was as ready to his hand as it was to that of Hall; and even after achromatism had been established, Biot (no mean authority) declared that it would be "impossible" to work achromatic objectglasses for the microscope on account of their diminutive size.

It is both amusing and instructive to take books written at different periods of the present century, and note how each writer in his turn expresses the conviction that now at last perfection has been reached. Thus Sir D. Brewster, in 1813, wrote that, "in the combination of single lenses to form the compound microscope, opticians have arrived at a great degree of perfection." In 1829, after the first achromatic object-glass had been successfully made, Dr. Goring wrote that "microscopes are now placed completely on a level with telescopes, and like them must remain stationary in their construction." Sir D. Brewster, later, wrote: "The ingenuity of philosophers and of artists has been nearly exhausted in devising the best forms of object-glasses and of eye-glasses for the compound microscope." What was written so lately as 1875 I have already referred to.

I believe that we are far from having arrived at the limits of the possible; but whether this view is accepted or not, I may, I think, assume that, however high may be the authority on which such a statement as that which I have referred to is made, there can be no necessity to spend any time in proving that much is still to be learnt that we all agree in the definition given of the character of the true philosopher, "hoping all things not impossible, and believing all things not unreasonable," and "are ready to encourage rather than to suppress anything that can offer a prospect or a hope beyond the present obscure and unsatisfactory state.'

What, in my view, is desirable is not that the Society should value less highly than they do now investigations in the various branches of natural science that can be made only by the aid of the microscope, nor that we should in the smallest degree diminish the appreciation which we have of those Fellows who bring the results of such investigations before us; but simply that more attention and encouragement than are given at present should be given by the Society collectively, and by the Fellows individually, to what I may call the subject of pure microscopy, which may be considered as standing in much the same relation to what is now accepted as "microscopy," as pure mathematics stands to applied mathematics (so called).

The optical principles of the microscope and its accessories form one branch, the other deals with the investigation (considered mainly as a problem of mathematics and physics) of the phenomena presented by objects viewed by means of the microscope, and the determination of their real properties, notwithstanding their deceptive visual appearances.

It would perhaps be only imitating the old quarrel of the logicians to discuss whether there can be any science of microscopy outside these limits; but if it be otherwise, the boundaries of the science must be as extensive as the world itself, the elephants and palms having as good a claim in that case to be considered "microscopic objects" as the rotifers and the diatoms.

I need not dwell on the first branch further than to point out that our text-books give the uninstructed reader the impression that the microscope stands in point of principle on no higher level than the telescope. This is far too low an estimate, and it would be truer to say that the microscope stands to the telescope at as great a relative distance as the chronometer stands to the sun-dial. Without having before them the means of comparison, it will, I know, be difficult, if not impossible, to convince the Fellows how much there is in this respect of which we know absolutely nothing when the comparison has been made, the absurdity of the chapter in our books which professes to deal with "the optical principles of the microscope" will be fully appreciated. Whilst as M. Robin, the French histologist and microscopist, says, "it is absolutely necessary to be familiar with all that concerns dioptrics when one has to make use of an instrument whose invention has been inspired by the discoveries made in this part of physics,' I do not know a book that even attempts to instruct the microscopist as to the course of the rays in passing through the ordinary objective of a compound microscope, or ventures upon anything beyond the barest mention of diffraction-the most common of all microscopical phenomena, and most intimately concerning not only the theory but the practical working of the microscope.

At the present time there is nothing extant which constitutes even a commencement of a systematic theoretical treatment of the subject of illumination, yet, being purely optical, it is obviously capable of being so treated, and great practical advantages would undoubtedly follow from the development of an exact theory on the subject. In nothing has the ingenuity of microscopists been more exercised than in the invention of novel modes of illumination for lined objects; but however clearly these various appliances may bring out particular appearances, there is good reason to believe that in the majority of cases they are illusions, originating in the character of the illumination employed, and that all possible methods of illumination may be reduced from the fifty or more kinds now existing to less than half a dozen at the most.

With regard to the second branch, the conditions under which microscopic vision takes place necessitate (at any rate, in our present stage of experience) a more or less laborious reasoning process before we can recognize what it is we really see,

though long experience and habit have enabled us (apparently) to dispense with any such reasoning in the case of ordinary vision. The appreciation of this necessity has in modern times been a little lost sight of, and there has been too great a tendency to depend on mere sense, instead of on sense and reason combined, or, in other words, to merely view the object rather than to investigate its true nature. "The impressions of sense," says Whewell, "unconnected by some rational and speculative principle, can only end in a practical acquaintance with individual objects."

For this reasoning process data are in the first instance. required. These data, obtained from a systematic and scientific investigation and recording of the varied experiences of microscopic vision, considered, so to say, in the abstract, are of the highest importance, and would in time serve to render microscopic observation almost wholly free from the fallacies and uncertainty which now beset it.

Although it is a stereotyped expression of our authors that in the case of the microscope "seeing is not believing," the subject is left with the vague warning, that "no rules can be given for the avoidance of such errors, since they can only be escaped by the discriminative power which education and habit confer."*

I venture to think, however, that there can be no difficulty in framing such rules. It is only necessary that microscopists who have acquired the power referred to should record the results of their discrimination and experience.

If each observer keeps the results of his observations for his own exclusive use, little or no advance will of course be possible; but progress will be greatly accelerated if such records are made, for new workers are able to take up their investigations where their predecessors left off, and not only avoid the waste of time and misdirection of energy involved in going again over ground already exhausted, but also the discouragement which necessarily arises from the uncertainty whether what they propose to do has not been done before. One of the most useful offices of such a Society as ours is the assistance it is able to give to this object, so that it is not necessary that anyone should write a complete treatise on the subject, but by means of our Proceedings' can note isolated facts for the use of future students.

The phenomena to be investigated range over a very wide field, and it is not possible within the limits of this paper to present a complete analysis of the subjects in regard to which systematic investigation would be valuable.

Among them would be the appearances presented in consequence of the refraction of light by objects of various regular or irregular forms, spherical or cylindrical, with waved or other

* Carpenter, 5th ed., p. 195.

surfaces, hollow or solid, and of different densities. The effects produced by the reflection of light from objects in numerous modes. The varied and deceptive appearances brought about by the interference of light, a subject which in England, at any rate, is in its relation to the microscope almost untouched. The effects produced by double refraction and polarization. The variations, in differing circumstances, in the colours of bodies. The large range of phenomena involved in the appearances presented by the same object with different kinds of illumination, or in media of different refractive powers. The determination of the indices of refraction and dispersive powers of objects (matters which materially aid in the determination of their true nature). The discrimination of holes from mere depressions, and other variations of structure.

A few clearly settled generalizations would enable a large group of phenomena to be resolved.

As an example of the way in which what is only one small item of this subject may be treated, I may refer to the discussion by Nägeli and Schwendener of the interpretation of the image of a hollow cylinder, a typical form of microscopic object.

They discuss the theory of the formation of the image in four groups :

1st. The peripheral rays which traverse the walls of the cylinder without entering the cavity.

2nd. The peripheral rays which strike the internal surface of the cylinder very obliquely, and are there reflected.

3rd. The rays which penetrate into the cavity of the cylinder and are reflected on the walls, then arriving at the objective after having undergone two refractions (that is in all, four refractions and one reflection).

4th. The rays which traverse the cavity of the cylinder in a straight line and undergo a quadruple refraction.

Thus is shown on theoretical principles the appearances which such objects will present in different media, or in the other varying conditions in which they may be placed.

I have disclaimed the necessity of having to prove the practical use of such investigations; but "without prejudice" (as the lawyers put it) to that position, I may ask if it can be doubted that such generalizations would be of the greatest assistance to other observers, and the practical results important and useful?

There are numerous instances of the way in which the appreciation of purely optical or physical principles has served in the past to elucidate biological questions, and may serve to elucidate others in the future. I remember having read (though I have been unable to verify the passage) that Harvey himself attributed his discovery of the circulation of the blood to the investigations he had previously made on the pressure of liquids in tubes.

So simple a matter as the experiences of Welcker on the effects produced by globules of air or oil immersed in a fluid of greater or less refractive power than themselves, has enabled subsequent observers to distinguish more readily and with more accuracy elevations from depressions, and to determine the true structure of a large class of objects, so that vacuoles need no longer be mistaken for nuclei.

The supposed tubular structure of human hair can be shown to be erroneous by the application of such principles, and the belief in the solidity of the lacunæ of bone was disposed of by a consideration of the refractive effects of Canada balsam.

The determination of the refractive index of a substance will often show that it belongs to one class of bodies, such as the albuminoid, and not to another, and enables proper deductions to be drawn of the real as opposed to the apparent size of cavities, such as those in the interior of starch grains. If an object exhibits double refraction it cannot be fluid, and the examination of muscular fibre by polarized light will determine whether it is at rest or in the state of contraction.

66

A paper by Mr. Lowne, just read before the Royal Society, on the Eyes of Insects," will furnish another instance of the assistance the naturalist would derive from being able to refer to an established theory of microscopical observation, an important part of the conclusions come to in the paper turning upon the results of experiments on the effects manifested by the transmission of light longitudinally through glass tubes and threads."

Our friends the histologists have arrived, as some of them conceive, at the limit of the resolution of structure; and my senior colleague, who is ready to seize with such avidity on any process that seems to indicate the possibility of further knowledge on histological subjects, would, I am sure, rejoice if he could be guaranteed the power of determining more of the ultimate structure, say of a muscular fibre, than he is now able to do.

I believe that guarantee might be given if the work I am advocating were undertaken, and that it would be found in the result that the histologist best grounded in such work was the best authority in the determination of structure,† and many at present obscure problems would be in a fair way of solution.

* Since printed in 'Proc. Roy. Soc.,' vol. xxvii. 261.

Since this paper was written I have seen the lecture on "Microscopes" (in vol. i. of the 'Science Lectures at South Kensington'), by Mr. Sorby, F.R.S., the late President of this Society, in which he points out (p. 203) that "much may be learnt by the study of mineral structures, since in the case of crystals and of solid portions of glass and other analogous objects we know what their character is, whereas in the case of minute organic structures we have rather to infer what is their structure from what we see; therefore, in forming some general idea of illumination, I think we may learn a great deal by studying what we see in small crystals and in inorganic bodies of pretty well known form."

VOL. I.

L

And