SCIENCE 



NEW YORK, MARCH 3, 1893. 



LAWS AND NATURE OF COHESION. 



BT REGINALD A. FESSENDEN, LAFAYETTE, IND. 



In a previous note (Science, July 33. 1892, and Elect. World, 

 Aug. 8, 1891) a number of reasons were advanced for believing 

 that cobesioa is due to an electrostatic force, and it was shown 

 that the results predicted by such a theory agree very closely 

 with the results of experiment. 



This theory was, however, only extended to the phenomena of 

 rigidity, elasticity, and tensile strength. It was purposed to fol- 

 io iv it with another note on the phenomena of conductivity, sur- 

 face tension, solution, refraction of light, and compression of 

 gases. Pressure of other work and the necessity of making ex- 

 periments to determine some doubtful points, will prevent such 

 publication for some time, and it was therefore judged best to 

 give a short preliminary statement of a few of the results so far 

 obtained. 



I. Relative closeness of the atoms. It appears to be generally 

 considered that the atoms are at distances from each other which 

 are large in comparison with their diameters, even in the solid 

 state. As an example of the extent of this belief may be men- 

 tioned the fact that in a recent article on magnetism. Mr. 

 Steinmitz made the statement that Professor Ewing's theory 

 could not be correct, unless the atoms were close together, but as 

 they were far apart, his tlieory must be wrong. This conclusion 

 has not been attacked up to the present time But the facts are 

 that all our evidence points the other way, and it is almost abso- 

 lutely certain that in the solid state the distance between the cen- 

 tres of two neighboring atoms is almost the same as their diame- 

 ters. 



For instance, from Van der Waals' equation we hare, at the 

 critical point: — 



Volume of gas = 12 times the volume of the atoms themselves, 

 or, the distance between the centres of two atoms is 2.3 times 

 the diameter of a single atom. And this is just at the critical 

 point, so that from the curves of volume, pressure and tempera- 

 ture, the solid elements must have a volume of, at the most, six 

 times that of the atoms themselves, reducing the distance be- 

 tween centres to 1.8 times the atomic diameter. 



Again, when a body is at absolute zero it is extremely difficult 

 to conceive why the atoms, having no kinetic energy and the co- 

 hesive force still in existence, should not join together so closely 

 as is possible, i.e., till they touch. (We may discard the old 

 ." force point " atom as obsolete and without reason for existence, 

 all modern research and theory being in favor of the idea that 

 atoms have most exact and well-defined boundaries.) 



If, then, the atoms of silver in the solid state at 0° C, say, 

 were very far apart, then, since we know its change of volume is 

 very slight down to about — 300° C, there must be a most re- 

 markable and sudden change at some point in the last 73°. But 

 this is not to be believed, for it is impossible for any such vio- 

 lent change in the space occupied by the atoms to take place 

 without some change in the conductivity of the metals. And we 

 know from the researches of Dewar and others that the curve of 

 resistance is a straight one, and cuts the axis of temperature at 

 absolute zero, if produced. 



On the other side, after considerable search, there does not 

 appear to be any reason for believing that the atoms are widely 

 separated in a solid, and the writer would be glad to know of any 

 such reason, other than the fact that certain mathematicians 

 have seen fit to make the supposition because it renders son e of 

 the work on surface-tension, etc., a little easier to handle. 



There is, it is true, one fact w^ich is commonly considered as 



evidence of this nature, but which must rather be looked upon 

 as evidence to the contrary. This is the fact that some elements 

 have a greater volume by themselves than in combination. For 

 instance, 45.5 cubic centimeters of potassium combine with an 

 equivalent of chlorine to form a mass of potassium chloride 

 which occupies only 37.4 cubic centimeters. But a simple geo- 

 metric consideration will show us that even if the atoms of potas- 

 sium were actually touching one another in the solid state, the 

 45.0 cubic centimeters would be able to contract to 31.7 cubic 

 centimeters if the potassium were combined with an element 

 having an atomic volume of less than 18. Similarly, 33.5 cubic 

 centimeters sodium should be capable of combining with an ele- 

 ment having an atomic volume of 9.6 to form a compound hav- 

 ing an atomic volume of 16.5. 



To take another example, sodium chloride should have an 

 atomic volume of about -j(33.5x.93) -fl7j x ^'^ = 27.03. The 

 actual atomic volume of Na CI is 27. 1. Na OH should have an 

 atomic volume of 17. Its actual volume is 18. 



K O H should have atomic volume of 35.5. ■ .Actual volume is 

 37. 



Similarly with the salts of caesium, rubidium and the other 

 metals which have large atomic volumes. For, of course, it is 

 only with these elements which have great atomic volumes that 

 this contraction on combination will be very noticeable. 



The geometric explanation referred to is that in a monoplex 

 element (element having under the conditions taken only one 

 atom to the molecule), owing to the forces at work, the atoms 

 will take the positions that a lot of balloons would that were 

 fastened together by very short strings, thus, 



four atoms occupying four times the space of one. 



While if anew element is introduced, they will take this position 



(shown in two dimensions only) where the atoms occupy a space 

 /i = .70 of what they did originally. The fact that the calcu- 

 lated values are always a little smaller than the observed, and 

 never larger, is one of the strongest proofs that the atoms are 

 really fairly close together in the solid state. While this is to be 

 regretted from a mathematical point of view, it is very satisfac- 

 tory from a physical and crystallographic standpoint. 



[Note. — In passing it is curious to note that the number 

 of "space nets" into which an infinite number of points 



