362 



SCIENCE. 



a force that is directly proportioned to the mass of the 

 attracting particle and inversely to the square of the dis- 

 tance between them." The first question arising is, 

 what are we to understand by " particle " in this theory ? 

 Certainly not a mass of utterly indefinite size. Undoubt- 

 edly Sir Isaac meant a mass of unit size, since the very 

 terms of the proposition require this. For if every par- 

 ticle attracts every other particle with a certain vigor, 

 then it must necessarily attract two particles with twice 

 the vigor with which it attracts one. Or if a particle cf 

 unit mass attracts another with unit vigor, then it must 

 attract two others, or one other whose mass is double 

 the unit vigor. And as each of these two others attracts 

 it with the unit vigor, then their sum, or their double 

 mass, must attract it with double the unit vigor. It is 

 simply the principle, still c lder than Newton in its ex- 

 pression, that " action and reaction are always equal and 

 opposite." 



But if it be granted that such will be the reaction be- 

 tween a unit and a double unit mass, the whole question 

 is settled. For if the second mass may be doubled it 

 may be quadrupled, or may be increased a million fold, 

 without any difference in the principle. And likew ise 

 the first mass may be increased without affecting the 

 principle. A mass of one unit attracts a mass of ten 

 units with an energy equal to ten units, since it attracts 

 each of the ten with unit energy. And each unit of the 

 ten reacts on the one with unit energy, so that their 

 combined attraction equals ten units. Again, if the 

 first mass contain two units, each of these separately 

 acts upon each of the ten with unit energy. Thus as 

 each unit of the two exerts ten units of energy, the two 

 together exert twenty units. In other words, the energy 

 which the first mass exerts upon the second is propor- 

 tioned to the product of the number of mass units in the 

 first into the number of mass units in the second ; and 

 the acticn of the second upon the first also is in propor- 

 tion to the product of their units. 



This is the true principle of the attraction of gravita- 

 tion. We may take the unit mass of any size we wish. 

 In the action between the earth and the moon, for in- 

 stance, we may take the mass of the moon as the unit, 

 that of the earth being about 75 units. The moon will 

 attract each unit of the earth with unit energy, and the 

 whole earth with an energy of 75 force units. But 

 each unit of the earth will react upon the moon 

 with unit energy, and the whole earth will exert 

 on the moon an energy of 75 force units. Thus 

 the moon attracts the earth with precisely the 

 same vigor as the earth attracts the moon. Of 

 course the resulting motions are not the same, but 

 the resulting momentums are precisely equal. As the 

 earth is 75 times the weight of the moon a motion of one 

 foot per second in the earth would give it a momentum 

 equal to that given the moon by a motion of 75 feet per 

 second. It is well known that the moon does not re- 

 volve around the centre of gravity of the earth, but that 

 these two bodies revolve around their common centre of 

 gravity. But this common centre is within the mass of 

 the earth, and may be found by dividing the distance be- 

 tween the centres of the earth and moon by the ratio of 

 their weights. If we take this distance as 240,000 miles, 

 and divide by 75 — the weight of the earth as compared 

 with the moon — the common centre of gravity will ap- 

 pear to be 3200 miles from the earth's centre. 



Or we might consider this case from the principle of 

 inertia. The earth having 75 times the mass of the mcon 

 has 75 times the inertia, or resistance to exterior forces. 

 Thus its movement in response to lunar attraction is 

 only 1 -75th that of the moon in response to terrestrial at- 

 traction. But its weight being 75 times greater, its 

 momentum in response to lunar attraction must be pre- 

 cisely equal to the moon's momentum in response to the 

 earth's attraction ; or, in other words, their vigor of 

 action upon each other must be precisely equal. This 



movement of the earth under theact ; on of the moon does 

 not affect the line of its orbital movement, since it is less 

 than the length of the earth's radius. Its movement is 

 like that of a bead with a large aperture, which advances 

 along a string moving from side to side, but not leaving 

 the string. But as the earth moves about 46 millions of 

 miles in its orbit while completing one of these gyrations, 

 the effect is excessively minute. That of the moon, in 

 fact, which swings 240,000 miles to each side of the 

 orbit each fortnight, is very slight when compared with 

 the length of the orbit. 



But if, the earth being 75 times the mass cf the moon, 

 it also attracted the moon 75 times mere vigcr^usly than 

 the moon attracts the earth, this common centre of grav- 

 ity would befound by dividing 240,000 by 75- and would 

 be but 36 miles from the earth's centre. As to which of 

 these results is the more correct the books will show. 



I am, therefore, obliged to repeat the idea advanced in 

 my former article. An atom falling towards the earth 

 attracts it with as much energy as the earth attracts the 

 atom, and they move toward each other with equal mo- 

 mentums. But the great weight of the earth reduces its 

 rate of motion towards the atom to a speed inconceivably 

 small, while the small weight of the atom gives it an ex- 

 cessively rapid speed towards the earth. It would be 

 strange if, at this late date in the history of the theory of 

 gravitation, I had been the first to advance this idea as 

 Mr. Rachel seems to suppose. Perhaps my mode 

 of presenting it may be original, but I can readily quote 

 other expressions ot the same idea. Thus Dr. Ball, 

 Royal Astronomer of Ireland, speaks as follows, in his 

 article on Gravitation in the new edition of the Ency- 

 clopedia Britannica : " It has been found that the inten- 

 sity of the attraction of gravitation between two masses 

 is directly proportional to the product of those masses." 

 This is precisely the result I have reached in the above 

 argument. Again he says : " Let m, and ni be the 

 masses of two bodies, and let r be their distance. The 

 force with which m attracts ni is equal in magnitude 

 though opposite in direction to the tcrce with which 

 ni attracts ni. The reader may perhaps feel some diffi- 

 culty at first in admitting the truth of this statement. 

 We speak so often of the effects which the attraction 

 of the sun produces on the planets that it may seem 

 strange to hear that each planet reacts upon the sun 

 with a force precisely equal and opposite to the force 

 with which the sun acts upon the planets." He illus- 

 trates as follows : " Suppose the earth and the sun to be 

 at rest in space, and prevented from approaching each 

 other under the influence cf gravity by a rigid rod ex- 

 tending from one to the other. If now the sun pressed 

 toward the earth more vigorously than the earth to- 

 ward the sun the greater pressure of the sun must 

 overcome the lesser pressure of the earth, and the whole 

 arrangement would be driven through space in the 

 direction in which the rod points outward from the sun. 

 For there would be a motion producing vigor in the sun 

 I unopposed by a sufficient resistance in the earth. And 

 yet, in the event of such a movement, we would have 

 the kinetic energy of their motion created out cf noth- 

 ing, which is now weli known to be impossible." Such 

 is Dr. Ball's argument briefly stated. It leads to the 

 same result as mine, and I therefore claim to be in full 

 accord with the Newtonian law of gravitation. 



In regard to the other points of Mr. Rachel's letter 

 there is nothing on which I desire to dwell. As to the 

 use of the phrase " Latent Heat," the scientific world 

 will be very ready to give it up if a term can be sug- 

 gested more significant of the character of the energy 

 indicated. But there would be nothing gained by 

 simply substituting one unmeaning name for another. 

 Mr. Rachel himself uses the phrase " Radiant Heat," 

 yet he must be aware that the mode of motion so called 

 is very different from ordinary Heat Motion. Radiant 

 Heat is readily convertible into Static Heat ; but so is 



