268 



NA TURE 



[Aug. 6, 187 



W^ 



THE FORM OF COMETS* 

 III. 

 ''E are now arriving at a conclusion, for the condi- 

 tions mentioned are very narrow. In order that a 

 force exerted by the sun may present at any point what- 

 ever of the trajectory of a moving body these two radial 

 and tangential components, it is sufficient, and it seems 

 to me absolutely necessary, that this force should not be 

 propagated instantaneously like attraction, but succes- 

 sively, i.e. at a definite rate. In order that it may drive 

 to a distance the rarest materials of comets, at the same 

 time exerting only an extremely weak action upon their 

 much more dense and more compact nuclei, it is necessary, 

 and it is sufficient, that this force should be one of surface 

 and not of mass, like attraction. If the light of the sun 

 werejdue, as was long believed, to 'the emission of innu- 

 merable atoms moving at the rate of 77,000 leagues a 

 second, the force exerted by these atoms would fully 

 satisfy these conditions. Unfortunately, the emission hy- 

 pothesis has been sh^wn to be false, and is now replaced 

 by that of the undulations of an imponder.able fluid on 

 which attraction has no hold. If statical electricity, in 

 order to produce attractions and repulsions, had no need 

 of a particular material medium, such as our atmosphere, 

 we might perhaps be able to call in the aid of that force ; 

 but it would still be necessary to prove that the sun is 

 electrical, and that it is able to develop a very marked 

 e'ectric state in comets without acting similarly upon 



other bodies. As to magnetism, which appears indepen- 

 dent of any medium, wc know very well that it is not a 

 surface-action, but an entirely specific force, capable of 

 attracting or repelling the densest materials ; and besides, 

 the phenomena of terrestrial magnetism scarcely leave 

 room for attributing to the sun a magnetic power sensible 

 at such distances. Finally, electricity and magnetism 

 are polar forces which impart to bodies opposite powers 

 of attraction and repulsion, while cometary phenomena 

 argue only a simple repulsive force. 



There remains the repulsive force of solar heat. In 

 all bodies heat gives rise to a force among the molecules 

 which tends to separate them more and more ; it is this 

 which enables our steam-engines to work, and which 

 forces projectiles from our guns. It is evidently a sur- 

 face-action, and not one of mass ; and at least, in main- 

 taining that it is sensible only between the molecules of 

 bodies, i.e. that its sphere of action is infinitely small, it 

 is natural to think that the surface of a heated body 

 exerts its repelling action all round it, as well as towards 

 the interior. Moreover, there is nothing opposed to the 

 supposition that this force is propagated successively, 

 since its cause, heat, is itself propagated in planetary 

 space with a definite speed, that of light. 



Here is our hypothesis formulated. By introducing 

 this repulsive force, acting by successive propagation, into 

 • CoQtLQued from p. 248, 



the differential equations of the movement of comets, 

 along with that of attraction, we see that there springs 

 from them the established phenomenon of their accelera- 

 tion with its most delicate characteristics.* The analysis 

 which I made has been latterly revised and verified by an 

 illustrious Italian geometer, M. Plana, with developments 

 which leave nothing to be desired in point of mathemati- 

 cal rigour, while the hypothesis of a resisting medium 

 starts, as I have said, with conditions incompatible with 

 the principles of mechanics. It only now remains for us 

 to see whether the same force will also account for the 

 highly complicated phenomena of the figure of comets. 



Let us set out from this distinctive characteristic : — 

 The repulsive force exercised at a dist.ince by the 

 incandescent surface of the sun is a surface-action, 

 the more capable of driving off a body, the smaller the 

 density of the body is. According to an estimate deduced 

 from the observed acceleration of Encke's comet, it will 

 be sufficient to reduce, in the proportion of 1,000,000 to i, 

 the density of the nucleus of that comet to represent the 

 excess of this repulsive force over attraction. The ques- 



tion, then, is, to discover if such great variations of density 

 are exhibited by tlie various appendages of comets, of 

 which the most compact parts ha\e already so small a 

 mass under so enormous a volume. But this is precisely 

 what facts establish in the most exact and striking manner. 

 The figure of Donati's comet, which 1 am about to bring 

 before you, shows that the nucleus, in proponion as it is 

 subjected to the heating action of the sun, emits vapours 

 which go on dilating more and more, so as to form around 

 the nucleus envelopes having a radius ten or even a 

 hundred times greater. But if the matter of a sphere with 

 a radius equal to i expands into a sphere having a radius 

 equal to 100, it is sufficient to make the density become 

 one million times less. In fact, .all the matter of the 

 nucleus is not thus disseminated in the head of the comet ; 

 this dilatation affects only a very small portion of the 

 primitive mass, and we see how the density of the extreme 

 layers of the head may fall much bslow the figure given 

 by the above calculation. 



* The progres-^ive change of two elements alone, to wit, me.ia motion and 

 eccentricity : nothing on the position of the plane of the orbit : for the rest, 

 simple periodic inequalities scarcely sensible, but differing, however, from 

 those \»hich the resistance of a medium would givi. 



