I may observe, that I was rather surprised to see these images on globules of mercury even as large as 1-70th of an inch in diameter, especially as they occupied a part of the globule exactly opposite to that on which the light coming directly from the condenser fell. The illumination of this part of a globule cannot be attributed to radiated light, as none of the rays coining from below can reach it, and a mere image on a reflecting surface cannot be supposed capable of absorbing light, and therefore it cannot radiate it.

I may observe also that I found considerable difficulty in determining the cause of this fact, chiefly because the different circumstances under which it was examined gave such contradictory results. I first thought that an image was formed in the microscope which was reflected upon the upper surface of the globule, which I afterwards found to be only partially correct. My friend Dr. Bristow suggested the probability of its being a reflection from the lower surface of the object-glass, which was also in part correct ; but as neither of these suppositions satisfied all the conditions under which these images were seen, I made the following experiments with a view to simplify, and therefore to facilitate, the examination as much as possible.

I removed all the lenses from Gillett’s condenser, and employed only the diaphragm with the flat side of a mirror, when I found, on examining globules of mercury with achromatic lenses of different magnifying powers, that images of the stops were formed as before, though very much more minute, and much less perfect. Hence I concluded that the appearances above described, although much exaggerated by condensing lenses, are not entirely produced by them.

I next examined with a simple lens, of about one-inch focus, globules of mercury illuminated by Gillett’s condenser, and I found that when they were not covered by a piece of thin glass no image was formed upon them, but when they were covered, the thin glass being 1-200th of an inch above them, that a distinct image of the stop was seen upon their upper surface.

Hence in this instance, no doubt could exist as to the cause of the image, as it could only have been produced by the reflection of the rays proceeding from the source of light, and impinging obliquely upon the under surface of the cover backwards upon the upper surface of the globule, the figure of the stop being occasioned only by the quantity of light which it intercepted, and thus prevented from falling upon the glass, and consequently from illuminating the globule.

I next substituted for the simple lens achromatic lenses of one and two inch focus, and the result was precisely the same ; that is, when no cover was placed upon the object there was no image, but when it was, there was a distinct one. In all these cases the cover was l-200th of an inch from the object : if this distance be increased beyond a certain limit, images will not be formed on the globules. The greatest distance for perfectly flat glass is about l-30th of an inch : but if the glass be convex and the globule be placed beneath the centre of its convexity, the distance is very much increased, the amount of increase depending upon the degree of the convexity of the glass cover.

I then examined an uncovered globule of mercury with a lens of l-4th of an inch focus, on which I could perceive two imperfect and distorted images of the stop of the diaphragm. They were of different size, and did not appear to be-exactly upon the same plane ; the smaller one was the nearer and seemed to be much darker than the other. As in this case the distance of the object-glass from the object was less than l-30th of an inch, I concluded that the glasses composing it had reflected the images on the globule, especially as there were two images, in the same way as the glass cover had done in the experiment with the simple lens and the low powers.

Lastly, I substituted a half-inch for the quarter, and the result was the same as when the latter was used, excepting that one of the two images was very distinct and permanent, whilst the other one was fugacious, appearing and disappearing with the slightest movement of the head. The distance of this lens from the object exceeded the 1-30th of an inch, the limit at which images are formed on flat glass ; but as it did not exceed the limit at which images are formed on convex glass, I concluded that these images were reflected by the glasses composing the objective, in the same way as when the quarter of an inch lens was employed, especially as two images were apparent.

The inference, then, to be drawn from these experiments is, first, that the image of the source of light is larger with condensing lenses than with a plane mirror ; secondly, that when low powers are used to examine covered objects the images are produced by the reflection of the rays coming from the source of light, and falling obliquely upon the cover, backwards upon the object ; but that, when high powers are used, those coming near to the object, the lenses themselves reflect the images on the object.

But the formation of images like those above described is not confined to opaque metallic globules, since all transparent substances of a globular figure are well known to have the property of reflecting the images of objects thrown upon them by a reflector. However, the explanation just given does not apply to transparent but only to opaque globules. Among transparent bodies I have particularly observed this fact in some minute spherical calcareous bodies which were found on the capillaries of the brain ; also in globules of oil, provided they are not too much flattened ; in air bubbles, starch granules, spherules of glass, &c. &c. There is one circumstance respecting all transparent globular objects worthy of notice, which is, the position of the image on the globule. If a globule be of a refractive power greater than that of the medium in which it is examined, the image of the source of light will be seen on its anterior surface, or a little in front of it : if these conditions are reversed it will be seen on its posterior surface, or a little behind it. Hence, if globules of oil be examined in water, the image of the stop of Gillett’s condenser will be seen on their anterior surface, whilst, on the contrary, if globules of water be examined in oil, the image will be seen on their posterior surface. If a minute spherule of plate-glass be examined in water, the image of the stop will be seen on its anterior surface, but if the same spherule be examined in oil of cassia it will be seen behind it ; whilst if the spherule be examined in Canada balsam, which has nearly the same refractive power-as glass, no image will be visible.

This fact furnishes the means of distinguishing one body from another by its refractive power, and is particularly applicable to very minute particles. If, for example, there were suspended in water very minute spherules of calcareous matter, such as those I have mentioned, which look more like air than anything else, and globules of air, these would be readily distinguished by the position of the image of the stop, the former having the image on its anterior surface, the latter on its posterior.

As the distinctness of these images will depend upon the degree of transparency and homogeneousness of the bodies on which they are formed, and as their form will be very much influenced by the greater or less perfection of the spherical figure of the surface which reflects them, the strange appearances which, from this cause, may mask and disfigure the true characters of microscopic objects, will be almost endless. And it must be remembered that these defects are common to all kinds of illumination of transparent objects in some degree or other.

Notwithstanding these defects, from which I have shown that the most modern methods of illumination are not free, we have in the latest improvements the means, not only of rendering them of but little account, but of converting them into advantages as useful aids in microscopic analysis.

In the experiments on the globules of mercury it was observed that when a number of globules were in one field of view, an image of the stop of Gillett’s condenser was seen on all of them. Now, it must be further observed, that as all these appearances are secondarily the reflection of only one magnified image of the stop, which can be seen by a low power, situated on a plane posterior to that on which objects are visible, and exactly in the axis of the microscope, only that globule whose axis coincides with that of this image can have upon it a perfectly symmetrical figure of the stop ; upon all the others this image will be distorted, the degree of distortion being proportional to the remoteness of the globule from the axis of the microscope.

This applies equally to all objects, transparent as well as opaque. Hence we see, that all appearances of an object which are not the same when it is placed in the centre of the field of view as when it is placed near its margin are spurious. It must be remembered that the difference of focus, although never so slight, consequent on removing the object to different parts of the field, must be taken into consideration, and that when the object is removed from one part of the field to another each position requires a fresh focus.

I will give one example. If one of the pale shells of the guano be illuminated by Gillett’s condenser, the smallest stop being under the lenses, and examined by a lens of one-eighth focus, it will present a reticulated appearance, the true nature of which is not very evident ; however, as thus illuminated, the meshes will present different appearances, according to the focus at which they are seen, and these appearances will vary as the object is being removed from one part of the field to another, showing them to be the reflection of something situated in the axis of the microscope. If, now, the object is so focused that the dark spots in those meshes which are situated in the centre of the field is made as distinct as possible, and the condenser is rotated, the spots occupying these meshes will be seen to move, and be recognisable as the images of the stop of the diaphragm of the condenser.

The appearance, although much less distinct, will be precisely the same as that presented by the compound cornea of a very minute insect, when examined under the same circumstances. Hence the true structure of such shells as these is manifestly lenticular, that is, each space is filled up by transparent material in the form of a convex lens.

I might give many other examples, but this will probably suffice to show to what use the facts which I have mentioned may be applied. The use of Mr. Gillett’s condenser in this kind of analysis might be extended, if something more characteristic than a stop were placed in one of the perforations of the diaphragm, as, for instance, a small cross.

I will now conclude this paper by some observations upon dark-ground illumination, as shown by Mr. Gillett’s condenser, and Mr. Wenhain’s paraboloid.

If a globule of mercury, illuminated by Gillett’s condenser, with one of the stops under the condensing lens, be examined by a very low power—a one or two inch lens—it will have the appearance of a dark disk surrounded by a circle of light, and if it be covered with thin glass, there will be an image of the stop at its centre, but not otherwise. In this case the object is seen on a dark ground, which is the magnified image of the stop interposed between the object and the light, and thus all the central rays of the illuminating pencil are cut off ; and, as the rays .which are thrown immediately upon it are considered to have a degree of obliquity given to them by the margin of the stop, too great to allow of their entering the microscope, the object is thought to be rendered visible only by the light which it radiates as if it were self-luminous. As this mode of illumination is precisely the same as that with the paraboloid, I will defer the further consideration of radiated light until the action of that instrument is explained.

For this purpose it will be necessary to repeat the examination of the globules of mercury, when illuminated by the paraboloid, first when uncovered, and afterwards when covered with a piece of thin glass, situated about l-200th of an inch from the object. In the first case the globules will appear to be surrounded with a circle of light, in which the cross-bar contained in the tube of the paraboloid, or any other object reflected upon the tube by the mirror, can be seen. In the second case there will be two circles of light—an external one, which is the same as that just described, and an internal one ; the latter is the image of the end of the paraboloid reflected upon the mercury by the glass cover. The cross-bar and other objects are also seen, as in the first case.

I may observe that in all these experiments I have not thought it necessary to notice the various appearances produced by the reflection of different parts of the microscope, as the extremity of the object-glasses, &c., upon the objects, as these can be easily recognised.

Now, according to the theory of the illumination of microscopic objects by radiated light, “all objects, either transparent or opaque (excepting white), absorb some of the rays of light falling upon them,” and are rendered visible by the portion which they radiate. Hence Mr. Wenham observes, “that no rays from the source of light should enter the object-glass by passing through or around the object, which must be illuminated by very intense light, thrown on it, in all or in opposite directions, at an angle exceeding the aperture of the object-glass, so that the light which enters the microscope should be that which radiates only from the object as if it were self-luminous.”

As a great part of the luminous appearance presented by the covered globule of mercury has been shown to be due to the light first reflected from the glass parabola upon the glass cover, and then by the latter upon the upper surface of the globule, that much of the appearance cannot be the effect of radiated light. The glass cover having in this instance served the purpose of a Lieberkühn, has made the object appear in a false light ; and as nearly all microscopic examinations are made on covered objects, the paraboloid is in this respect defective, and the error must always be allowed for. It is true that all objects are not spherical, and, therefore, do not possess the property of reflecting perfect images, yet they will derive some portion of the rays by which they are illuminated from the reflection of the source of light upon them, in the same way as if they were globular.

With respect to the illumination of uncovered objects, experiment is equally at variance with a leading postulate of the radiated-light theory, which is, that no rays from the source of light passing around the object enter the object-glass ; for if this were true, the image of objects reflected by a plane mirror up the tube of the paraboloid could not be seen by a two-inch lens of 12° angle of aperture.

This will be best understood by referring to the adjoining diagram, in which A is to represent the paraboloid, B a compound microscope, CD an object-glass of two-inch focus and 12° of angular aperture. Now, suppose (m, n) a ray of light coming from a part of the window-frame, or from close to the outer side of the cross-bar within the tube of the paraboloid, to be thrown upon the point (n) of the parabolic reflector, it will be so reflected as to pass through the focus (f), and continuing in the direction (n, f, g), it cannot, under the conditions specified, enter the microscope, and consequently the part from which it emanated would not be visible. But these are not the sole conditions ; for, suppose a globule of mercury to be placed at then it is very easy to see how this same ray (n,f), by being reflected in the direction f,c, and making the angle of reflection equal to the angle of incidence, would pass through the object-glass, CD, and form an image of the point from which it had proceeded, according to the common laws of refraction ; and it is in this way the object is seen. Now, as what is true with respect to this ray applies equally to every other ray thrown by the parabola upon the margin of the globule, we may conclude that it is the light which is reflected from its entire circumference which produces the appearance of the circle of light before described ; and so also if there were any number of globules, each would be surrounded by a ring of light reflected from it in the same manner.

But if we suppose any other substance, possessing in a much inferior degree the property of reflecting light, to be situated in the place of the globule of mercury, it will be illuminated in the same way by the rays concentrated upon it by the parabolic reflector, which rays it will reflect also according to the same law ; and such an object would no more be seen by radiated light than the picture of a portion of the window-frame on the upper surface of a globule of quicksilver would be. This explanation of the manner in which objects are seen as illuminated by the paraboloid, is equally applicable to the same objects when illuminated by Gillett’s condenser, and examined by a low power. I may further add that this explanation is in accordance with the simplest laws of optics, that it agrees in every respect with experiment, and that it assumes no endowment of material substances with properties which they are not well known to possess.