152 



• KNOWLEDGE • 



[March 9, 1883. 



■T:(T- 



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 AND DIRECTED ENVELOPE BE ENCLOSED. 



ON THE FOEMATION OF COMETS' TAILS. 



[747]— In the December number of the Philosophical Magazine 

 for 1878, I propounded a theory to account for the repulsive force 

 on the matter forming a comet's tail, which agrees in all essential 

 respects with that published by Mr. Eanyard in Knowledge for 

 Feb. 16, 1883. 



The calculation of the repulsive force due to evaporation was there 

 given for the first time. When I wrote my paper, I was not aware 

 that the force arising from evaporation had been previously sug- 

 gested as a possible explanation of the phenomenou, but in a letter 

 received from Mr. Ranyard, shortly after my paper was published 

 he informed ^me that at a meeting of the Royal Astronomical 

 Society in 1874, he had said something on the subject of my paper, 

 of which an account was given in the March number of the 

 Astronnmical Register for 1874, but he stated that he had not 

 eutered into a discussion of the magnitude of the force, as I had 

 done, nor did he know of any evaluation of the accelerations which 

 might be caused by evaporation, such as I had attempted. I was 

 surprised therefore to find that in his paper, in which he is pre- 

 sumably putting forward original views, ho enters into a discussion 

 as to the adequacy of the force of evaporation to produce the 

 repulsion observed, which, in so far as it is correct, is the same as 

 that previously published by me. 



The following is a quotation from my paper in 'which the same 

 reasoning is employed as that given by Mr. Ranyard, though in a 

 more complete and correct form : — 



"In the first place the mass of a comet is so small, that the force 

 of gravitation towards the centre on any of the bodies at some dis- 

 tance from the nucleus must be so small that it may be left out of 

 consideration. We know that a molecule of matter in the gaseous 

 condition has at ordinary and high temperatures a very quick mo- 

 tion of translation. A molecule, as it evaporates from the surface 

 of one of the bodies composing the comet, must acquire a velocity 

 relative to the body of several hundred yards j)er second. The 

 body must, in consequence, suffer a recoil'in an opposite direction 

 to that in which the molecule escapes. Now, since the evaporation 

 is caused by the sun's heat, it must take place chiefly on that side 

 of the body which is exposed to the sun's rays. The resultant 

 effect of all the small recoils due to the evaporation of the differ- 

 ent molecules will therefore be to drive the body in a direction 

 away from the sun. If the body has a motion of rotation, the 

 whole surface might in turn become exposed to the sun's rays, and 

 evaporation would probably take place even on the side turned 

 away from the sun. But unless the body be of a regular shape, 

 the effect of evaporation will be to gradually stop any rotation 

 which it might at first have ; for the force of recoil from the 

 evaporation would act upon it in the same way as the wind does on 

 a vane, and it would at length take up a position with its longest 

 axis in the direction of the sun. 



"Now let V be the average velocity relative to the bodv with 

 which the molecules escape from it. Let M be the mass of the body 

 just before the escape of a molecule of mass /x from it. Then the 



velocity due to the recoil as this molecule escapes will be —v. 



Now the molecules as they evaporate will start off in various 



dircctiong, but almost always more or less towards the sun. Let 

 us suppose, as being not far from the truth, that the inclination 

 which their directions have to a straight line passing throagh the 

 sun is on the average 45° ; then the average velocity due to recoil 

 acquiied by the body on the evaporation of mass dm will be 



— . , and the velocity acquired while the mass of the body is 



m ../'I 

 being reduced by evaporation from m, to m.,. will be 



V /''"id»>i ,, , /.„ . m, 



-_ / ' V X l-Oa X logic— '. 



>J I J -i m Wj 



Now the average velocity of hydrogen molecules at 0° C. is 1'06, of 

 oxygen •206, and of water vapour So mile per second. For the 



sake of illustration, let us suppose that 'V^ = '35, and — .'=1000000, 



these being the values we should have to assign if the body were 

 block of ice containing one gramme of sand or any other non- 

 volatile substance, the block itself being equal in mass to a cubic 

 metre of water. The velocity due to recoil by evaporation would 

 then bo 342 miles per second, or about 295,000 miles per day. A 

 tail would thus be formed which would increase in length nearly a 

 million miles in every three days. The visible portion of this tail 

 would consist of solid or liquid matter which had resisted evapora- 

 tion ; but there would also be present in the tail a large portion of 

 the gas formed during evaporation ; for since the evaporating gas 

 has a velocity relative to the body from which it is evaporating 

 of '35 mile per second, those portions of the gas which have 

 evaporated since the body acquired by recoil a velocity greater 

 than "35 mile per second will be also carried backwards into 

 the tail. The estimate of the rapidity of tail-formation I have 

 just made has been made on the supposition that the temperature 

 of the escaping gas is 0° C. If the absolute temperature in Centi- 

 grade units of the gas be t, we must multiply the ai)ove estimate by 



Now, in no case has the rapidity of tail-formation 



greatly exceeded one million miles in three days, except in the case 

 of those comets which have approached very near to the sun, and 

 where, consequently, the temperature at which the evaporation has 

 taken place must have been very great." 



The expression given by Mr. Ranyard for the velocity of the 

 evaporating body, or particle, after half its substance has evaporated, 



. V . \ 



IS — , I.e. 



1-42 ^/2 



It will be see from my formula given above, that putting — != 2, 



V 2^- 



the correct expression is — > 



Nap. log 2, or -^ X SSS. 

 v/2 



Mr. Ranyard has apparently assumed that the effect of the 

 successive evaporations of the different particles would be the 

 same as if all the particles had parted from tlic evapo- 

 rating body at the same moment ; but this would not be 

 so, for in the latter case all the evaporating particles would 

 acquii-e a velocity, "V, relative to the evaporating body, and, there- 

 fore, also relative to the general mass of the comet, whilst in the 

 former case the particles evaporating after the body had acquired 

 a backward motion, though they would still have a velocity, Y, 

 relative to the body, would have a different velocity relative to the 

 general mass of the comet. The momentum produced in the un- 

 evaporated portion being in both eases equal and opposite to the 

 resultant of the momenta of all the evaporated particles, must be 

 less in one case than in tlie other. 



There are some other considerations relating to this evaporatioB 

 theory which I hope to be allowed to lay before your readers in 

 some future number of Knowledge ; but I must not now trespass 

 further on your space. Arthur S. Davis. 



Cheltenham College. 



PURIFYING GAS. (?) 



[748] — A correspondent referring to the statement in Knowledge, 

 No. 67, of February 9, 1883, page 85, 1st col., 2ud par, regarding 

 the Albo-Carbon Light Co., that each " Burner is accompanied with 

 a means for piiri/i/i)!;?," &c., writes as follows: — 



" As a gasman who has been in communication with their agent, 

 allow me to say that the essence of the patent is the addition of 

 something, say naphthaline, to the gas in transit from the service- 

 pijjo to the hurner, whereby the illuminating power is slightly in- 

 creased. The something in question does not contain any chemical 

 absorbent capable of catching any impurity, say ammonia, or 

 sulphur, or carbonic acid; and it is not necessary, as the gas is 

 tested daily, and often by a chemist duly appointed, and whose 

 certificate, no doubt, is to bo had in pursuance of Act of Parlia- 



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