatic 

 layer, and then diminishes. It is found that the variations 

 of this theoretical value are inconsiderable throughout the 

 greater part of the range. From this it follows that there 

 must be diffusion of kinetic energy from without inwards, 

 and considerations of the same kind show that when a 

 planet consolidates there must be a cooling of the middle 

 strata both outwards and inwards. 



We must now consider the nature of the criterion which 

 determines whether the hydrostatic treatment of a meteor- 

 swarm is permissible. 



The hydrodynamical treatment of an ideal plenum of 

 gas leads to the same result as the kinetic theory with 

 regard to any phenomenon involving purely a mass, when 

 that mass is a large multiple of the mass of a molecule ; 

 to any phenomenon involving purely a length, when the 

 cube of that length contains a large number of molecules ; 

 and to any phenomenon involving purely a time, when 

 that time is a large multiple of the mean interval between 

 collisions. Again, any velocity to be justly deduced from 

 hydrodynamical principles must be expressible as the 

 edge of a cube containing many molecules passed over in 

 a time containing many collisions of a single molecule ; 

 and a similar statement must hold of any other function 

 of mass, length, and time. 



Beyond these limits we must go back to the kinetic 



' This is one of the results e<^tablished by M. Ritterin a series of papers in 

 the Annalen der Physik iind Chemie from 1878 onwards. 



theory itself, and in using it care must be taken that 

 enough molecules are considered at once to impart 

 statistical constancy to their properties. 



There are limits, then, to the hydrodynamical treatment 

 of gases, and the like must hold of the parallel treatment 

 of meteorites. 



The principal question involved in the nebular hypo- 

 thesis seems to be the stability of a rotating mass of gas ; 

 but unfortunately this has remained up to now an un- 

 touched field of mathematical research. We can only 

 judge of probable results from the investigations which 

 have been made concerning the stability of a rotating 

 mass of liquid. Now it appears that the instability of a 

 rotating mass of liquid first enters through the graver 

 modes of gravitational oscillation. In the case of a 

 rotating spheroid of revolution the gravest mode of 

 oscillation is an elliptic deformation, and its period does 

 not differ much from that of a satellite which revolves 

 round the spheroid so as to graze its surface. Hence, 

 assuming for the moment that a kinetic theory of liquids 

 had been formulated, we should not be justified in apply- 

 ing the hydrodynamical method to this discussion of 

 stability, unless the periodic time of such a satellite were 

 a large multiple of the analogue of the mean free time of 

 a molecule of liquid 



Carrying, then, this conclusion on to the kinetic theory 

 of meteorites, it seems probable that hydrodynamical 

 treatment must be inapplicable for the discussion of tuch 

 a theory as the meteoric-nebular hypothesis, unless a 

 similar relation holds good. 



These considerations, although of a vague character, 

 will afford a criterion of the applicability of hydro- 

 dynamics to the kind of problem suggested by the 

 nebular hypothesis. And certain criteria suggested by 

 this line of thought are found in the paper ; they give a 

 measure of the degree of curvature of the" average path 

 pursued by a meteorite between two collisions. 



After these preliminary investigations, we have to con- 

 sider what kind of meeting of two meteorites will amount 

 to an "encounter" within the meaning of the kinetic 

 theory. 



Is it possible, in fact, that two meteorites can consider- 

 ably bend their paths under the influence of gravitation, 

 when they pass near one another ? This question is con- 

 sidered in the paper, and it is shown that unless the 

 bodies have the dimensions of small planets, the mutual 

 gravitational influence is insensible. Hence, nothing 

 short of absolute impact is to be considered an encounter 

 in the kinetic theory, and what is called the radius of 

 " the sphere of action " is simply the distance between the 

 centres of a pair when they graze, and is therefore the sum 

 of the radii of a pair, or, if of uniform size, the diameter of 

 one of them. 



( To be continued^ 



SOME CURIOUS PROPERTIES OF METALS 

 AND ALLOYS} 



'T^HE lecture consisted mainly of experimental demon- 

 -*• strations of the changes induced in metals, either 

 by slight variations in the treatment to which they are 

 subjected or by rendering them impure by the addition of 

 small quantities of metals or metalloids. 



Prof. Austen began by pointing out that for centuries the 

 early n-.etallurgists mvestigated the action of exceedingly 

 small quantities of matter upon masses of metal ; and he 

 said that, strange as it may seem, the promulgation, in 

 1803, of Dalton's atomic theory threw a flood of light upon 

 chemical phenomena, but cast into the shade such investi- 

 gations as those of Bergman, which dealt with influences 



' Abstract of a Lcciure delivered by Prof. W Chandler Robert ^-Austen, 

 F.R.S., at the Royal Institution, on May 11, 1888. 



