NA TURE 



[August 2. 1 ^494 



aV THE NEWTONIAN CONSTANT OF 



GRA VITA TIONy 



I. 



IT is proliably within the knowledge of most of those present 

 that Sir Isaac Newton, by his great discovery of graviia 

 tion and its laws, was able to show that a single principle, 

 ideally simple, viz. that every particle in the universe attracts 

 any other particle towards itself with a force which is » propor- 

 tional to the product of their masses divided by the square of 

 the distance between them, would completely and absolutely 

 account for the three laws of planetary motion which Kepler 

 had given to ihe world. 



Newlon also showed that a spherical body, whether 

 uniformly dense or varying in density according to any law 

 from the centre to the surface, would attract bodies outside with 

 the same force that it would do if it could all be concentrated 

 at its centre, i.i.-. that all the attractions varying in amount and 

 direction produced by particles in all parts of a sphere need not 

 be considered separately, but may be treated in this simple way.' 

 Nevertheless, though Newton's great discovery is sufficient 

 to bring the whole of the movements of the planets and their 

 satellites, whether their simple Keplerian motions or the dis- 

 turbances produced by their mutual gravitation, the motions of 

 comets, of binary stars, of the tides, or the falling apple, under 

 the domain of a single and simple principle, though it enables 

 one to compare the masses of the sun, the planets and their 

 satellites, and of those binarj' stars whose parallax has been 

 determined, one thing can never be made known by astro- 

 nomical research alone, though we may know that twenty-eight 

 suns would be required to make one Sirius ; that the sun is I 

 equal to 104S Tupiters, that Jupiter is more than double all the 

 rest of the solar system put together, or that the moon is I So of 

 the earth ; no observations ol these bodies can ever tell us how 

 many tons of matter go to make up any one of them. 



Though we know from first principles of dynamics, by the 

 mere consideration of centrifrugal force, that the whole sun 

 attracts each ton of the earth with a lorce equal to a weight here 

 of a little more than one pound, and that if it were not for 

 this, every ton of the earth would continue its journey into 

 space in a straight line for ever, and though we know in the 

 same way that the whole earth attracts each ton in the moon [ 

 with a force equal to the weight of ten ounces and no more, 

 we cannot tell by any astronomical observation whatever, how ' 

 many tons there are m all. 



Newton showed that to complete his law and to put in the | 

 numerical constant (the Newtonian Constant of Gravitation) 

 that would convert his proportion into an equality, two methods 

 are available: we may either make observations on the dis- 

 turbance of the earth's gravitation by the action of isolated 

 parts of it, we may either find the relative attraction of an 

 isolated mountain or the strata above the bottom of a deep 

 mine, or we may make an artificial planet of our own and find 

 Ihe attraction which it exerts. 



The Newtonian Constant will he known if we know the 

 force of attraction between two bodies which we can completely 

 measure and weigh. Employing the C.G.S. system of measure- 

 ment, the Newtonian Constant is equal to the force of attract- 

 tion in dynes between two balls weighing a gramme each, with 

 their centres one centimetre apart. Of course it may be referred 

 to pounds and inches or Ions and yards, bul as soon as all the 

 quantities but G in Newton's equation 



Mass X Mass 

 Distance'^ 



are known, no mailer in what units Ihe quantities are measured, 

 G i» known. The conversion of its numerical value from one 

 lyslem of measurement to another is of course a mere matter of 

 arithmetic. 



Of the first method of finding G, depending on the atlraclion 

 of a mountain first attempted by Bouguer at ihc risk of his life 

 in Ihc hurricanes of snow on Chimborazo, of Ihe experiments of 

 Miskelyne, of Airy and of others, I cannot now find time to 

 ■peak ; I can only refer to I'oynting's essay on the subject. It 

 is the second method with an arlificial planet that I have to 

 describe to-night. 



■ A Ircturc delivered at ihc Royal Intiituiion on June 8, by Prof. C. V- 



Ii..i . I P :-- 



rlinicullyof proving this. ondnol 

 th , ttwt delayed the publicalion of 



K 



Force = G 



Now let me give some idea of the minuteness of the effect 

 that has to be measured. Is a wall built true by the aid of a 

 plumb-line vertical, or does it lean outwards ? Newton s prin- 

 ciple shows that the plumb-bob is attracted by the wall, yet it 

 hangs vertically. The attraction is. so small that it cannot be 

 detected in this way. Even the attraction of a whole mountain 

 requires the most refined apparatus to detect it. Do two marbles 

 lying on a level table rush together? .\ccording to Newton's 

 principle they attract one another ; yet if they were a thousand 

 times smoother than they are, no movement of attraction could 

 be detected. 



Leaving matters of common experience, let us go into the 

 physical laboratory where instruments of the highest degree of 

 precision and delicacy (at least so they are called) are found on 

 every table. What precautions are taken to prevent the at- 

 tr.actions of the fixed and moving parts from interfering with 

 the result which they are constructed to measure? None. The 

 attractions are so small, that in no apparatus in use for the 

 measurement of electrical, magnetic, thermal, or other constants 

 are they ever thought of, or is any provision necessary to pre- 

 vent their falsifying the result. Nevertheless, the attractions 

 exist, and if only the means are delicate enough they can be 

 detected and measured. The Rev. John Mitchell was the first 

 to devise a successful method. lie was the first to invent the 

 torsion balance with which Coulomb made his famous electrical 

 researches, and which bears Coulomb's name. He devised and 

 he made apparatus for this purpose, but he did not live to make 

 any experiments. 



.■\fter his death Cavendish remodelled Mitchell's apparatus and 

 performed the famous Cavendish experiment. By means of the 

 apparatus, of which for the second time I show a full-size model 

 in this theatre, Cavendish measured the force o( attraction 

 between two balls of lead, one 12 and the other 2 inches in 

 diameter, and with their centres S S5 inches apart. The same 

 experiment has since been made by Reich, by Baily, and mor^ 

 recently by Cornu and Bailie with greatly superior apparalu^ 

 one quarter of the size. .\U these observers actually del' 

 mined the attraction between masses which could lie wei;;li 

 and measured, and thus found with dilTerent degrees of accur.i-;, 

 the value of G. 



Let me explain now that this G, the gravitation coiistant, or 

 1 as I prefer lo call it, for the sake of distinction, the Newtonian 

 Constant of Gravitation, has nothing to do with that other 

 ! quantity generally written .;, which represents the attraction at 

 the earth's surface. This is a purely accidental quantity, which 

 depends not only upon G, but also upon the size of the earth, 

 its mean density, the latitude, the height above the sea, an.l 

 finally upon the configuration and the composition of the neigh- 

 bouring districts, i' is eminently of a practical and useful 

 character; it is the delight of the engineer and the practical 

 man ; it is not constant, but that he does not mind. It is of the 

 i earth, arbitrary, incidental, and vexatious. Prof. Greenhill 

 should spell his name with a little,:;. G, on the other hand, 

 represents that mighty principle under the inllucncc of which 

 every star, planel, and satellite in the universe pursues its allotted 

 course; it may possibly also be the mainspring of chemical action. 

 ] Unlike any other known physical influence, it is independent of 

 medium, it knows no refraction, it cannot ca.st a shadow. It 

 I is a mysterious power, which no man can explain ; of its pro- 

 pagation through sDace, all men are ignorant. It is in no way 

 dependent on the accidental size or .shape of the earth : if the 

 solar system ceased to exist it would remain unch.anged. I 

 cannot contemplate this mystery, at which weignorantly wonder, 

 without thinking of the altar on Mars' hill. When will a St. 

 Paul arise able to declare it unto us ? Or is gravitation, like life, 

 a mystery that can never be solved? 



Owing 10 the universal char.acler of the constant G, it seems 

 lo me to be descending from the sublime to the ridiculous to 

 describe the object ol this experiment as finding the mass of 

 Ihc earth or the mean density of the earth, or, less accurately, 

 the weight of Ihe earth. I could not lecture here under the 

 title that has always been chosen in connection with this 

 investigation. In spile of the courteously expressed de- 

 sire of your distinguished and energetic secretary, that 1 

 should indicate in the title that, to put it vulg.irly, I 

 had been weighing Ihe earth, 1 could not introduce as 

 the object of my work anything so casual as an accidenla 

 property of an insignificant planet. To the physicist this would 

 be equivalent lo leaving some great international conference to 

 attend to the alVairs of a county council, I might even say of a 



NO. 1292, VOL. 50] 



