be written (R3+4) Si. Moreover, oligoclase has similarly the oxygen ratio of Hornblende = (†R3+4¤) Sia. Hence we may look upon Leucite, and Andesine, with Pyroxene, as in a certain sense trimorphous. Still, their relation to the feldspar series is such that they are naturally classed with the other feldspars.

The zeolites, if the water be excluded, have the oxygen ratios of the feldspar-section, as shown in the following table; the oxygen of the water in the zeolites is annexed to the name of the species:

Some of the species are correspondingly isomorphous with feldspar species, as Analcime with Leucite, Ittnerite with Sodalite; and the ratio 1:3: 12 produces oblique forms in both series. But we do not intend to draw a general parallelism, as the water whatever its relations, must in some cases modify the ratios. But as regards the origin of the species, the table is an interesting one. Bischof remarks on the identity in the ratio between the oxygen of the bases and silica in chabazite and that of Hornblende, and thereby explains the occurrence of pseudomorphs of chabazite after hornblende.

Pyrrhotine (Fe S3) and Greenockite (Cd S).—As Pyrrhotine and Greenockite are homoeomorphous, they are naturally arranged in the same group, although the former has a little too much sulphur. The formula 5Fe S+ Fe S3, may perhaps be written FeS [+Fe S3], the latter term being unessential to the type.

ART. XXII.-On Microscopes with large Angles of Aperture; by Dr. E. D. NORTH.

We have no fuller or more careful statement of the mode in which an enlarged aperture increases the efficiency of a Microscope than that of Mr. Pritchard in his "Microscopic Illustrations," which is copied by Mr. Quekett. After explaining that since the whole diameter of the front lens receives a pencil of rays from each minutest point of the object, and that, consequently, when these pencils from each point are large, more light is received from the points separately as well as from the entire object, he adds :

"But it may perhaps be supposed from this reasoning, that if we throw a greater quantity of light upon an object, so that more may be collected by the object-glass, we shall be better able to define a structure; which would probably be the case if the additional light could be thrown only upon those minute parts of the object which we wish to examine, and not upon the whole object. But as we cannot do this, as the increase of illumination cannot be made to increase the relative proportions of light which proceed from those minute parts, the intended advantage will not be derived."

This paragraph involves implications directly opposite to some of the most important facts in regard to using Microscopes successfully. The second sentence says in effect, that when, with an object-glass of small aperture, and in a faint light, we discover a certain degree of minuteness of structure, we shall, under a strong illumination, discover no more, which is directly contrary to the fact, unless the objective is miserably deficient in correction. Indeed, a most important quality of first rate objectives, is their ability to bear a strong illumination.

It is also taken for granted that an increase of the relative proportions of light upon minute striæ and other markings, would enable us to see them better. On the contrary, the true requisite is that the objective shall be so perfectly corrected as to preserve the relative light, shade, and variations of color on adjoining minute portions, thus exhibiting the object precisely as it would appear were its smallest parts large enough to be visible to the naked eye. If some parts could be illuminated more than others, a false instead of a true appearance would be the result. By destroying the natural shading, we should get the appearance of a different object.

The limit of beneficial intensity of light depends rather on physiological than on optical conditions, being different with different individuals; one person's eye being pained and dazzled, when another's is aided. The direct light of the sun enables the aged to read without spectacles. It will be well, however, to notice that, although intrinsic brightness may be the same and very intense, yet if all the light entering the pupil comes from a minute surface, the eye is less affected on the whole. Place a card with a pin-hole at each end of a tube, and hold the latter near the eye, and we can gaze steadily at the small portion of the sun thus visible. But in general, the dazzling and blinding effect of intense light is owing to contrast, as when one comes from a dark room into sunshine. The contrast may be of surrounding objects, as in viewing in a darkened room the light of a galvanic battery.* In reference to extreme intensity of illumination, the

*By means of this contrast of light on a black ground, fine displays may sometimes be made of lines on test objects: thus, by using sunlight with Mr. Wenham's admirable condenser, the transverse lines of the Grammatophora subtilissima, (Greenport, in balsam,) are shown at regular intervals and sharply defined, the objective being Smith & Beck's, of largest angle.

following observation is most important. Artists, such as painters, engravers, sculptors, never employ a strong light on their work. The most important discriminations for them, are delicate gradations of color, of shadows, or of the mingling of the two. Their eyes, according to our observation, are by natural constitution very easily pained and dazzled. The finest artistic effects are possible only in a subdued light. An able writer on painting, remarks: "It is the property of (strong) light to convert objects into its own whiteness, and to take away color." Dimness of light and indefiniteness of outline, assist an active imagination. Faint illumination in the microscope may gratify an artist's eye by making the representation more pictorial, and especially by assisting the imagination in regard to depth. Such pictorial effects are suited to the popular eye, and it is allowable for the most accurate and reliable observer to gratify himself and friends with them as exhibitions of a peculiar kind. The object of the common Stereoscope, is to produce a pictorial, rather than a geometric impression on the mind: yet the brief reports as yet published respecting stereoscopic vision applied to the microscope, have not often discriminated these two kinds of effect.

The most minute objects now examined under the microscope, are colorless and transparent, and consequently do not need a diminished illumination for bringing out delicate variations of color, and, as is the case with the naked eye, it may be said in general that the inore the light, the more distinctly will the minutest portious cast a shadow or reveal themselves by their refractive and dispersive effect, up to that degree of general brightness of the image which a given eye can bear.

But what constitutes the extremest minuteness in regard to visibility? Simple and obvious as the answer is to this question, yet writers on the microscope speak of an increased angle as if it could in all cases compensate for a higher magnifying power.

As is the case with the telescope, or with the naked eye, an area is visible when it subtends an angle at the eye of at least "more than half a minute of a degree." Or, it may "be assumed that one minute of angle is a good general measure for the visibility of areas"-"therefore, that areas are visible at a distance of about 3,000 or 4,000 times as great as their diameter." "But though such a spot can be seen, it cannot be defined as square, circular, &c." "To be thus clearly defined to the naked eye, black spots on a white ground, must have a diameter of about 12% of radius." But black stripes can be separated when areas cannot be defined, and the whole is greatly dependent on illumination. As no two persons' eyes have precisely the same power of minute vision, the limitation in question must be to some extent indefinite; it deserves, however, and will doubtless receive further investigation.

Yet it is important to keep in mind that there is a limit which no illumination or enlargement of aperture will overcome without increase of magnifying power. It may lead to serious error to be accustomed to strain the eye with a low eye-piece or objective, when a more extended amplification of image ought to be employed for more decidedly separating lines or points. M. Robin argues for employing high powers in anatomical investigations, with an earnestness which proves a then prevalent error. Probably such mistakes have contributed to establish an impression of there being often a danger of using too much light. When endeavoring to look into minute structure with a low or medium power, when a high one is what is needed, one will unconsciously strain and prolong his attention, until, if the light be strong, he brings on confusion, dazzling and pain, which a weaker light may alleviate, and at the same time be sufficient for what the given amplification can reveal. As long as an increase of light assists the mind it can be borne by the eye, as is indeed proved by the present fashion of employing sun-light. Not only high powers, but well corrected medium ones, and even rather low ones, may thus be used, and that too with no diminution of light by obliquity. Fatigue and dazzling of the eye result also from aberration, as we shall presently show.

It may be well to mention a curious effect which is quite liable to result from attempting to accomplish too much with a given objective. When an object-glass is thus overstrained, a test may exhibit a set of lines, or even two sets, crossing each other, and forming dots, which are not the true lines, because two or three of them are united into one. The case is not similar to the doubling of lines, which is so often noticed. Although not well defined, those now in question are seen in focus, and although thickened and badly defined, are yet plainly visible and easy to count in micrometrically measuring their distances. Among other experiments in proof, the following is selected: The ribs of Pinnularia major were viewed with a low objective and intense lamp light, (sunlight is still better,) at an obliquity, very near the degree which produces a dark back-ground. The ribs were strongly visible, though not entirely across the semi-breadth of the valve. Being easily counted, the micrometer gave their distances and of an inch in different circumstances, with sufficient accuracy for the experiment. But when with the same light and illumination, a th objective was employed, the ribs were visible in their whole length, and with a perfect definition. Their distance was, in the specimens examined, beyond all room for doubt, found to be very accurately equal to only inch. Two acute microscopists and practiced observers, one of them an able microscope maker, witnessed, and themselves repeated this demonstration, and confirmed its reliability. The experiment

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will be found instructive and also easy by microscopists in general. A friend also mentions that he had noticed the same optical effect; and with sun-light had shown to two persons, one being a distinguished microscopist, that even when a power so low as one inch (a remarkably good one, however, by Mr. Grunow) was employed on the Navicula Angulata, lines of the true obliquity in reference to the sides were brought out, although so far apart and few in number, as manifestly to consist of but one in a space which really contains as many as three or four. The finest scales of the Lepisma Saccharina, with an objective of 11⁄2 inch, or probably the coarser scales with a power even considerably lower, are convenient for this purpose. Undoubtedly, tests of very close markings are often supposed to be resolved, when in fact only half the number of lines is seen, and these thickened, flattened, and badly defined. We do not see how the performance of an objective can be stated scientifically, except on Nobert's lines or when it is confirmed by the micrometer.

It is obvious that as the image of a faint star in the telescope, so is an indivisible point or line in the image formed by the objective of a microscope. In both instruments the necessary condition of visibility is that light enough come from a point in the image to stimulate the optic nerve sufficiently. Hence when the desideratum is not to separate two points, but to perceive the existence of a solitary one, to magnify in a higher degree without at the same time admitting more light, may cause the point to vanish from sight. Low eye-pieces are appropriate for discovering faint markings, higher ones for separating those whose obscurity comes from being extremely near to each other.*

The demand for light in using high magnifying powers is enormous. A minute anatomist when dissecting under a low magnifier, or with the unaided eye, illuminates a tissue with as much light as possible, often employing two condensers of artificial light, yet as the brightness of an image is diminished in inverse proportion to the square of the linear magnifying power, an ultimate fibrilla of voluntary muscle, when magnified 1000 diameters (and as much or more amplification is needed), would have only 1,5th part the light on its image, were it not for the large aperture of the objective.

With a microscope just as with a single eye, we judge of depth and form, by means of geometrical foreshortening and infinitely delicate gradations of light, shade, and sometimes color; assisting our conclusions by change of focus and directing attention to different parts and presentations. Nothing shows more strikingly

*The President of the London Microscopical Society remarks that although Mr. Wenham thought the apertures which he had gained were of no utility beyond 150°, yet to himself they seemed to have greater power of discovering or indicating the existence of lines, though they were insufficient for defining them. In this remark the same principle is recognized.

SECOND SERIES, Vol XVII, No. 50.-March, 1854.

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