JULV 22, 1892.] 



SCIENCE. 



49 



of the observer, various regularities or laws were at once apparent, 

 and it is for the purpose of pointing out one of these that the fol- 

 lowing paper has been written. 



This piece of paper, taken as a whole, has certain properties, a 

 certain size, a certain weight, a certain motion, and is the seat of 

 a. certain force which attracts other ponderable bodies to it. A 

 single atom of matter has its weight, motion, size, and force. The 

 weights of the atoms form the basis of electrometric chemistry, 

 their motion that of the kinetic theory of heat. To their size less 

 attention has been paid, we have only Mendelejeef's curve and 

 •certain experiments of Roberts-Austen, who has showed that the 

 tensile strength of gold is weakened, not in proportion to the 

 weight of the metal alloyed with it, but to the volume, in the 

 same way as ten lumps of gravel weaken a casting more than ten 

 grains of sand. Of the force — the force of cohesion — still less 

 is known, in fact absolutely nothing, and the object of this note 

 is to point out what the nature of this force is and what its laws 

 are. 



In its early youth science was riotously extravagant of ethers, 

 and any puzzling phenomenon was considered warrant enough for 

 the creation of a new one. As it has grown older it has grown 

 also more economical, until at the present day the scientist who 

 .should ask for an appropriation of a new ether, to help him out of 

 .a difficulty, would be pounced upon. For this reason, if no other, 

 we will confine ourselves to examining the various means by which 

 our present ether has been supposed capable of producing the 

 forces which cause cohesion. 



1. Gravitation. There have not been wanting eminent scien- 

 tists who have considered that gravitation could account for co- 

 'hesion, and there have been many ingenious theories proposed, for 

 instance that of Watts, who supposed that (since the effects of 

 gravity on the moon's path may be supposed to consist of two 

 parts, one independent of the shape of the earth and varying 

 inversely as the square of the distance, the other dependent on 

 the sha pe and varying inversely as the cube of the distance) if 

 the atoms were of irregular shapes it might account for the ef- 

 fects. But no theory with gravitation as its basis will hold, first, 

 ■because Ihe effects are much too small; second, because, as we 

 .shall see, the cohesive force is totally independent of the weights 

 of the atoms and depends on the size only. 



3. Condensation and rarifactiou of the ether caused by the mo- 

 tion of the atoms. If wo hold a pith ball near a tuning fork the 

 pith ball will be attracted up to a certain distance, and will then 

 be repelled if brought closer. This theory has been a favorite 

 with many, but, as such an attraction would vary with the motion 

 ■of the atoms in a way that we know the force of cohesion does 

 not, it also must be dismissed. 



3. Electricity. That the force of cohesion was due to electricity 

 lias long been vaguely suspected. On the same principle appar- 

 ently that electricity was considered to be the cause of life, i.e., 

 ■"Life is a wonderful thing and unexplainable, electricity is a 

 wonderful thing and unexplainable; therefore electricity is 

 life " — the argument being possibly aided by an instinctive rec- 

 ollection of the Athenasion creed, which states that " there is only 

 ■one incomprehensible." The writer is not aware that any evidence 

 in favor of this theory was ever offered, so it was probably merely 

 a guess. 



Having rejected theories 1 and 3, we may see how the facts 

 .agree with the theory that cohesion is an electrostatic effect. 



IE we electrolyse a solution of silver nitrate, we know from 

 Faraday's work that every atom of silver deposited on the elec- 

 trodes carries over a certain quantity of electricity. This quantity 

 is always the same, no matter how or when or where we perform 

 the electrolysis, and this quantity seems to be related to the 

 .atoms in the same way as a pint of water to a pint measure. We 

 may calculate the quantity on each atom in the following way. 

 One cubic centimeter of silver weighs about 10.5 grammes. One 

 coulomb is carried over by evei'y 1.12 milligrammes of silver de- 

 posited, therefore the chai'ge on the atoms contained in one cubic 

 10300 



we may call its size 10 ~^ centimeters. In a cubic centimeter of 

 silver then there would be 10" atoms, which would give as the 

 charge on each atom 10' -=- 10-* = 10""^° coulomb. The ca- 

 pacity of an atom having a diameter of 10 ~' centimeter is 



lV^ = *^-^^ 10— farads. 



The potential on each silver atom will therefore be about one 

 volt. We may look at the cubic centimeter of silver as being 

 made up of planes, each plane consisting of one layer of atoms. 

 The distance between the centres of any two layers would be 

 10 ~' centimeters. The potential on the atoms being one volt, 

 the attraction between any two layers would be 



4.5xio->>xr ., ,„„ , 



,g grammes per cm^ = 4500 kg. per cm^ — cal- 

 culated tensile strength of silver = 45 kg. per sq. mnr. 



From Wertheim's results we have observed tensile strength of 

 silver 38 kg. per sq. mm. That the calculated and observed re- 

 sults should be so close is of course only a piece of good fortune. 

 We had no right to expect it, as the data upon which the calcula- 

 tion is based are not known with sufficient accuracy. Still, the 

 result is a remarkable one, and places beyond question the fact 

 that the known electric charges on the atoms can produce effects 

 of the same order as those observed. 



Having shown this, we may follow up the theory by investi- 

 gating in what way the cohesion of the metals would vary if this 

 were the case. Evidently (since every atom, large or small, has 

 the same quantity of electricity, and the larger the atoms of a 

 metal the farther away the centres of the atoms would be) the 

 cohesive force should be inversely proportional to some power of 



G H 



■ i)> > p 



kA 



<centinieter of silver is 



1.13 



10* coulombs. 



As the sizes of the atoms vary from 10 ' to 10 " centimeters 

 ia diameter, and silver is a small atom (1 the size of potassium), 



the size (or atomic volume, as it is called, and which is got by 

 dividing the atomic weight by the density of the substance). The 

 following table shows this to be the case. In the first column 

 are the names of the metals, in the second their relative sizes, or 

 atomic volumes, in the third their rigidity, as given by Mr. Suther- 

 land in the Philosophical Magazine of August, 1891 : — 



I. II. III. IV. ~ V. 



Iron 7.1 750 x 10» 483 x 10» 550 x 10' 



Copper 7.1 430 483 550 



Zinc 9.3 3.50 314 340 



Silver 10 2 280 370 270 



Gold 10.3 270 370 370 



Aluminium 10.4 350 350 260 



Magnesium 14. 150 134 143 



Tin 16. 136 122 100 



Lead IS. 84 100 83 



Cadmium 13. 170 



As will be seen, the agreement is perfect, with the exception of 

 iron, and those who are familiar how greatly the properties of 

 iron are changed by the least particle of impurity will possibly 

 agree with me in thinking that absolutely pure iron would be less 

 rigid ; in fact, some recent experiments show that it is so, being 

 nearer 600 than 750; but I have not inserted this value, because a 

 comparison with a set of observations made by one observer at 

 one time and by one method would have a greater value than 

 comparison with a lot of picked results from different observers. 



Assuming the electrostatic theory, we can easily calculate the 

 exact function which rigidity should be of the atomic volume in 

 the following way. 



Suppose Figs. 1 and 2 to represent two cubic centimeters of 

 different elements, of which the atoms of one are twice the diam- 

 eter of the other, or, to put it more accurately, the distance be- 

 tween centres of atoms is twice as great in the one case as in the 



