July 30, 1874] 



NAl^URE 



247 



in order to live, i.e. to resist the external forces which 

 tend to death. Those that have in themselves a sufficient 

 resisting force are developed and found persistent races ; 

 the feeble succumb and disappear.. The same law reigns 

 in the heavens. A body would subsist eternally by virtue 

 of its internal forces if it were alone ; but every neigh- 

 bouring body becomes for it a dissolving cause by virtue 

 of the attraction which the former exercises on the latter. 

 The strong resist ; they are the planets : the weak yield 

 and end by succumbing ; they are the comets. 



Mechanics will convince us of this. Let us take a 

 comet far away from the sun, leaving out of consideration 

 at first the very weak attraction to which the former is 

 subject ; we can do this, for it is then sensibly the same 

 for all its parts. Its solid, liquid, or gaseous materials are 

 under the influence of their mutual attractions and of the 

 feeble heat which they receive from without, freely dis- 

 posed in regular layers, superposed so as to form a globe 

 spherical like the earth, a globe whose centre will be 

 occupied by the most compact parts and whose surface 

 will be formed of the lightest parts. Whether this globe 

 be at rest or in motion, if things remain thus, the comet 

 will subsist ; you will see its bright nucleus surrounded by 

 a less luminous but quite sunny nebulosity, and this same 

 form will indicate to you a body in which the forces which 

 act on all its parts are directed towards the centre. Such 

 is the first forrti in which we have represented Donati's 

 comet (Fig. 3). 



But if the comet comes nearer to the sun, the solar 

 attraction will rapidly modify this state of things. The 

 parts nearest to the sun will be attracted more strongly 

 than the centre, and will have a tendency to separate 

 from it ; the difference of the solar attraction on the 

 various parts of the comet will have the effect of elongat- 

 ing that body somewhat in the direction of the radius 

 vector ; this is a phenomenon quite like that of the tides. 

 The second sketch (Fig. 4) of the comet of 1S5S offers an 

 example of this ; but already the eccentricity of the 

 nucleus ought to put us on our guard against any 

 incompleteness in our present reasoning, founded upon 

 the sole considei'ution of attraction. Nevertheless, you 

 see, the body remains entire ; the solar action being very 

 feeble, at that great distance, the attraction of the comet 

 on its exterior strata still preponderates, and the resultant 

 of these various forces at each point is still turned towards 

 the interior ; the layers which compose it are everywhere 

 convex externally, and do not show any symptoms of 

 dissolution. 



But bring the comet still nearer to the sun ; the attrac- 

 tion of that body will no longer be limited to the produc- 

 tion of an elongation ; you will see the external layers 

 become still more deformed and finally open out so as to 

 let matter escape. 



There exists, for every body placed within the sphere 

 of action of our sun, a surface limit beyond which its 

 matter may not pass, under pain of escaping to that body 

 and falling within the domain of the solar action. This 

 surface limit depends on two things — the mass of the 

 body and its distance from the sun. For a planet like 

 the earth, whose mass is so considerable, this surface 

 limit is very distant, and yet, within the still terrestrial 

 region of its satellite, the moon, a child could lift, without 

 much difficulty, a body which would weigh for us 36,000 

 kilogrammes, so feeble does the attraction of our globe 

 become at that distance of 60 terrestrial radii. A little 

 beyond the lunar orbit, a body would cease to belong to 

 the earth, and would enter the exclusive domain of the 

 sun. But for a comet, this surface limit is much nearer 

 the nucleus, and, moreover, it dr.\ws nearer and nearer, in 

 proportion as the comet approaches the sun. One of the 

 most eminent professors of the high education, M. E. 

 Roche, of Montpellier, has submitted this question to 

 analysis, leaving aside accessory circumstances such as 

 the rotatory movement of the body under consideration 



and the curvature of its trajectory ; he has thus been 

 enabled to discover that the surface which so limits a 

 body in the vicinity of the sun presents two singular 

 points in the direction of the radius vector, setting out 

 from which this surface is widened out into conical net- 

 work, in such a manner that the dissolution of a body 

 the matter of which reaches or passes beyond these 

 boundaries, is effected principally in the vicinity of the 

 points referred to, flying, so to speak, into two pieces, 

 thus obeying at once the attraction of the comet and 

 especially the thenceforth preponderating attraction of 

 the sun. 



And it ought not to be objected to this that there is no 

 reason why the matter of a body should tend thus to be 

 separated from its centre and to fill a volume greater and 

 greater, so as to reach or surpass the fatal limit. This 

 tendency exists ; it proceeds from the increasing heat 

 which a body that approaches nearer and nearer to the 

 sun experiences, and from the progressive expansion 

 which thence follows in the matter. Certainly if the earth 

 were drawn nearer to the sun, the dilatation of its solid 

 nucleus would be a small matter, but thenceforth the seas 

 would be reduced to vapour and would pass wholly into 

 the atmosphere. In the case of comets, in which the 

 matter presents a much less marked degree of aggregation 

 — doubtless because its original heat, due to the union of 

 the particles which compose it, was not sufficient to 

 bring about all the chemical reactions — the solar heat 

 produces an expansion comparable to that of gases. 

 According to my calcvdations, this expansion dilates the 

 radius of the concentric zones which we can distinguish 

 so well in the head of Donati's comet, at the rate of 19 

 metres per second. So long as these zones remain in the 

 interior of the surface-limit, they are not dissolved ; but if 

 they should happen to go beyond it, their material^ go 

 off at the bidding of the sun's attraction. 



Thus all the conditions of instability are found united 

 in comets. Their mass is extremely sniall, and, conse- 

 quently, the surface limit is very near the centre of gravity. 

 Their distance from the sun diminishes rapidly in the 

 descending branch of their trajectory ; consequently this 

 surface limit becomes more and more contracted. Finally, 

 their enormous volume tends unceasingly to dilate, be- 

 cause of the increasing heat of the sun, and to cause th§ 

 cometary matter to shoot out beyond this surface limit. 



What becomes of this matter after it is set free by the 

 action of the sun.' Having escaped from that of the 

 comet, it will none the less preserve the original speed, i e. 

 the speed which the comet itself had at the moment 

 of separation ; this speed will scarcely be altered by 

 the feeble attraction of the cometary nucleus, or by the 

 internal movements of which I have spoken, since these 

 are measured by a few metres per second, while the gene- 

 ral motion round the sun takes place at the rate of 10, 15, 

 20 leagues and more per second. The molecules, sepa- 

 rated and thenceforward independent, then describe 

 isolated orbits around the sun, differing very little from 

 that of the comet. Thosj which ?re found in advance 

 go a little faster and take the lead ; those which are 

 behind remain a little in the rear ; so that the aban- 

 doned materials are divided along the trajectory of 

 the comet in front and in rear of the nucleus. In time 

 these materials are separated considerably from the body 

 from which they emanate, and are more and more dis- 

 seminated ; but considered at the moment of emission, 

 they will form two visible appendages, two sorts of tails 

 opposed and stratified on the orbit of the comet. 



We touch here on the decisive point of our re- 

 search. To take the final step it will be sufficient for us 

 to consider the two figures 6 and 7. The first represents 

 the successive shapes C, C, C", which a comet must take, 

 according to the precedmg theory, if there were no other 

 force in play than that of attraction. Fig. 7 represents 

 the actual f.tct, /.<'. the forms which a comet assumes in 



