fluid. A tench consumes, at an average, fifty thousand times less oxygen than a man. Yet respiration is indispensable to the existence of the fishes. Confined in a small body of water, which is excluded from the contact of the external air, they soon become faint and oppressed; and their sufferings evidently increase in proportion as the oxygen is abstracted and consumed. The gold fish, cyprinus auratus, which is extremely vivacious, introduced under water that had been carefully purged of its air by

distillation and recent boiling, was

almost instantly affected. In ten minutes it was seized with violent convulsions, followed by utter prostration of strength; but its functions were again speedily restored, on admitting into the receiver a portion of river water. In the mammiferous animals, the whole oxygen inhaled by them is again expired in a state of combination with carbon. But the carbonick acid that fishes reject, never amounts to four fifths of the quantity of oxygen which they had previously abstracted from the mass of water. What becomes, then, of this surplus oxygen : Is it absorbed into their system : And is it the cause of that superiour irritability which they display : It is another distinguishing circumstance, that fishes absorb a very large portion of azote, nearly equal, sometimes, to the oxygen itself. This phenomenon was proved, by subsequent experiments, to be in no respect accidental, but to depend on the regular principles of their organick assimulation. Some fishes were introduced under water which had been impregnated with azote, oxygen, and hydrogen, by exposing it newly boiled to a mixture of these gases, the hydrogen assisting, by the play of double affinities, the union of the oxygen: in the space of three hours, they were taken out almost dead; and the water being

then distilled, yielded back only its share of hydrogen, the oxygen and azote having both disappeared. Water, charged with carbonick acid, powerfully affects the nervous system, and acts on small fishes as a mortal poison. Tench, confined in it only for a few minutes, expire in convulsions. The oxygenated muriatick acid is scarcely more prompt in its effects. It was of importance to determine, whether fishes extract air from water by the action of their gills only, or have, besides, a power of absorption diffused over the surface of their body. The most lively tench were selected for this trial. Their heads were cased in collars of cork lined with wax cloth, which spread out into a covering fastened by means of sealing wax to the top of a cylindrical vessel containing, river water. This cylinder was next inverted into a bucket filled likewise with river water; and the more effectually to prevent any communication between it and the water in which the body of the fish was immersed, a small layer of quicksilver covered the ring about the neck. A tench would live in that constrained position for the space of five hours, without experiencing much inconvenience. The water contained in the cylindrical vessel now furnished, on being distilled, nearly the same aërial products, as if respiration had actually been performed in it. The venous blood must, therefore, attract oxygen, and transmit carbon through the fine expansion of the skin, with an energy similar to what is exerted by the proper organs of the bronchials themselves. The skin, however, shows no action at all on the ambient air. But the bronchials are capable of performing a double function; they not only separate oxygen from water, but can inhale it from the atmosphere. A fish, placed in a vessel containing a very small quantity of water, is soon obliged to rise to the surface, and project its head, for the sake of breathing. The water, which had been robbed of its oxygen, indeed, attracts this again from the atmosphere, and gradually communicates it to the lower strata; but the process of restoration is so extremely slow, that, if the fish be prevented from getting to the surface, languor and exhaustation will quickly supervene. Various kinds of fishes were introduced into the several permanent gases. In common air and oxygen gas, they opened their gills very wide,' but did not absorb that vital nutriment in a larger proportion than if water had been the medium of communication. Under azote, they became languid, and apparently dead, in the space of four or five hours. The effects of hydrogen were still more deleterious. But carbonick acid acted with such envenomed force, that though the fishes hastened to shut their gills against its influence, they were yet absolutely killed by it in a few minutes. Since the respiration of fishes is so very limited, we should scarcely expect any notable evolution of heat from that process. Accordingly, it was found, that the most delicate thermometers, inserted in their mouths, indicated no visible differ

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tainly throw considerable light on the physiology of fishes. We are only disposed to doubt a little, whether their accuracy can be entirely relied on. The analysis of the gaseous products was evidently imperfect; for water, which has been thoroughly boiled, will still continue to discharge a notable residuum of air, if placed under an exhausted receiver. But the indications of the eudiometer are, from a variety of causes,

peculiarly liable to inaccuracy, and

depend much on the skill and manipulation of the experimenter. The observations of Provençal and Humboldt, however, are decidedly more complete than any of a like nature; and, after making every deduction, we cannot hesitate to regard the general results as, at least, near ap" proximations to the truth. They are not incompatible, however, with those conclusions which Biot’s experiments appeared to countenance. A fish that inhabits the depths of the sea, under such enormous compres" sion, living in circumstances extremely different from one which plays near the surface, may be expected to exert a far superiour energy. If a small river fish can, by the action of its gills, overcome the adhesion of air to the encompassing liquid, may we not suppose an inha: bitant of the ocean to be capable of developing an organick force sufficient to dissolve that union of oxygen with hydrogen which constitutes water itself? On any other hypothesis, indeed, the minute portion of oxygen dispersed near the bottom of the sea, must have, in time, become exhausted; nor could it again be sensibly restored by the very slow absorption at the surface, and the still slower communication through such a lengthened series of incumbent. Strata. On the Motion of Light in Diafthamous Media. By M. Laplace. The curious phenomena of double refraction is produced by various mineral substances. It was first ob


served in Iceland spar, or the rhomboidal crystals of the carbonate of lime, in which it appears very conspicuous; but several other crystals manifest a similar property, though differently modified. If a dot made on a sheet of paper be viewed through a piece of Iceland spar laid over it, two dots are constantly seen in the direction of a diagonal joining the obtuse angles of the rhomboid, and separated from each other by an interval generally proportioned to the thickness of the crystal. It is evident, therefore, that, in penetrating into rhomboidal spar, a ray of light must, besides the usual refraction, suffer an extraordinary one, bending it towards the obtuse solid angle of the crystal. When light traverses the substance, the opposite sides of the rhomboid being parallel, it must always escape at the same inclination with which it entered; but the part that suffered the extraordinary refraction, emerging at a different point, will, according to the length of its internal passage, occasion a small shifting or parallax, thus forming the secondary image, which likewise, for that reason, appears at a less depth. The cause of this double refraction has long tortured the ingenuity of philosophers. Huygens, who, with the finest taste for geometry, and the most exquisite skill in conducting mechanical analysis, unfortunately blended some prejudices, derived from the Cartesian school, advanced an hypothesis, repugnant, indeed, to the sober principles of induction, but which seemed to furnish an easy explanation of the leading facts. He supposed light to consist in the undulations of an etherial fluid, highly elastick, of extreme tenuity, and diffused through universal space. Those undulations, in ordinary cases would, from their equable expansion, form spherical shells; but, in entering Icelandick spar, each incipient undulation would, he conceived, assume the shape of an oblate sphe

roid, whose centre is the point of incidence, and its axis parallel to the short diagonal of an equilated piece of the crystal, and having, to the perpendicular diameter, the ratio of nine to ten. As ordinary refraction depends on the sine of inclination or the ordinate of the circle, so extraordinary refraction was made to depend on the ordinate of the generating ellipse. An hypothesis so fanciful and arbitrary, sunk, on the triumph of the Newtonian philosophy, into hopeless neglect, from which a concurrence of circumstances has again drawn it into notice. This memorable instance may teach us, that, while in physical matters, we ought to proceed with the utmost caution, yet we should not hastily reject, even the wildest hypothesis. To proscribe the workings of the fancy, would, in many cases, be to arrest the progress of science. If an hypothesis be not allowed to warp the understanding, it may serve at least usefully to connect certain insulated facts, until their true explication be discovered. The earliest attempts of Kepler were employed in tracing the relation between the periods and the distances of the planets. Struck with the mystical properties of numbers, he tried the multiplied combinations; and the result which he thus obtained, was the offspring of a teeming and restless imagination. But the speculations of that sublime though irregular genius, afterwards guided the steps of Newton, and finally merged in the great law of gravitation. Our learned countryman, Dr. Woollaston, who has, on many occasions, shown such uncommon felicity in adapting to practice the known principles of . science, lately invented a very simple apparatus, which enabled him to determine, with equal ease and accuracy, the refractive power of the smallest fragment of crystal, or of the minutest film, whether solid or liquid. He was hence led to examine

narrowly the constitution of rhom

boidal spar. He remarked, that the deviation of the extraordinary from the ordinary refraction, is not a constant angle, as Newton had inferred; and pursuing his observations, he discovered, that the force which produces this extraordinary refraction, is itself variable, and depending on the position of the refracted ray. Thus, he found the refractive power to be greatest, in a line bisecting the obtuse solid angle of the rhomboid, and least in the transverse direction, the index of the former being 1,571, and that of the latter only 1,488. In the intermediate positions, those measures followed a certain law; which Dr. Woollaston could not unravel, till he was referred to the Huygenian hypothesis, with which they seemed perfectly accordant. This unexpected and singular coincidence has been since confirmed by some delicate experiments of M. Malus. However then, we may value the hypothesis of luminous undulations, as an attempt at philosophical exposition, we cannot, with justice, refuse, it the merit of connecting the chief phenomena, and of accurately marking the various results. Impressed with that sentiment, M. Laplace has sought to arrive at the same legitimate conclusion, by combining the principles of dynamicks with the higher calculus. His investigation is founded on the celebrated law of least action, first proposed by Fermat, next improved and extended by Maupertuis and Euler, and afterwards deduced by Lagrange from the primary condition of motion. According to this law, a particle of light, in its passage between two given points, one without, and another within the crystal, must describe such a route, that the distance traced before it enters the crystal multiplied by its velocity, and the distance traced after its entrance multiplied by the corresponding velocity, shall, together, form a sum which is a minimum. M. Laplace

hence derives two differential equations, in which the internal velocity is an indeterminate function of the angle which the refracted ray makes with the shorter axis of the rhomboid. He then examines two simple cases, in which these equations are modified. The first is, where the square of the velocity of light within the crystal is increased by a constant quantity, and which it is well known, obtains generally in diaphanous media. The second case is, where the expression of the action of the crystal is of the same form as that of the square of the internal velocity, or where this square is further augmented by a term proportional to the square of the cosine of the angle made by the refracted ray with the shorter axis. The measure of deflection being the same on either. side of the axis, it was obvious that the even powers only of the sines or cosines, and which are always positive, could be admitted into the expression for the effect. Having thus restricted the equations of partial differences, M. Laplace subjects them to a variety of operations, and brings out, after the usual reductions and substitutions, certain integral formule which comprise the phenomena of refraction, and are entirely consonant with the Huygenian hypothesis. He, therefore, concludes, that we may regard this result with confidence as an established law of nature. We are disposed to give full credit to the penetration, the expanded views, and the rich and varied talents of Laplace. In the management of the calculus, he cannot, indeed, rival the clearness and elegance of Euler; but he surpasses that great master of analysis in the extent of his acquirements, and the general soundness of his physical ideas. The present memoir may be considered as a fine specimen of analytick art; but here we are inclined to think that its praise should stop. It is grounded on assumptions

just as gratuitous and arbitrary as those involved in the hypothesis with which it is contrasted. If Huygens supposed his spherical undulation to flatten regularly into a spheriod, Laplace thinks himself entitled, by the theory of functions, to round the expression of the square of the internal velocity, by an additional term of the same form, which might coalesce into a shapely compound. But this is only a mode of conception, and surely not the genuine interpretation of Nature. Fancy will, according to the taste or prevailing habits of the individual, amuse itself alike in contemplating the properties of figure, or the relations of quantity. Huygens, as a geometer, looked to the transformation of curves; Laplace, as an analyst, has preferred the symmetry of functions. Much as we admire the lofty flight and commanding skill of the continental mathematicians, we are not blind to their defects and errours. They have long overrated the real value of the art of analysis; and have in many cases applied it to objects which it is not capable of attaining. Forgetting that the most refined calculus can only facilitate the combinations of thought, and can educe no principle but what was previously infused into it, these inquirers appear sometimes to imagine themselves occupied with contemplating the connexion of actual existences. In marshalling their symbols, and performing the grand evolutions, they are apt to overlook those smaller occasional movements on which the final position really depends. Several of the most eminent mathematicians of the continent seem almost to have persuaded themselves, that without recurring to external observation, they could demonstrate the laws of motion, and the primary relations of space, and consequently establish the principles of physicks and geometry, by a dexterous application of the methods of analysis . That all this is mere illusion, requires no proof; but we may

remark how imperceptibly the more obvious truths steal upon us, and become blended with the structure of a laborious and intricate process of calculation. We cannot help thinking, that the continental philosophers, in their physical researches, are by far too much disposed to generalize. The conditions of the problem, under its widest aspect, they instantly embody in symbols, and proceed, by various changes and contractions, to reduce the principal expression to a manageable form; and not until then does the serious attack commence. Such a procedure might remind us of the toil of Penelope. It would surely be wiser to moderate the pretensions of analysis, and avoid the glaring abuse of symbols. If, as at a former period, the necessary restrictions and abbreviations affect. ing the nature of a problem were previously introduced, the differential expression that results would always be much simpler, and less apt to bewilder. We would not particularly object to the choice which M. Laplace has made of the law of least action. Yet, though it is now derived from a legitimate source, it is but too apt, we think, to betray the vagueness of its metaphysical origin. The subject of this memoir might, we presume, admit of a simple investigation, from the fundamental principle of accelerating or retarding forces. Since the differential of the square of velocity is equal to the product of the force into the differential of the space, it easily follows, that a ray of light which undergoes the ordinary refraction, has the square of its . velocity increased by a constant quantity; and, therefore, from the decomposition of motion, the sines of the angles of incidence and of refraction are proportional. But when a ray suffers the extraordinary refraction, it is moreover attractéd in the direction of the short diagonal of an equilateral rhomboid. Now,

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