124 



SCIENTIFIC NEW^S. 



[Feb. 10, i88«. 



or one thousand millionth of a cubic inch, to be dissolved 

 in a cubic mile of water. One drop of the solution would 

 contain one molecule of salt, if the mixture were well 

 stirred up ! If, as Sir W. Thomson suggests, we imagine 

 a drop to be magnified to the size of the world, the mole- 

 cules would appear from half an inch to two inches in 

 diameter. Or we may imagine the grain to be dissolved 

 in a wineglassful of water, say three ounces ; take a drop 

 of this and put it in another wineglass, and fill it up with 

 water; take a drop of this and repeat the operation until 

 we have five glasses ; a drop from the fifth glass may be 

 imagined to contain about ten molecules of salt. One of 

 these molecules might be divided by chemical or electri- 

 cal means, but the halves would no longer be salt : one 

 would be sodium, and the other chlorine. These state- 

 ments are given before the following figures, because the 

 latter fail to convey any impression to the mind, while 

 the former may perhaps give some faint idea of the size 

 of a molecule. 



From a number of different arguments it is be- 

 lieved that the size of a molecule is about one 

 400,000,000th of an inch, and that there are about 

 64,000,000,000,000,000,000,000,000 to a cubic inch of 

 solid matter, and about 300,000,000,000,000,000,000 to a 

 cubic inch of air. This seems to be a marvellously small 

 size, but it is merely small in comparison with our usual 

 standard of measurement — an inch. The present writer's 

 pulse has beaten about 1,200,000,000 times ; this number 

 is large merely because his lifetime has been long com- 

 pared with a pulse beat. When we have to deal with 

 measurements of quantities which differ very greatly 

 from the unit of measurement it is convenient to express 

 the number by giving the first digits, or significant figures, 

 and then to indicate how many cyphers there are by 

 powers often — thus 3 X 10 is the number of molecules 

 in a cubic inch of air. 



Not only is a lump of salt composed of molecules of 

 salt, which are in turn made of two atoms — one sodium 

 and the other chlorine — but every substance which we 

 can touch, see, taste, or smell is composed of mole- 

 cules, and most of these are composed of at least two 

 atoms. The theory of divisibility is very old. Lucretius 

 wrote a remarkable poem on " The Nature of Things." 

 Part of it treats of atoms, and contains several statements 

 which are in perfect accordance with the latest discoveries, 

 though the "atoms" of Lucretius are physical, not 

 chemical, and must be looked upon as chemical mole- 

 cules. 



One of the earliest estimates of the size of a molecule 

 was arrived at by Cauchy, the French mathematician. 

 He was investigating the refraction and dispersion of 

 light, and found that, to account for dispersion or the 

 separation of a beam of light into colours [see Scientific 

 News, old series, vol. i. page 86], it was necessary to 

 suppose that the distance between the ultimate particles 

 or the molecules cannot be immeasurably less than the 

 length of a wave of light. Now, the average length of a 

 -wave of light is about the 40,000th of an inch. The size 

 of a molecule must be very much smaller than this, for, 

 if it were not, the dispersion would be very much greater 

 than it actually is ; on the other hand, for similar reasons, 

 it is probably not less than one io,oooth part of the length 

 of a wave of light — that is, about one 400,000,000th of an 

 inch. Some doubt has been cast upon this calculation, 

 and it is stated that it yields results which are consider- 

 ably different, but it is given here as one of the first 

 attempts to arrive at the size of a molecule. 



Another method is due to the German mathematician, 

 Clausius, who has greatly developed the molecular theory 

 of gases. It is assumed that the molecules are hard, 

 elastic globes, all one size, darting about with a velocity 

 which Dr. Joule has calculated from the weight and pres- 

 sure of hydrogen to be more than 6,000 feet per second. 

 They are constantly coming in collision with each other, 

 and every particle has on an average 17,700,000,000 

 collisions per second. In the air the number of colli- 

 sions for each particle is only about half as great, and 

 the average velocity about one-fourth of that in hydrogen, 

 or seventeen miles per hour. The average length of the 

 distance a molecule will travel between the collisions, or 

 the " mean free path," can easily be calculated from 

 these figures. Imagine a number of molecules side by 

 side, just touching each other, in a row of the length ot 

 the mean free path. It can be shown by geometry that 

 eight and a-half times this number is equal to the number 

 of times a gas must be compressed in order that it may 

 be liquefied. It is found that in liquefying gases by 

 submitting them to enormous pressure, assisted by 

 intense cold, that the volume is reduced about 40,000 

 times. There would therefore be about 40,000 divided 

 by 8|, or 4,700 molecules in the row. The length of 

 the free path has been calculated by several different 

 methods. Taking the figures already given, viz., 6,000- 

 feet per second, and 17,700,000,000 collisions in the 

 same space of time, the length of the free path comes- 

 out one 240,000th of an inch ; there would therefore be 

 1,128,000,000 molecules in a row an inch long. This is. 

 about one-third of the size found by Cauchy's method. 

 It should be observed that this calculation is one 

 which indicates the smallest probable size of the mole- 

 cule. 



Sir William Thomson has suggested several entirely 

 different methods of calculation, and they are found to 

 give results which agree, not, of course, in actual figures, 

 but in the order of magnitude. The tension of the film 

 of a soap-bubble is about sixteen grains per square inch, 

 and when it is stretched it becomes cooled, just as com- 

 pressed air is cooled when it is allowed to expand. Sir 

 William Thomson has calculated that, in order to main- 

 tain the temperature constant while the film is being 

 stretched, half as much energy must be supplied in the 

 form of heat. Therefore, twenty-four inch grains of 

 work must be done in order to increase the size of a 

 film by one square inch. Now, supposing the film to be 

 stretched to anything like one 25,000,000th of an inch im 

 thickness, the work done on it, both in stretching and in 

 maintaining the temperature, would be sufficient to 

 instantly vaporise it. There is evidently some flaw in the 

 reasoning, and the only way out of the difficulty is to 

 admit that at such an extreme thinness the tension 

 would not be so great, and this decrease in tension would 

 be due to there being only a few molecules in this thick- 

 ness. 



Another.method due to Sir W. Thomson depends upon 

 the amount of heat produced by the chemical union of 

 copper and zinc to form brass, and this argument gives 

 one 700,000,000th of an inch as the probable 

 minimum. 



Not only is it utterly impossible that we shall ever be 

 able to see molecules by any improvements in micro- 

 scopes, but if the minutest creature that can be observed 

 were provided with the best possible instrument, in due 

 proportion to its own size, it would hardly be able to see 

 them. 



