<;KA\ ITATION 



367 



deductions Newton showed tlmt if tin- sun attracts 

 tin- earth or other planet, the direction of thin 

 .at motive force mu-t )> in tin- line joining tlieir 

 centres; from tin- lirsi and third lie proved thatitH 

 intensity must be inversely proportional to tlie 

 square of their inutnal distance (HO that at double 

 that distance the intensity of attraction would be 

 mi- I'niirtli ; at tlnee imi<-~ (lie distance, one-ninth ; 

 and -> DM ). l..-1-i l\ . the proof that the attraction is 

 |>roportional to the product of the maxses is found 

 in the fact that the weight of any l>ody is under 

 all circumstances proportional to its mass. To test 

 the truth of his deductions, Newton studied the 

 motion of the moon round the earth, and found 

 that this satellite is retained in its orbit by an 

 attraction which is exactly the same as that which 

 causes a body near the earth's surface to fall with 

 an acceleration of (about) 32'2 feet per second. 



It must, however, be remembered that Kepler's 

 laws are themselves only approximately true, 

 owing to the attraction of one planet on another 

 interfering with what might be termed the ideal 

 state of things, and thus producing those small 

 superposed motions of a planet which astronomers 

 have tormedperturbationt. But it is just in this 

 that the confirmatory proofs of the law of gravita- 

 tion are found ; for not only are all these perturba- 

 tions completely explained by its means, out they 

 have also l>een discovered and measured by it. 



The action of gravitation is independent of the 

 mi tn re of matter, thus differing from magnetic 

 attraction, which is only found in a restricted 

 class of bodies. At the same time the manner 

 in which magnetic and also electric attraction 

 depends upon distance is the same as gravitation, 

 (iravitation is not affected by the presence of other 

 matter ; in other words, the weight of a body is the 

 sum of the weights of its parts. 



The intensity of gravity at the earth's surface is 

 measured by the acceleration of a body falling 

 freelv under its influence ; it is usually denoted by 

 g. It is found, from pendulum experiments, to 

 vary slightly with the latitude, and also with the 

 height above sea-level of the observing station. 

 For any locality in the British Islands it is, how- 

 ever, little different from 32 - 2 feet per second. The 

 following table gives the value of g for several 

 places in the northern hemisphere : 





Mta, 



Latitude. 



Value of g 

 In feet per second. 



Equator V 32-091 



Paris 48 5V 32-183 



Greenwich 51 Wf 82'191 



Berlin 52 3O* 32'194 



Dublin 53 21' 32-196 



Manchester 53 29' 32'196 



Edinburgh 55* 27' 32'203 



Aberdeen 57 9' 32"206 



NtiithPole 90 y 32-255 



I 'mm these figures it will be seen that a body 

 apparently gains weight as it is carried from the 

 equator to higher latitudes. This is due to two 

 causes. First, owing to the ellipsoidal shape of 

 the earth, gravitational attraction at the poles is 

 iJ , greater than at the equator; (2) owing to 

 the ' centrifugal force' of the earth's axial rotation, 

 bodiM at the equator are ,| ff lighter than at the 

 jK>les, where this cause does not affect their weight. 

 These two fractions together make up the differ- 

 ence, T ii, between equatorial and polar gravity. 

 The fraction denoting diminution of weight due to 

 the centrifugal for.-.- of the earth's rotation, may be 

 employed to find at what speed the earth would 

 need to revolve in order that gravity would just be 

 balanced by 'centrifugal force.' It is found that, 

 to fulfil this condition, the earth would require to 

 revolve at seventeen times its present speed ; when 

 revolving at this rate bodies would not have any 

 tendency to remain on the earth's surface, and with 



an increased speed they would be projected into 

 -pace. Taking also into consideration tin- diminu- 

 tion of gravity with increiiHe of height, the value of 

 terrestrial gravity in expressed by the formula a = 

 :<_' 1 7.'{ <*_> c, ,s '-2 >. -OOOOO.S It where >. in the lati- 

 tude, and h the height, in feet, above sea level. It 

 must be remembered that this value of tj in different 

 from that which would be obtained were there no 

 axial rotation of the earth ; under the latter cir- 

 ' 11 instances, the value of gravitational attraction 

 alone would be y = 32 '525 - '026 COH 2 X. 



To account for the phenomenon of gravitational 

 attraction several theories have been advanced ; 

 but in spite of the best efforts of mathematicians 

 and physicists, the real cause remains undiscovered. 

 Nor is there any physical reason in evidence of the 

 tnith of the several assumptions upon which these 

 theories have been based. As Clerk-Maxwell has 

 pointed out, their chief value lies in their suggestive- 

 ness, and in there being an incentive to the deeper 

 and more prolonged research after possible causes 

 for gravitation. The earliest speculations on the 

 subject were, of course, almost wholly metaphysi- 

 cal, and therefore misleading, if not absolutely 

 erroneous. To begin with, tlie assignment of an 

 attraction between the earth and sun as the cause 

 of the earth's motion was set down as being 

 impossible, on the plea that a body could not act 

 in the place where it was not. Again it was urged 

 that such a cause would be simply ' action at a 

 distance,' and hence impossible. Newton's only 

 speculation on the subject showed that he looked 

 to some intervening medium as the agent by means 

 of which attraction between bodies was exerted ; 

 that if bodies rarefied this medium round them at 

 a rate lessening as the distance increased, gravita- 

 tional attraction might thus be accounted for. 

 Another hypothesis, and one of an entirely novel 

 kind, was put forward in 1818 by Le Sage. He 

 piesupposeu that space contains an exceedingly 

 large number of small bodies moving rapidly in all 

 directions. To these bodies he gave the name of 

 ultramundane corpuscles. They would impinge 

 upon any single isolated body in space in all 

 directions, the result being that the oody would 

 not be moved, the impacts oeing equal on both its 

 sides. But with two bodies in space, one would 

 screen the other from a certain number of blows, so 

 that on their opposed faces there would be a fewer 

 number than on their distant faces ; in consequence 

 of this excess of impacts on one side over those on 

 the other, each body would tend to move towards 

 the other. The attraction between the two would 

 be inversely as the square of their distane, and 

 proportional to the surface of the bodies resolved 

 normally to the line joining their centres. So that 

 if mass be proportional to surface, there should be 

 coincidence between the results of the hypothesis 

 and the observed law. The chief objection to this 

 hypothesis is that it would require not only that 

 the corpuscles be infinitely small compared with 

 the molecular distances in ordinary matter, but 

 that they move at a speed enormous compared 

 with anything we are acquainted with. Moreover 

 the amount of energy required to maintain the 

 gravitational attraction of a comparatively small 

 body near the earth's surface would, if converted 

 into heat, be sufficient to raise the earth to the 

 temperature of incandescence. Sir William 

 Thomson has shown that gravitation might be 

 explained 1>\ the a-- umption of the existence of an 

 incompressible fluid filling all space, being either 

 created in each particle at a rat* proportional to 

 its mass, and flowing off everywhere to an infinite 

 distance ; or by each particle absorbing a quantity 

 proportional to its mass, the supply coming in all 

 directions from an infinite distance. Another 

 method of accounting for gravitation is that of 



