7S7 



ATTRACTION." 



ATTRACTION. 



The cohesive force ia an absolute phenomenon, but if we suppose the 

 particles of matter not in contact, it then becomes necessary to admit 

 a new repulsive force, of which the sphere of action is ulterior to that 

 of the cohesive force. Complete interstices can only exist upon the 

 supposition that, at a certain distance, the cohesive force is destroyed, 

 or at least overcome, by a counterbalancing repulsion. From the 

 known effects of heat, it is supposed that caloric, a name which indicates 

 the cause of heat, plays a prominent part in the production of the 

 repulsion. Nothing positive, however, has yet been established on 

 this subject : we can only make use of phenomena as they exist, to 

 overturn the common impressions, by means of which forte, the great 

 agent of the universe, meaning the cause of visible display of motion 

 excited or motion prevented, is postponed to notions of matter, or 

 impenetrability, or similar words, which, if made accurate by close 

 attention, and freed from such latent assumptioua as arise from the 

 unassisted senses, will be found to amount to the same idea. 



The arguments against absolute contact are almost insuperable : if 

 we yield to them, we are immediately obliged to admit that particles 

 really act on each other at a distance. Nor will any suppositions as to 

 caloric afford us the means of avoiding such a conclusion. If caloric 

 be matter, we must first explain its cohesion or repulsion before we can 

 apply it to explain that of other matter : if caloric be not matter, we 

 g:iin nothing in the way of avoiding difficulty ; for an agent which is 

 not matter, but something else, with new properties superadded to the 

 common and visible properties of matter, is as difficult as ordinary 

 matter with the express addition of power over other matter at a 

 distance. And it must be observed, that if we are rationally compelled 

 to allow such power to a particle upon a particle, there is no new 

 difficulty in the attraction of yrarilatiun. If A can act upon B at the 

 millionth part of an inch, there is no d priori difficulty in the notion 

 that two A's together can act on B at twice the distance with as much 

 visible effect as a million of A's collected can act at a million of times 

 the distance, and so on. It must not, however, be supposed that we 

 mean to infer that gravitation and cohesion are both referable to the 

 Newtonian law of attraction, although this has been since reduced to 

 more than a possibility. This remarkable addition to the nascent 

 theory of molecular forces ia the work of 0. F. Mossotti, and was pub- 

 lished in a pamphlet entitled ' Sur les Forces qui regisseut la consti- 

 tution intcrieure des corps, apercu pour servir a la determination de la 

 cause et des lout de 1'action moleculaire,' Turin, 1833, 4t<>. This paper 

 ia translated in Taylor's ' Scientific Memoirs,' vol. i. ; and Mr. Pratt, in 

 the second edition of his ' Mechanical Philosophy ,' observing that 

 Mo8otti's analysis, though conducted with an ultimate view to complex 

 application, is really, for the present, only applied to simple cases, has 

 given the mathematical view necessary to include those simple cases 

 and no more, in a perfectly sufficient manner. 



The observed facts are, that particles which are very nearly in contact 

 with one another repel each other in a manner which certainly depends, 

 among other things, on the temperature ; but that at a certain distance 

 they cease to repel, and begin to attract each other, and that with con- 

 siderable force ; at a still greater distance that attraction becomes 

 comparatively feeble, and coincides with what is called the attraction 

 of gravitation, varying inversely as the square of the distance. That 

 this attraction of gravitation, and no other, exists at ordinary sensible 

 distances, is fully proved by the Cavendish experiment. 



Many hypothetical laws might be constructed which fulfil all these 

 condition* ; but the great interest of Mossotti's investigation, and 

 perhaps much of its value, consists in his having taken a theory actually 

 existing, imagined upon grounds with which his views had no necessary 

 connection, and upon his having given a basis of the utmost simplicity 

 to the numerical law on which he proceeded. This basis is no other 

 than that all molecular attractions and repulsions vary inversely as the 

 squares of the distances. 



When JEpinuB explained Franklin's electrical theory, his hypothesis 

 was that the particles of matter repel one another, and also the particles 

 of the electrical ether, which he supposed to exist and to be attached 

 to particles of ordinary matter. But he supposed the particles of ether 

 to attract the particles of matter ; so that of the two species of particles, 

 called matter and ether, each repels the particles of its own kind and 

 attracts those of the other. .Epinus even went so far as to suppose 

 that the attraction of gravitation might be a necessary consequence of 

 uch a theory, on the supposition that the attraction of the matter and 

 ether was a little greater than the repulsions. So far Mossotti has 

 adopted his views; but, by applying mathematical analysis, he has 

 shown what ^Kpimu could not have had the least reason to suppose, 

 namely, that attraction of cohesion, the repulsion which takes place 

 when the distance is smaller than that of cohesion, and the attraction 

 of gravitation, which exists at distances too great for cohesion, are all 

 to be found among the consequences 'of this theory. 



If there exist in space molecules of matter which repel each other, 

 in a fluid or ether of which the particles also repel each other, while 

 the particles of the matter attract those of the ether, it is obvious that 

 each of the particles of matter will, by its attraction, collect about it a 

 condensed atmosphere of ether. If the attractions and repulsions be 

 all inversely as the squares of the distances, Mossotti finds that, in con- 

 H equence of the atmospheres of ether, two molecules at a distance r 

 (the attraction of the particles of matter for those of ether being 

 presumed a little, and but a little, greater than the repulsion of the 



ATS A>'D SCI. CIV. VOL. I. 



particles of matter from each other) will repel each other with a force 

 represented with great approximation by the formula 



ar)e~ gr B 

 ~~ 



where A, a, B, are certain positive constants. To make the results 

 agree with observed facts, a must be considerable, and A much greater 

 than B. When the formula ia positive, repulsion is represented ; when 

 negative, attraction. When > is very small, the formula is positive, 

 and represents repulsion ; when r increases to a certain value, it 

 vanishes, and afterwards becomes negative : at the value of r just 

 mentioned there is stable equilibrium. As r still increases the attraction 

 increases, becomes a maximum at another certain value of r, and after- 

 wards, if a be considerable, diminishes as the inverse square of the 

 distance, or in a ratio incomparably near to it. All this agrees with 

 the facts of observation, and with the numerical law of the facts as far 

 as we know it ; to which it must be added that an increase of the 

 density of the ether would increase the distance at which particles are 

 in equilibrium, which is generally done by increase of temperature. 



We may also make it apparent to the mathematician that laws of 

 attraction may very easily be expressed which shall combine the leading 

 circumstances connected both with gravitation and cohesion in one 

 formula. Let us suppose, for instance, that at the distance r, the 

 accelerating force of two equal particles on each other is expressed by 



SHIM 



positive values denoting attraction, and negative values repulsion. If 

 a and m be made sufficiently small, the first term may be made in- 

 sensible at all finite distances, and the second as near as we please to 

 the Newtonian law. But when r is very small, the second term 

 becomes insensible, and such a value may be given to n that the first 

 term shall be of sensible value, as follows : Let c be greater than b, 

 both being quantities of that order of smalluess at which the Newtonian 

 term becomes insensible. Then when r is little greater than c, the 

 first term is negative ; when r lies between c and 6, it is positive ; and 

 when r is less than c, it is negative again. 



The solid, fluid, and gaseous states of matter show the rise and 

 progress of a repulsive force generally produced by the action of heat. 

 In the first, the particles absolutely attract, in the third they absolutely 

 repel, each other ; but in the second the repulsive force almost counter- 

 balances the attractive force, leaving only enough to create that weak 

 degree of cohesion which exists in fluids, or at most that semi-cohesion 

 which is observed in bird-lime, in gum-water, and the like. The tran- 

 sition from complete solidity to the gaseous state appears to be made 

 through various degrees of fluidity, and the gradual hardening of melted 

 sealing-wax is a familiar instance of a part of the gradation. 



We now come to the question how the attraction of the particles of 

 one heavenly body on those of another is established. For details of 

 this very extensive subject, see GRAVITATION. The resum6 of the 

 argument is this : the phenomena which do take place in the heavens 

 are those which common and undisputed mechanical and mathematical 

 reasoning show would take place if the Newtonian law be true. Thin 

 law is, that the force of attraction is inversely as the squares of the 

 distances between the attracting bodies. Now, every phenomenon of 

 importance has been gradually brought under the consequences of this 

 law by various analysts. To recount instances would be to make a 

 summary of astronomical terms ; but we will select one, which, in one 

 sense, is the most dubious, namely, the phenomena of the tides. For, 

 whereas the place of the moon or a planet is predicted within from 

 half a second to a second of time, the time of high water cannot yet be 

 predicted within some minutes, at least in a port. How much this 

 phenomenon may be affected by winds or the nature of the coast, is 

 not difficult to conceive ; but the following result is a striking specimen 

 of accordance between theory and fact. If the tides proceed from 

 Newtonian gravitation, the mean tide-day, or interval between succes- 

 sive times of high water, must be equal to the time between the 

 moon's coming on the meridian above and below the horizon, or, 

 roughly speaking, two tide-days make a lunar day. It is found by 

 analysis, that if the Newtonian theory be true, the average tide-day 

 must be exactly equal to half the average lunar-day, though particular 

 instances of the two may differ many minutes. This is found to be the 

 fact: for if the tide-day were more than half the lunar-day by as much, 

 as one-tenth of a second on the average, that is, if the tides lagged, one 

 with another, by ," daily, two thousand years would have seen high 

 water at every possible part of the lunar-day. But for two thousand 

 years it has never been denied that high water takes place at every 

 port within a certain time (usually less than four hours) of the moon's 

 coming on the meridian. Again, a permanent retardation would, in 

 course of time, bring high water when the moon was precisely on the 

 meridian, for a long succession of days together : a result which never 

 has been observed, and which, according to the Newtonian theory, is 

 impossible. [ACCELERATION OF TIDES.] 



An immense number of accordances between theory and observation, 

 and there being no assignable discrepancy whatsoever, of any consider- 

 able amount,form the nature of the proof of the Newtonian law. And it 

 must be observed that thin has not been done in a day, or by one person, 



