1910] on Halley's Comet. l^^l 



time to make calculations of the effects which Jupiter and Saturn 

 would actually produce, though the planets Uranus and Neptune, 

 which also contributed something to the perturbation, were as yet 

 undiscovered. These calculations foreshadowed a greater delay than 

 had been anticipated, and the comet did not return to perihehon until 

 1759. But the delay, the causes of which Halley had so expi-esslj recog- 

 nized, really added fresh laurels to his success in prediction. The comet 

 went round once again, and reappeared in IsSo : once again, and has 

 come back to us once more. It has been photographed and seen in 

 telescopes of moderate power. In May, we hope it will be easily seen 

 with the naked eye. Until recently the calculations of the circum- 

 stances of return had been chiefly made by foreign astronomers, but 

 for the present return, Messrs CoAyell and Crommelin of the Royal 

 Observatory at Greenwich have outdistanced all competitors and been 

 awarded the prize of the Astronomische Gesellschaft for their most 

 successful prediction. They used special methods for the work, such 

 as had been devised shortly before by Mr. Cowell for dealing with the 

 exceptional case of the tiny eighth satellite of Jupiter. To understand 

 the difficulties and the method of meeting them, let us recur for a 

 moment to the statement of the law of gravitation, and consider what 

 it means in detail. Suppose we are at a distance of IG feet* from an 

 attracting centre and tind the pull is 1 lb. If we halve the distance, 

 i.e. go 'S feet nearer, then the pull is 4 lb.; if we go 4 feet nearer 

 (halving the distance again), the pull is 10 lb.; 2 feet nearer and it 

 is 64 lb.; 1 foot nearer and it is 25 G lb. Notice particularly that as 

 we approach the centre the force is not only itself greater, but in- 

 creases more rapidly. At 16 feet distance, an error of 1 foot would 

 not much matter : at 2 feet distance it makes the enormous difference 

 Ijetween 64 and 256 lb. pull. 



From the great increase in the force itself in the neighbourhood 

 of the attracting body, it is readily understood that when a body, 

 such as the moon, is very close to the earth, and remote from the 

 sun, the attraction of the earth, in spite of its much smaller mass, 

 affects the motion more than that of the sun ; and the motion of 

 the moon is thus mainly controlled by the earth. Although we 

 cannot solve the problem of the movements of these three bodies (or 

 any other three) in finite terms, we can solve it by a series of approxi- 

 mations. First we may suppose the sun non-existent, when the moon 

 will describe an elhpse round the earth in a focus. Next we may 

 consider how the distant sun disturbs this elhpse ; but then we 

 immediately find troubles arising from the second feature of the law 

 of gravitation above noticed — the fact that a slight change of posi- 

 tion of an attracted body, when near a centre of attraction, makes a 

 large difference in the attraction. The disturbance of the moon 

 from its elhpse by the sun may be shght, but it alters considerably 



* These figures were illustrated by a practical experiment. 



