the same time to the eye, and we diminish the brighter one until it becomes of equal intensity to the feebler. The quantity of this diminution measured as a fraction of the primitive intensity expresses the comparative brightness of the two lights. In place of estimating directly the equality of the brightness of the two images, we can oppose them one to the other, giving birth to phenomena such as will render their perfect equality more sensible-for example, by transforming and transmitting the inequality of intensity into the production of color. The photometers of comparison which possess the greatest perfection can perhaps be called photometers by opposition; such are those of Wild, Bunsen, Dove, and one of Arago's photometers. The essential part common to all photometers by comparison and by extinction is that which is designed to diminish the intensity of the light, under the condition that the quantity of this diminution shall be exactly measurable. To this end, recourse has been had to the eight following methods: First, the absorption of the light by an apparently transparent medium of variable thickness. Second, reflection from a polished surface at a variable angle. Third, reflections from one, two, three, or more surfaces respectively, at an invariable angle. Fourth, the reduction of the intensity by a deviation by means of reflection of a portion of the light. Fifth, reduction of the intensity by two polarizing systems or planes of polarization by inclining them to each other at an invariable angle. Sixth, reduction by bifurcation of the ray in a double refracting prism. Seventh, reduction by the increas ing separation of the rays of a conical pencil. Eighth, exclusion of a portion of the beam of light which enters the pupil of the eye. This exclusion may be accomplished by means of a diaphragm placed either near the eye or in front of the objective of the telescope, or within the terrestrial telescope at the place occupied by the small diaphragm of the quadruple ocular. Of all the combinations that we have enumerated, Thury has chosen one of the most simple, viz., a photometer having a variable diaphragm and reflecting mirrors. His instrument is adapted to a four-and-a-half-inch refractor of excellent defining power, and has since 1868 been applied especially to the nebula and the components of double stars. The photometric system adopted is, there

fore, that of the visual photometer by extinction. The enfeebling of the light is obtained by reflection from one or more mirrors situated between the objective and the ocular, and by a diaphragm having a variable opening placed in front of the objective. This diaphragm is composed of sixteen thin rectangular plates, sliding simultaneously and uniformly each in the direction of its length, and the direction of the radius that passes through the centre of the objective. The polygon of a variable diameter and symmetrical form is the real aperture of the objective. When the aperture of the telescope is diminished too much, the dimensions of the false disks of the stars increase, and the diffraction rings that surround the false disk become so modified that the conditions of visibility are no longer the same for two stars viewed with very different apparatus. It is necessary, therefore, to correct this source of error by diminishing the brightness of the brightest stars, not by contracting the aperture, but by introducing the use of mirrors. A comparative table is given, showing the relative effects of mirrors and diaphragms. Two classes of scales have been adopted in expressing the orders of brightness of the stars. The photometric scale of Sir John Herschel was based upon the simple fact that the intensity of light diminishes as the square of the distance. The brightness of the stars belonging to the first, second, third, etc., magnitudes on his scale was therefore respectively one quarter, one ninth, one sixteenth, etc. The system more generally followed is such that the brightness of a star of any order is always a certain constant fraction of the brightness of a star of the next succeeding order, so that the arithmetic series of magnitudes corresponds to a geometrical series of intensities. The constant ratio in this system would naturally be so chosen as to change as little as possible the magnitudes that have been somewhat arbitrarily assigned to the stars by many generations of astronomers. The actual photometric series of Sir John Herschel accords remarkably well with the ordinary scales of magnitudes, if we simply multiply his magnitudes by 1.41, and take for the unit of intensity a star equal to that of Alpha Centauri. But the photometric scale of this astronomer of fers grave inconveniences, which have hitherto prevented its being adopted. The smallest star visible in the twenty-foot

reflector of Sir William Herschel, and which is at least of the twentieth order of magnitude according to the scale used by this astronomer, belongs in fact to the three hundred and twentieth order of magnitude on the photometric scale. The geometric scale offers none of these inconveniences, although, on the other hand, it leaves something arbitrary in the choice of the constant factor of the progression. In both scales the standard of magnitude must be adopted as the fixed point of departure; this is an arbitrary point, whose selection demands much careful consideration. The choice of this unit of brightness may depend upon the following considerations: First, it may be a star of invariable brightness (if such exist). Second, it might be an artificial light, if we take means at hand for producing a light of constant value. Third, it may be determined by the effect upon either the eye itself, or upon the inert bodies that are employed in the photographic process. As regards the eye, it should be remembered that the image found upon the retina depends upon the more or less perfect adjustment of the eye of the observer, and, second, that the aperture of the pupil is va riable within very considerable limits. These two latter sources of uncertainty may be remedied by simple means, when it will be found that it is highly convenient to adopt as a standard the faintest stars visible to the normal eye. This unit having been determined by many observers for many stars, the average of all will be a unit representing the average sensitiveness of the human eye, and independent of fluctuations in the brightness of the stars, and which therefore is sensibly constant.-Bibliothèque Universelle, 1874, 209.

FLOW OF AIR THROUGH ORIFICES.

An extensive series of observations has been made upon the flow of air through orifices, and its discharge under great pressures, by Professor Fliegner and Dr. Zeuner, of the Polytechnic School at Zurich. The velocity of discharge can be obtained theoretically from the kinetic theory of the constitution of gases, according to which theory the molecules are, at relatively great distances from each other, moving in straight lines, except when they impinge on each other, or on the walls of the contained vessel, in which cases they rebound as if perfectly elastic. Applying

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 0 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 spherule, 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

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 of an inch, appears something like the 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 plano-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 due 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.