July 1, 1896.] 



KNOWLEDGE. 



157 



that Schulhof at once, without waiting for additional 

 ohservations, assumed a period very nearly that which 

 BruDuowhad assigned for the 18 i4 coraet, and recomputed 

 elliptic elements which subsequent care and additional 

 information have not materially improved. Here is the 

 first link in the chain of evidence, namely, that the motion 

 of Swift's comet can be represented by elements whose 

 period is suggested by that of De Yico's comet. But fifty 

 years is a long time, and many alterations more or less 

 serious must be expected to take place in the pure elliptic 

 motion of a comet which runs very nearly in the plane of 

 the ecliptic, and must cross and recross the orbits of Mars 

 and Jupiter several times, with the chance of approaching 

 those planets more or less closely. To compute the pertur- 

 bations of a comet for fifty years is a task which, though 

 it would effectually remove the objection, is not lightly to 

 be undertaken ; and to enter upon such an enquiry we 

 want what we have not got — either very accurate know- 

 ledge of the elements in 1H44, or the present condition of 

 things in 1894. Errors accumulate with the time. Dr. 

 Brunnow had assigned 5-') years for the period of 

 De Vico ; Schulhof preferred 5-8 years for Swift. So far 

 as these figures go, at each return the error would be 

 increased by three-tenths of a year. But mathematical 

 analysis has been able to indicate the direction that pertur- 

 bations will take without the labour of actual calculation, 

 and it has been demonstrated by M. Callandreau that in 

 the case of a comet having a small inclination to the plane 

 of the ecliptic, and moving about the sun in the same 

 direction in which the planets revolve, the action of the 

 planets will continually tend to increase the longitude of 

 the perihelion and diminish that of the node. Fortu- 

 nately the means were at hand to settle this question. 

 Le Verrier had believed that the comet of 1844 was the 

 reappearance of one that had been seen in 1678. If this 

 be the case, the fact that it lay dormant, so to speak, for 

 so many years is typical of its more recent behaviour ; but 

 in investigating this question Le Verrier had carried back 

 the perturbations and supplied elements for various dates 

 in its past history. We are simply concerned in the 

 motion of the perihelion and the node, and for these Le 

 Verrier gives 



while M. Schulhof's hastily computed element gives 

 For 1894 345' 20' 43° 41' 



Here we have clearly exhibited the direct motion of the 

 perihelion and the retrograde motion of the node, 

 tending to complete the train of evidence in favour of 

 identity. But the argument is not yet complete. Dr. 

 Bruimow's elements showed that De Vico's comet 

 should approach Jupiter towards the end of 1885. Dr. 

 Schulhof's elements show that the 1894 comet was 

 actually near Jupiter in 1885-80, and this might well 

 explain the alteration of the period from 5-5 years to 5'8 

 years. 



At this point Prof. Chandler, whose name is so well 

 known in connection with the variation of geographical 

 latitude, took up the subject ; and after having improved 

 the elements by incorporating Prof. Barnard's latest 

 observations, computed the perturbations of the comet 

 back to the time before the last approach to Jupiter 

 occurred. It is not possible to compute these perturbations 

 with absolute certainty, because the unavoidable errors in 

 the elements do not permit the distance of the comet from 

 Jupiter — on which, of course, the amount of disturbance 



Actual 

 Orbit, 



depends — to be determined with accuracy. The result of 

 his calculations, however, is to show that all the elements 

 have a tendency to approach those that Dr. Briumow 

 assigned in 1S44, when brought up to the same date. 

 These are given side by side. In the first column are 

 Brunnow's elements brought up to 1882 ; in the second 

 the most probable elements that can be assigned before 

 the very considerable perturbations by Jupiter were 

 effected ; in the third the most trustworthy elements 

 Prof. Chandler could derive from the inadequate materials 

 at his hand. 



Before 

 Bnu:uow,1^2. Perturbation, 

 1883. 



Are between perilielioii liud node 278° 49' 283° 7' 296» 3-t' 



Longitude of nwle 64" 20' eO" 24' 48=- 41' 



Inclination to ecliptic 2° 55' 2" 53' 2" 58 



Eceentricitr 061765 060282 Oo7190 



Nearest approach to sun . l-l?64 1-254S 1-3920 



Period in years ... ... ... 5466 5'615 5863 



Here the agreement is very satisfactory and grati- 

 fying, since the greater part of the observed difference 

 between Brunnow's orbit (1844) and Chandler's (1894) 

 has disappeared. 



There still remains the question. Will time fight on our 

 side, and by adding fresh information remove any shadow 

 of doubt which hangs over the question of identity ? 

 Evidently, if we should see the comet again six years 

 hence, we could get a very accurate idea of the mean 

 motion, and so trace back the path of the comet with 

 greater certainty. We have, however, to face the fact that 

 in 1897 a still closer approach to Jupiter is certain ; and Mr. 

 Chandler, in summing up the probability of the new con- 

 ditions under which the comet will find itself, says : " I am 

 inclined to anticipate that, with the present appearance, 

 our acquaintance with this interesting body will unfortu- 

 nately be brought to an end. The present perihelion 

 distance wiU probably be changed by Jupiter in ls!)7 to 

 one considerably beyond the orbit of Mars, so that unless 

 a favourable reversion of the change in brilliancy which 

 apparently took place between 1844 and ls'.)4 should occur, 

 it will in all likelihood hereafter be invisible ; at least 

 until, at some future approach to the critical point of dis- 

 turbance near longitude 165°, simultaneously with Jupiter, 

 it shall be thrown into a path in which, near perihelion, 

 it will be again in reach of our telescopes.'' 



I have dealt with this comet at length because it offers 

 a typical instance of the difficulties and of the degree of 

 success that attend inquiries of this nature. The history 

 contains all the uncertainties that arise from imperfect 

 knowledge of the actual path in which the comet is moving 

 at the time of observation, the laborious nature of the 

 arithmetical calculations involved, and of the uncertain 

 element that lapse of time introduces. There is, it is true, 

 another test, easy of application, known as •' Tisserand's 

 criterion;" but this test, for reasons which I shall hope to 

 explain hereafter, is peculiarly apt to speak with uncertain 

 sound. I have not introduced it here, though applicable, 

 for its use can be better illustrated in the case of some of 

 the other comets of which mention has been made in the 

 first paragraph. In the case of De Vico's comet, here 

 considered, it will be admitted that the final result appears 

 gratifying; but no light is thrown on the further interesting 

 question of actual identity as opposed to an intimate con- 

 nection. In the present state of our knowledge, or of our 

 ignorance, of the internal constitution of comets, it is not 

 possible to apply mathematical analysis. The problem 

 presents itself simply as one of disturbed elliptic motion, 

 and the interest turns on the ingenuity with which various 

 astronomers have successfully encountered and overcome 

 the intricacies of the subject. 



