Oct. 12, 1883.] 



KNOWLEDGE 



227 



certainty about this result, and the consequence is obvious. 

 If we have the means of weighing the earth in comparison 

 with the sun, then the distance of the sun can be imme- 

 diately deduced. 



How, then, are we to place our great earth in the 

 weighing scales 1 This is the problem which Leverrier has 

 shown us how to solve, and he does so by invoking the aid 

 of the planet Mars. If Mars in his revolution around the 

 sun were solely swayed Vjy the attraction of tlie sun, he 

 would, in accordance with the well-known laws of planetary 

 motion, follow for ever the same elliptic path. At the 

 end of one century, or even of many centuries, the shape, 

 the size, and the position of that ellipse would remain 

 unaltered. Fortunately for our present purpose, a dis- 

 turbance in the orbit of Mars is produced by the earth. 

 Although the mass of the earth is so much less than that 

 of the sun, yet the earth is still large enough to e.xercise an 

 appreciable attraction on Mars. The ellipse which Mars 

 follows is not always the same. The shape of that ellipse 

 and its position gradually change, and the position in 

 which the planet is found depends upon the mass of the 

 earth. The place in which the planet is found can be 

 determined by observation ; tlie place which the planet 

 would have had if the earth were absent can be found by 

 calculation. The difference between the two is due to the 

 mass of the earth, and when it has been measured the mass 

 of the earth can be ascertained. The amount of displace- 

 ment increases from one century to another ; but, as the 

 rate of growth is small, ancient obser\'ations are necessary 

 to enable the measures to be made with accuracy. 



A remarkable occurrence, which took place more than 

 centuries ago, enables the place of Mars to be determined 

 with great precision. On the 1st of October, 1672, three 

 independent observers witnessed the occultation of the 

 star ip Aquarii by the planet Mars. The place of the star 

 is known with accuracy, and hence we are provided with 

 the means of accurately defining the point on the heavens 

 occupied by Mars on the day in question. From this 

 result, combined with the modern meridian observations, 

 we learn that the displacement of Mars by the attraction 

 of the earth has in the lapse of two centuries grown to 

 about five minutes of arc (29-t seconds). It has been 

 maintained that this cannot be erroneous to the extent of 

 more than a second, and hence it would follow that the 

 earth's mass is determined to within one three-hundredth 

 part of its amount. If no error were present, this would 

 give the sun's distance to about one nine-hundredth part 

 part, which approaches very closely to the limit we have 

 indicated. 



Notwithstanding the intrinsic beauty of this method, 

 and the very high auspices under which it has been intro- 

 duced, it will, I think, hardly be found to fulfil all the 

 needful conditions. We make no impeachment of the 

 fidelity of the observations, and we feel no doubt that the 

 displacement of the planet is mainly, if not entirely, due to 

 the disturbing effect of the earth's attraction ; but it seems 

 quite impossible to be sure that some other cause, minute 

 though it must be, may not also have contributed to the 

 result. We cannot be absolutely sure that the theory is 

 above suspicion. Interesting and beautiful though this 

 method may be, we must rather regard it as a striking 

 confirmation of the law of gravitation than as aflbrding an 

 accurate means of measuring the sun's distance. 



Several other methods have been employed by which we 

 can place the earth in the weighing scales. Perhaps none 

 of these methods is free from objection as a means of 

 measuring the sun's distance. I must, however, mention 

 one of them which has special claims on our attention of a 

 very peculiar kind. 



This time we invoke the aid of that erratic member of 

 our system known as Encke's comet. The comet com- 

 pletes a circuit around its ellipse in a period but little more 

 than three years. It does not, however, move with uniform 

 velocity. Around the remote part of its path the comet 

 creeps languidly ; but as it turns round and commences to 

 approach the sun the 'pace gradually improves, and the 

 comet itself swells up in dimensions and in splendour. 

 Encke's comet, although so famous, is one of that numerous 

 host of telescopic objects which seldom or never become 

 bright enough to be visible to the unaided eye. It 

 can only be seen when comparatively close to the sun. 

 All around the outer part of its path it \ totally 

 invisible in the most powerful telescope. The comet 

 itself is shown here. It is a dull hazy spot of light, 

 evidently composed of materials of a filmy, or almost 

 spiritual texture. A great comet is usually attended by a 

 long tail. This small telescopic comet is not so decorated. 



Notwithstanding the insignificance of Encke's comet, it 

 is capable of giving us very interesting information ac- 

 quired during its somewhat eccentric travels through the 

 solar system. It is, for instance, able to weigh the earth, 

 and thus to aflford the means of measuring the sun's dis- 

 tance. The elliptic path which the comet describes is, of 

 course, mainly due to the preponderating influence of the 

 sun's attraction. If there were no source of disturbance 

 the comet must follow that eclipse inflexibly and never 

 deviate therefrom. But the planets insist on asserting 

 their power, the orbit of the comet is disturbed, and that 

 orbit is so eccentric that the disturbances occasionally attain 

 to enormous dimensions. 



For instance, when the comet draws near the sun it 

 passes very close to the track of Mercury. It has happened 

 that the comet ariives at Mercury's orbit at the same 

 moment that Mercury arrives at the comet's orbit. Such a 

 rencontre may bring the comet and the planet within a 

 couple of million miles, which is quite an insignificant 

 distance in measures of this description. In such a case 

 the comet and the planet attract each other with vehe- 

 mence. The solid mass of Mercury drags the comet from 

 its path, though the flimsy and unsubstantial comet can 

 impress no measurable disturbance on the movements of 

 Mercury. In its outward career the comet sometimes 

 approximates to Jupiter, in which case the great planet 

 contributes its potent aid to the derangement of the comet. 

 The earth, also, although its path lies more distant from 

 the track of the comet is still able to contribute a little 

 further disorder, so that the path which the comet really 

 pursues is one of amazing complexity. It is the task of 

 the astronomer to .survey that path, to determine its shape 

 and its position, and to ascertain the epochs at which the 

 comet accomplishes each successive stage on its never- 

 ending journey. 



This work being done, the problem is now one for the 

 mathematician. It is for him to decompose the complicated 

 movement into its constituent elements. He discriminates 

 first the great elliptic motion due to the attraction of the 

 sun. Superimposed on the elliptic motion he finds the 

 smaller and more perplexing movements due to the plane- 

 tary disturbance. He can disentangle the eU'ect due to the 

 earth's attraction from that due to Mercury and to Jupiter. 

 This work has been done in a masterly manner by the late 

 distinguished Russian astronomer Von Asten, and he has 

 elicited the mass of the earth from a most recondit«< 

 inquiry, embracing some twenty complete revolutions, 

 during which thecomet has been observed. It would, 

 liowever, be unwise to assign much weight to the distance 

 of the sun, which may bo "deduced from these researches. 

 Notwithstanding the labours of many astronomers, the 



