Feb. 24, 1876] 



NATURE 



of lines at equal intervals, like Xobert's bands or the 

 markings on Diatomaceie, it is possible so to manage the 

 illumination that the dark fringes of interference may 

 coincide with the true lines of structure, and give rise to 

 good definition, even beyond the normal limit, and also 

 agrees wnth the fact that lines less than 1^0 (m*^ of ^"^ 

 inch apart can \iQ photographed. XkiOM^ seen with extreme 

 difficulty, if indeed truly resolved, except under very 

 peculiar and exceptional conditions ; since the waves of 

 light at the blue end of the spectrum, which are concerned 

 in photography, are short enough to give good definition 

 of lines so near together that the interference fringes due 

 to the longer waves at the red end would give an indis- 

 tinct image. Taking everything into consideration, the 

 agreement between observation and the theory is so close 

 as to make it extremely probable, and to justify the con- 

 clusion that the normal limit of distinct visibility with the 

 most perfect microscope is \ of the wave-length of the 

 light. If so, we must conclude that, even with the very 

 best lenses, except under special conditions, light itself is 

 of too coarse a nature to enable us to define objects less 



'^^ soooo^.^ O'' loo'ooo ^^ °^ ^^ ^"^^ ^P^"^' according as 

 a dry or an immersion lens is used. We must also conclude 

 that, as far as this question is concerned, our microscopes 

 have already reached this limit, whatever improvements 

 may remain to be made in other respects. 



2. The Size of the Ultimate A to 7ns of Matter. 



After discussing the results obtained by Stoney, 

 Thompson, and Clerk- Maxwell, mainly derived from the 

 properties of gases, I come to the conclusion that in the 

 present state of our knowledge the best approximation 

 that we can make to the size of the ultimate atoms of 

 matter is the mean of their determinations. I adopt for 

 simplicity roVoth of an inch as the unit of length, and 

 J oV^th of an inch cube, or i^go( ?oouOo th of a cubic inch, as 

 the unit of volume. In the case of a true gas the number 

 of atoms in the length of rvVrrth of an inch at 0° C, and a 

 pressure of one atmosphere, would be 21,770, and hence, 

 in TTi'TTuth of an inch cube, about 10,320,000,000,000. 



If this gas were a mixture of two volumes of hydrogen 

 and one of oxygen, on combining to form water there 

 would be a contraction to ?,, and on condensing into 

 liquid water a contraction to -^ of this ; but since the 

 molecules of the resulting liquid would contain three 

 atoms of the gases, the total number of molecules of 

 liquid water in a given volume would be 5 X 770 X J = 

 385 times the number of atoms of a gas. This gives for 

 the number of molecules of liquid water in njV^th of an 

 inch cube about 3,900,000,000,000,000. 



As an illustration of a far more complex substance I 

 take albumen, and calculating as well as one can from its 

 chemical composition, and from the specific gravity of 

 horn, I come to the conclusion that the diameter of the 

 ultimate molecule of dry albumen is about 3 82 that of 

 the molecules of water, and that rwuth of an inch cube 

 would contain about 71,000,000,000,000. 



If such be the case, we must conclude that in the 

 length of jTiriootii of an inch (the smallest interval that 

 could be distinctly seen with the microscope) there would 

 be about 2.000 molecules of liquid water lying end to end, 

 or about 520 of albumen. Hence, in order to see the 

 ultimate constitution of organic bodies, it would be neces- 

 sary to use a magnifying power of from 500 to 2,030 times 

 greater than those we now possess. These, however, for 

 reasons already given, would be of no use unless the 

 waves of light were some TuWth part of the length they 

 are, and our eyes and instruments correspondingly per- 

 fect. It will thus be seen that, even with our highest and 

 best powers, we are about as far from seeing the ultimate 

 structure of organic bodies as the naked eye is from 

 seeing the smallest objects which our microscopes now 

 reveal to us. As an illustration, I have calculated that 

 with our highest powers we are as far from seeing the 



ultimate molecules of organic substances as we should be 

 from seeing the contents of a newspaper with the naked 

 eye at the distance of a third of a mile ; the larger and 

 smaller types corresponding to the larger and smaller 

 molecules of the organic and inorganic constituents. 



3. General Conclusions to be deduced frotn the abo7>e facts. 



When we come to the application of these principles to 

 the study of living matter we are immediately led to feel 

 how very little we know respecting some of the most 

 important questions that could occupy our attention. As 

 illustrations I do not think I can select better than the 

 facts bearing on the size and character of minute germs, 

 and on Darwin's theorj- of ultimate organised gemmules. 



For the sake of simpUcity I will take into consideration 

 only the albuminous constituent of animals, using the 

 term albumen in a sort of generic sense. WTiatever be 

 the special variety of this substance, it is so associated 

 with water in living tissues, that in most, if not aU, cases 

 they would cease to live, if thoroughly dried. Much of 

 the water is no doubt present simply as water mechani- 

 cally mixed with the living particles ; but it appears to 

 me that we ought to look upon some portion as being in 

 a state of tnolecular combination. The existence of such 

 a state of union is clearly proved by the optical cha- 

 racters of various solutions of the same coloured sub- 

 stance. These are by no means such as would result 

 from the mere mechanical diffusion of ver>' minute par- 

 ticles of the solid substance in the liquid, and cannot be 

 explained unless we suppose that the coloured substance 

 is to some extent in the state of molecular combination 

 with the solvent This molecular affinity is also in some 

 cases manifested by a swelling up of a solid substance 

 when placed in certain liquids, even when perfect solution 

 occurs to a very limited extent. Such a condition appears 

 to be very characteristic of the li\'ing tissues of animals. 

 and makes it very probable that the ultimate Uving particles 

 are molecular compounds with water, and not molecules 

 of free dry albuminous substances. So little is known 

 of the true proportion of water thus combined, that the 

 only course now open is to suppose, for illustration, that 

 living albuminous matter contains half its volume of 

 water mechanically mixed, and one-fourth of free albu- 

 men, united with one-fourth of molecularly combined 

 water. On this supposition a sphere of such living matter 

 Ti?5-uth of an inch in diameter would contain the following 

 number of molecules : — 



Albumen 



Water in molecular combination 



10,000,000,000,000 

 5 20,000,000,000,000 



5 30,000,000,000,000 

 The very small relative amount of dry matter in some 

 living animals makes it probable that the molecularly 

 combined water plays such an important part in their 

 ultimate structiue, that we may base our pro\'isional con- 

 clusions on this total number of molecules. 



Theory of Invisible Germs. 



Calculating then from the various data given above, we 

 may conclude that a spherical particle one-tenth the dia- 

 meter of the smallest speck that could be clearly defined 

 with our best and highest powers, might nevertheless 

 contain no less than one million structural molecules. 

 Variations in number, chemical characters, and arrange- 

 ment would in such a case admit of an almost boundless 

 variety of structural characters. The final velocity with 

 which, such particles would subside in air must be so 

 slow that they could penetrate into almost every place to 

 which the atmosphere has access. 



Darwin^s Theory of Pangenesis. 



Full particulars of this theory \\\\\ be found at p. 374 

 of vol. ii. of his work on the variation of animals. He 

 nowhere gives any opinion as to the actual size of gem- 



