172 



KNOWLEDGE. 



May, 1913. 



as to the aphelion distance above is still true, there 

 is, in point of fact, no close approach at all. This is 

 exemplified by Halley's comet, which, having its 

 orbit inclined to the ecliptic at about 18°, never 

 passes near the path of Neptune, to whose group it 

 belongs. 



In discussing the difficulty, we must remark that 

 for " capture " to take place, it is only necessary that 

 the aphelion focus should be in the plane of the 

 ecliptic. Since this is not the case, there must have 

 been a secular rotation of the major axis, which had 

 moved the aphelion from its original position. If 

 this rotation does not exist, then the " capture " 

 theory must be abandoned. This applies to the 

 more distant comets, for Jupiter's group is generally 

 acknowledged to have been " captured," and in its 

 case the inclination is usually small. 



It is interesting to notice in the orbit of Halley's 

 comet (the only distant comet which has been verv 

 thoroughly investigated) there was a divergence of 

 two days in 1910 between the actual and calculated 

 times of perihelion passage, so that an unexplained 

 rotation of the major axis certainly exists. This is 

 not to be referred to any known mass in the solar 

 system, while an unknown mass must necessarily be 

 very considerably out of the plane of the ecliptic to 

 produce the observed results. 



At this point, much light is thrown on the subject 

 by a remarkable paper by Pickering*, which has just 

 appeared. If the translational motion of the solar 

 system through space experiences any resistance 

 from the ether, or from scattered matter, the effect 

 will be most visible in the case of comets, owing to 

 their small mass and large superficial area. The result 

 will be, that the aphelia will fall behind and will 

 tend to group themselves in a direction opposite to 

 that of the sun's motion. Pickering shows that this 

 actually takes place, and supposes that the diver- 

 gences which are visible are to be attributed either 

 to a motion of the absorbing medium, or to a curva- 

 ture in the sun's path. Here, then, is the explanation 

 of that secular motion of the major axis, which we 

 have shown to be required by the "capture" theory; 

 and the latter is, therefore, not inconsistent with the 

 facts. 



The assumption of a resisting medium naturalK- 

 raises some suspicion, for there is a danger of using 

 it as a dens ex machina, in the way of solving 

 astronomical difficulties. But it certainly exists in 

 the shape of meteoritic swarms, even if the ether be 

 itself non-resisting, and it is now fairly certain that 

 the cause of the anomalous motion of Encke's comet 

 is to be found in this direction. We may, therefore, 

 conclude that if a group of comets exists outside that 



of Neptune, it is a priori evidence for the existence 

 of a more distant planet. 



Now, unfortunately, the evidence is rather meagre. 

 GrignelH examined twenty comets, and deduced a 

 planet at a mean distance of 50-61 ; but the periods 

 of the comets are very far from certain. Comet 

 1862 III (related to the Perseid meteors) is supposed 

 to have a period of one hundred and twenty-one 

 years ; while there has been stated an identity be- 

 tween the comets of 1532 and 1661. In 1911 it 

 was pointed out that there was a distinct similarity 

 between the Kiess and Quenisset comets of that 

 year and comets 1790 I and III respectively. If 

 this could have been established, there would have 

 been much stronger evidence for the hypothetical 

 planet ; but in each case the differences were such 

 as to lead to the conclusion that the similarity was 

 merely fortuitous. It is necessary, therefore, to 

 search for comets whose periods can be irrefragably 

 shown to be in the neighbourhood of one hundred 

 and twenty -one years, i.e., they must be seen at two 

 apparitions at least. 



There have been one or two other investigations 

 concerning unknown planets. Pickering} stated 

 in 1910 that the orbits of comets and a certain per- 

 turbation of Neptune could be explained by the 

 existence of a large and very distant dark body in a 

 direction perpendicular to the ecliptic. Another in- 

 teresting suggestion is that of Professor Forbes §, 

 who gives some evidence for supposing that the 

 comet of 1556 was split into three in aphelion, about 

 the year 1702, by an ultra-Neptunian planet at the 

 the great distance of eighty-seven units. 



The conclusion reached in this paper is, therefore, 

 that the orbits of comets present the most hopeful 

 method of arriving at the unknown planet, their 

 results agreeing roughly, as to the mean distance, 

 with those derived from the perturbations of Uranus. 

 The " capture " theory is, however, only rough ; and 

 for a proper treatment it will be necessary to discuss 

 in general the motion of a comet under the combined 

 attraction of the sun and a planet. These "parabolic 

 orbits," as the)- may be called (since, for a small 

 disturbing mass, they are. approximately parabolas), 

 present enormous mathematical difficulties, even 

 compared with the case of orbits nearly circular. 

 In the lunar theory, a revolution was effected by the 

 suggestion of G. W. Hill, to treat the question as a 

 particular case of the problem of three bodies and to 

 solve by series. The parabolic case is complicated 

 by the non-convergence of any proposed series, and 

 practically nothing has been done in the way of 

 mathematical analysis. Nevertheless, it seems to be 

 a necessary step in the establishment of the existence 

 of the unknown planet. 



* "The Motion of the Solar System relatively to the Interstellar Absorbing Medium," Monthly Notices, Roy. Astr. Soc. 



LXXII. (1912, Suppl. No.) 



' See Nature, October, 1902. | See Science Abstracts, February 25th, 1911, 



j Monthly Notices, Roy. Astr. Soc. December, 1903, 



