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the formula thus deduced theoretically to the observations made by Zeuner, Weisbach, and Fliegner, it seems to result that, for the atmosphere, the “co-efficient of discharge," as determined by Weisbach, is equal to the exponent of discharge," as that term is used by Zeuner, and is represented by the number 1.41. In the investigations of this latter physicist, certain resistances have been taken into account, such that, in general, the co-efficient and the exponent of discharge will be different for different fluids. It is in those cases in which the internal resistance or viscosity of the fluid is o that the co-efficient and the exponent of discharge become equal.

THE INVISIBILITY OF MINUTE BODIES. The invisibility of minute bodies subtending a sufficient visual angle to be readily seen if properly defined, is a highly curious and important fact. This depends upon several causes that have been examined by Dr. Pigott, in a paper lately read before the Royal Microscopical Society. Minute bodies are often solely distinguished by the sharpness and decision of their outlines. The question is, can this outline be altered by the conditions of vision, or by any relation between the refractive index of the substance and the aperture of the objective? In examining minute globules of glass, or minute spherical bubbles within a larger mass of glass, we notice a very perfect picture of such objects as are beyond the globules, and the whole surrounded by a black band. The field of view is found to be precisely three fifths of the diameter of the bubble; the breadth of the band being the same when we look at the bubble for all objectives, whatever may be the aperture; but when we look at a solid sphernle, we find that the breadth of the band increases from nothing up, until it occupies the whole spherule as we diminish the aperture; the angular aperture at which the black band first appears varies with the refractive index of the glass bead. It results from these observations that the aperture of the objective regulates the appearance or disappearance of the circular black outline of minute refracting spherules, or the black bands of refracting cylinders. It thus appears that the aperture of the microscope objective must be adapted to the refractive index of

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the substance under examination, in order that we may be able to distinguish minute spherules, cylinders, or other bodies from each other. In the course of his paper, Mr. Pigott states that no glass yet constructed, whether microscopic or telescopic, has been adequate to present to the eye the real size of the image of the sun reflected from a small spherule. With a telescope, the disk, which ought to be the Tour of an inch, appears something like the 7 of an inch in diameter, or the spurious disk is five hundred times larger than the reality. He concludes from many careful experiments that microscope object-glasses are more finely constructed than the telescopic, but that great improvements are still necessary in that direction.--Monthly Microscopic Journal, Feb., 1875, 55.

RECENT IMPROVEMENTS IN THE MICROSCOPE. The President of the Royal Microscopic Society, in his late anniversary address, states that the past year has been marked with decided improvements in the construction of microscope object - glasses. A remarkably fine one - eighth inch has been made by Messrs. Powell & Lealand. The image borne by this lens bears amplification by deep eyepieces exceedingly well. Mr. Wenham has constructed a one-seventh inch on an improved formula, obtained by substituting two plavo-convex lenses for the single plano-convex posterior lens originally employed. The new lenses are superior in definition, and far superior in clearness and absence of fog or milkiness, to any other objective known to him. As regards fog, this defect is very conspicuous in the one-sixth inch made by Ross, which is constructed of a single front lens followed by three cemented combinations. There are some reasons for surmising that fog is partly dae to the multiplication of cemented contact surfaces; and if this be so, the general principles of analysis would lead to the conclusion that the amount of the defect in question would be in proportion to the square of the number of cemented surfaces. Thus, this one-sixth inch of Ross, which has four cemented surfaces, might be expected to present four times as much fog from that cause as the one-seventh inch recently made by Mr. Wenham, which has only two cemented surfaces.- Monthly Microscopic Journal, 1875, 98.

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TESTING MICROSCOPE OBJECT-GLASSES. Dr. Pigott advocates the method of testing the objectglasses of microscopes by examination of the miniatures reflected from small globules, especially the examination of the sun's image as seen reflected in small globules of mercury. In this method, an object-glass of fine quality is screwed into the sub-stage of the microscope in an inverted position. On black velvet there are scattered, from a syringe containing mercury, a number of mercurial globules; then, by means of a prism, a brilliant light is thrown vertically downward upon them. The object-glass to be tested is now screwed to the nose of the microscope. The two objectives are brought to a central position, so that their axes coincide, and the instrument is then adjusted to form miniatures of the globules for examination. The most beautiful effects are seen under sunlight. The miniatures develop appearances of marvelous beauty and variety. The aperture of the miniature-making objective should be at least as wide as the objective to be tested, and the lens of the finest quality obtainable. Among the innumerable illuminated objects that may be used, Dr. Pigott strongly recommends what he calls the fundamental experiment; that is, a disk of intense light as small as possible, viewed from a distance sufficiently great to develop the test diffraction rings. It is well known that the surface of the illuminated globules of mercury becomes more nearly spherical as they diminish in weight. The law of the curvature of these surfaces dependent upon the specific attraction of mercury has been investigated by Professor Bashforth, though not yet published. Under direct illumination, a minute spectrum of the sun may be described. The symmetry, beauty, and fineness of refraction rings exbibited by these miniatures from illuminated globules of mercury are severe tests of the objective, and afford delicate means of adjusting its corrections. - Monthly Microscopic Journal, 1875, 147.

ACCIDENTAL OR SUBJECTIVE COLORS. Mr. Plateau states that observations made by himself upon a number of persons of his own acquaintance have

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shown him that it is impossible to adopt the principle that
the accidental or subjective color observed when we cease
contemplating a bright object has always a tint comple-
mentary to that of the object itself. This subjective tint
depends upon the eyes of the observer; and the cases where
the principle is satisfactory constitute rather the exception
than the rule, at least so far as concerns blue and yellow.
Therefore, in a recent communication to the Belgium Acad-
emy,

he

says that he must continue to maintain the general theory, with reference to accidental colors, that he published forty years ago, and which he thinks has not been sufficiently considered by recent authors. His theory consists essentially in the following propositions: First, during the contemplation of a colored object, the retina exerts an increasing reaction against the action of the light which falls upon it, and tends to throw itself into an opposite state. Conscquently, after the disappearance of the object, it takes spontaneously, or, as it were, by inertia, its opposite state, whence results the sensation of the accidental or subjective color. Then it comes to repose by a sort of oscillation, in virtue of which it passes alternately from the accidental to the complementary tint, and vice versa. The physiological condition of the retina after the prolonged action of light is very nearly like the state of a body which, drawn from a position of stable equilibrium, then abandoned to itself, returns to repose by a series of decreasing oscillations. Second, analogous phenomena take place in reference to space; while one portion of the retina is submitted to the action of a col. ored light, the surrounding portions throw themselves into the opposite state; whence results, all around the colored image, an aureole of the accidental colors, and, finally, beyond this aureole there is a tendency toward a manifestaiion of a cloudiness of the same tint as that of the primitive image. Such a state of the retina can but be compared to that of a vibrating surface, in which the nodal lines are separated by vibrations in opposite directions. This theory has, he says, been adopted in France, but is quite rejected by the German and English physicists. He has been so oCcupied by his extensive researches into the phenomena of thin liquid films that he has not until lately found time to defend his theory. In the memoir in question he adduces

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numerous observations tending to disprove the theories of Scherffer, and of those who have followed him, as also the theories of Thomas Young and his followers.-Bul. Ac. Roy., Belgique, 1875, 100.

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REFLECTION OF THIN FILMS. Govi bas made a happy application of that principle in optics by which thin films can at the same time reflect and transmit rays of light according to their angles of incidence. He applies a film of gold to the hypothenuse of a right-angled prism of glass; the film allows direct rays to pass through the prism, while the latter reflects the oblique rays coming through the microscope. By placing this prism obliquely upon the ocular of a microscope, the magnified image is reflected upon a sheet of paper, where it can be drawn by the observer who looks through the gold film.Rev. Sci., 1874, 167.

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SIEMENS'S ELECTRICAL PYROMETER, AND DIFFERENTIAL VOL

TAMETER. We had occasion some years ago to give some account of the very elaborate investigations made by Weinhold in reference to the reliability of the various methods employed for ineasuring very high temperatures accurately, and to call attention to the fact that his researches fully substantiated the claim of Dr. Siemens that the electrical pyrometer, as constructed by him, was a thoroughly reliable instrument. It is now a pleasure to be able to refer to the very important memoir of Dr. Siemens himself, just published in the Journal of the Society of Telegraph Engineers. This memoir, which was in part delivered as a lecture in 1871, has been delayed in its publication, owing to the innumerable interruptions experienced by the author in consequence of his professional duties. The fullness of its details shows how large a series of experiments Dr. Siemens undertook to satisfy himself of the accuracy of his method of measuring temperatures.

His memoir consists, first of all, of a very suggestive chapter on the influence of temperature upon the electrical resistance of metallic conductors, which he expresses as a function not only of the temperature reckoned from the absolute zero,

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