Aug. 6, 1874] 



NATURE 



269 



- JWe shall understand better what precedes by examining 

 tor a little in detail some phenomena presented by the 

 head of the comet of 1858, at the time when the already 

 formed tail was continually fed by materials emitted by 

 the nucleus, and carried away by solar repulsion. (See 

 Fig. 8.) 



The concentric zones of a decreasing brightness, which 

 are noticed around the nucleus, on the side next to the 

 sun, are due to an intennittent emission of matter. This 

 matter is seen to dilate more and more with a very mode- 

 rate initial speed of about 19 metres per second, and 

 finally to reach the limits of the head of the comet ; a 

 second, a third, &c. emission closely follow the first, and 

 are developed in the same manner. The brightness, at 

 first very marked, of these successive envelopes of the 

 nucleus grows rapidly weaker in proportion as their density 

 diminishes. Finally, in the exterior layers, the more and 

 more rarefied materials become the prey of the solar re- 

 pulsion, which makes them turn back, driving them 

 towards the tail at a rate incomparably greater than the 

 former, for in twenty-five days the tail of Donati's comet 



had reached a length of 14,000,000 leagues ; it increased 

 in length at the rate, not of 19 metres, but of 8 leagues 

 per second. I showed, at the outset, to what excessive 

 rarefaction the materials of these immense appendages 

 attain. 



You see that upon such materials a surface-action like 

 the repulsive force must have beautiful play, while the 

 solar attraction, independent of the suiface and density, 

 t continues to act in the same manner upon all these mole- 

 cules. The struggle, then, between these two forces will 

 turn in favour of the former as soon as the progressive 

 dilatation of the cometary matter, gradually spreading 

 itself in surrounding space, will have brought it to a cer- 

 tain degree of diffusion, and there is nothing to hinder the 

 repulsive action thus becoming twice, three times, even 

 ten times more powerful than attraction. 



From the fact that this force, or rather that the radial 

 component of this force, acts in the direction of the 

 radius vector, from the fact that the expelled molecules 

 preserve very nearly the tangential speed which the comet 



possessed, it necessarily results, as we shall see, that the 

 tails, from the first, must be opposite to the sun and bent 

 in a backward direction. 



Fig. 9 represents the successive positions of a series of 

 molecules emitted by the nucleus of a comet so as to 

 constitute the axis of the tail. In this figure, we suppose 

 for the molecules a density such that the repulsive force 

 exactly counterbalances the solar attraction : thus their 

 motion, solely due to the tangential velocity of the comet, 

 takes place in a straight line. To simplify matters, this 



rate has even been supposed constant, as if the orbit 

 were a circle. 



On the first day, the comet being at O, a molecule ;«^ 

 is detached and subsequently follows the line ;«■ in^ /ii\... 

 On the second day, a molecule ;/;-, likewise leaves the 

 nucleus at C-, and subsequently describes the tangent 

 w- m' /«-... .Similarly, on the third day, for a mole- 

 cule m^, and so on. If we join by a continuous line the 

 series of positions occupied at the same time, the fifth 

 day, by all these molecules ///', w', ///■'. w", "/', we shall 



Fig. I-'. 



have the curvilinear axis of the tail ; this will be, in this 

 particular case, the involute of a circle. This constructicn 

 accounts for the three laws which have been ascertained 

 as the result of observation : — i. The tail, at its origin, is 

 sensibly opposed to the sun, S ;* 2. The tail is curved 

 backwards on its path ; 3. The axis of the tail is a 

 plane curve situated in the plane of the orbit. 



If the density of these molecules were still smaller, the 

 repulsive force would prevail over the solar attraction, and 

 these molecules would describe no longer straight lines. 



but sections of an hyperbola whose convexity would be 

 turned towards their common focus, S. (See Fig. io.)j 



The series of points //i', m'\ in\ /«*, emitted at C, C-, 

 Q?, C^, by the comet, gives yet another curve like the 

 former, but with a curvature much less pronounced and 

 nearer to the radius vector. 



There results from this theory a consequence to which 



adius 



* In reality thi 

 vector ; it makes 

 but which I thin 

 plicity. 



axis of the tail is not rigorously tangential at C^ to tl 



/ith this radius a small angle lor wlncll the theory accouats, 



may be neglected here for the sake of brevity and sim- 



