Page:The American Cyclopædia (1879) Volume XI.djvu/732

714 MOLECULE the centres of two adjacent masses in the liquid state. It is generally assumed that the per- fect elasticity of the molecules results from an elastic atmosphere, perhaps the ether, which surrounds them, and in a gas we distinguish between what we call the free path of the mo- lecule and that portion of its motion during which the path is changed hy collision; and the principal difference between a gas and a liquid seems to be, that while in a gas the molecules are almost all the time on the wing, in a liquid they are always in a state of close encounter with each other, and have hardly any free path. "When therefore we define the diameter of a molecule as the dis- tance between the centres of two adjacent molecules in the liquid state, we of course in- clude the molecular atmosphere, or at least so much of it as produces an appreciable effect in the collision. If then we thus define the diam- eter of a molecule, it is evident that we can determine the relative diameters of molecules of different substances by comparing their densities in the aeriform and liquid states. For the densities of the gases give us the rela- tive weights of these molecules, and the den- sities of the liquids the weights of the unit volume of the liquids. Hence, by dividing the latter by the former, we learn the relative number of molecules in these equal volumes, and from this we at once deduce the relative volumes of the molecules and their relative diameters. Moreover, as these results agree very remarkably with those obtained by other means, we feel great confidence in the assump- tion on which they are based; and if our knowledge in regard to them is not precise, it is at least approximate. We next come to a class of molecular data of which our knowl- edge is not only not precise, but not even defi- nite, and whose assigned values can only be regarded as probable conjectures. Loschmidt has deduced from the principles of molecular mechanics the following theorem: "As the volume of a gas is to the combined volume of all the molecules contained in it, so is the mean path of a molecule to one eighth of its diam- eter." Since we know at least approximately the other three quantities, we ought to be able by this proportion to calculate the absolute molecular diameters. Accordingly, Maxwell has calculated from Loschmidt's data that "the size of the molecules of hydrogen is such that two million of them in a row would occupy a millimetre, and a million million million mil- lion of them would weigh between four and five grammes ;" and further, that " in a cubic centimetre of any gas at standard pressure and temperature there are about 19 million million million molecules." Striking as these results are, they depend on so many uncertain elements that they must be accepted with caution. Still it should be added that from several wholly independent data, such as the lengths of lumi- nous waves, the thickness of soap bubbles, and the electric properties of metals, Sir William Thomson has deduced values of the molecular magnitudes which are consistent with the num- bers just given, and has proved that these mag- nitudes must fall within certain limits, which, though too wide to secure entire confidence in his methods, at least fix the order of the mag- nitudes. In preparing this article we have been greatly indebted to the lecture on mole- cules delivered before the British association at Bradford in September, 1873, by Prof. Max- well, and to sum up what we have said of the physical relations of molecules we repro- duce from this lecture the table of molecular magnitudes, in which the values are classed ac- cording to the completeness of our knowledge in regard to them : TABLE OF MOLECULAE DATA. BANK I. H-H 0=O OO CiO a Mass of molecule, in micro- I 9 on Ofl AA criths .................. f Velocity at 0C. (from mean ) square), in metres a sec- V 1859 466 497 ) ond 396 RANK II. 965 560 482 879 7646 9489 9720 RANK III. 46 736 644 1012 Mass,n()- 26 ofagramne Number of molecules in") one cubic centimetre of ( 19 million million millions, or any gas under normal f 19xl0 18 . conditions .............. J " These considerations will show how definite the idea of the molecule has become in the mind of the physicist. It is no longer a meta- physical abstraction, but a reality about which he reasons as confidently and as successfully as he does about the planets. He no longer con- nects with this term the ideas of infinite hard- ness, absolute rigidity, and other incredible as- sumptions which have brought the idea of a limited divisibility into disrepute. His mole- cules are definite masses of matter, exceedingly small but still not immeasurable; and they are the points of application to which he traces the action of the forces with which he has to deal. These molecules are to the physicist real magnitudes, which are no further removed from our ordinary experience on the one side than are the magnitudes of astronomy on the other. The old metaphysical question in re- gard to the infinite divisibility of matter, which was such a subject of controversy in the last century, has nothing to do with the present conception. Were we small enough to be able to grasp the molecules, we might be able to split them, and so were we large enough we might be able to crack the earth ; but we have made sufficient advance since the days of the old controversy to know that questions of this sort, in the present state of knowledge, are both irrelevant and absurd. The geologist