wooden floor touched the ends of the wire which formed the helix of the instrument with different metals, a deflection of several degrees was obtained. The two cells before mentioned, when connected by the floor, caused a deflection of 25°. The wooden floor was thus proved to be an incomparably better conductor than air heated to 400°.

When the strips of platinum were exposed to the direct action of the flame of a spirit-lamp, the first notice of the passage of electricity was obtained when they were placed at about three inches above its extreme point, and began to show signs of redness. The deflection increased as the strips were lowered into the flame, and attained its maximum at a small distance beneath the point of the cone into which the flame shaped itself. When the flame was strongest, there was a permanent deflection of 75°.

In these experiments care was taken to preserve the strips of platinum as nearly as possible at the same temperature. The two cells were removed, and the electricity of the flame itself was exhibited when the two strips were placed, the one above the other, within the flame, with their flat surfaces horizontal, so that they assumed different temperatures. The flame-current passed always from the hottest platinum strip through the separating interval of gas to the other strip.

Another attempt was made to ascertain the point at which heated gas permitted the passage of electricity. In the centre of the flame from a Berzelius's lamp is a cone-shaped obscure mass of air as yet unburned, but strongly heated by its vicinity to the flame; into this two platinum wires connected with the two cells were introduced from beneath; they were not heated to redness, but the gas nevertheless possessed a weak capacity of conduction. An approximation to the blue rim of the flame showed an increase of conductive power, and a deflection of several degrees was obtained.

When in this case one of the wires was caused to approach the blue edge of the flame, while the other remained at a distance, a deflection of 1° to 2° was obtained after the removal of the two cells; the deflection indicated the passage of a current from the hotter to the cooler wire.

The aperture through which the air passed upwards into the flame was stopped, and thus the dark interior of the flame became formed of the vapour of alcohol and the products of its decomposition; two isolated platinum wires were introduced through the stopping-cork into the central space, but as long as they were kept at some lines distant from the inflamed portion no trace of electricity passed from one to the other. When they were caused to approach the burning portion, the described phanomena exhibited themselves. In this case also a current was

observed to pass from the warmer to the less warm wire through the intervening space of gas.

The author concludes from these experiments, that air and other gases, when heated, and thus rendered conductible, excite electrically bodies plunged in them. Gases thus range themselves in the same list as other conductors of electricity. When two metallic wires, or other conductors which are connected at one end, are brought into contact with a sufficiently heated gas, we have, properly speaking, a closed circuit. If one of the places of contact with the gas be more strongly heated than the other, a thermo-electric current is the necessary consequence.

There is, however, another source of electrical excitation in the flame, as is proved by the following experiment :-One platinum wire was introduced into the obscure centre of the flame, the other was brought near its outer surface; a current immediately exhibited itself, which passed through the flame from the interior to the exterior wire. It continued to pass in the direction even after the outer wire had attained a bright red heat, while the inner one glowed but feebly. It is evident that the thermocurrent which would have passed from the hotter to the cooler wire, was in this case overcome by a current, the source of which was the place of contact of the flame and the air. The electricity here developed is so feeble, that the condensing electrometer is better suited to its examination than the multiplying galvanometer. It is easy to see, observes the author, how experimenters who have neglected to separate these two sources of excitation may have arrived at contradictory results.

By properly connecting a platinum wire, which was dipped into the centre of the flame, with a condensing plate, the latter became charged with negative electricity, and hence the author concludes that positive electricity is given off by the outer surface of the flame. The charging here is exceedingly slow, and can be greatly accelerated when a second wire, which is connected with the other plate of the condenser, is held over the flame.

One end of the galvanometer wire was connected with the platinum wire which dipped into the centre of the flame, the other end of the same was connected with the earth. The current thus obtained was too feeble to cause the slightest motion of the galvanometer needle. But when a spacious platinum dish containing water was brought over the flame and connected with the other end of the galvanometer wire, it required no very sensitive instrument to demonstrate the existence of a current.

"Hence," observes the author, "as the strength of the flamecurrent by an equal chemical activity and equal conduction of the inner portion of the flame is essentially dependent on the nature of the conduction from its upper portion, it must be con

jectured that the formation and carrying away of carbonic acid exercises only a subordinate influence in the matter."

Two pieces of charcoal, one of which is less heated than the other by the flame, deport themselves exactly as a pair of platinum wires under the same circumstances. Silver, copper, brass and zinc, have been also examined, all of which exhibited the same electrical deportment as platinum when brought into contact with heated air.

The following conclusions are drawn from the experiments above described :

1. Gaseous bodies which have been rendered conductible by strong heating are capable of exciting other conductors, solid as well as gaseous, electrically.

2. When a thermo-electric circuit is formed of air, hydrogen or carburetted hydrogen, alcohol vapour, charcoal, or finally a metal, whether combustible or incombustible, an electric current is developed, which proceeds from the hottest place of contact through the air to the less warm place.

3. The development of electricity which has been observed in processes of combustion, and particularly in flame, is due to thermo-electric excitation, and stands in no immediate connexion with the chemical process.

4. The products of combustion do not therefore by any means occupy the relation to the burning body which has been assumed by Pouillet; if positive electricity rises with the ascending gases, it is only in the degree in which the burning body and the air exterior to the place of combustion, or rather exterior to the place of hottest contact, are connected by a proper conductor.

XXIII. Notices respecting New Books.

A Treatise on Problems of Maxima and Minima, solved by Algebra. By RAMCHUNDRA, Teacher of Science, Delhi College. Calcutta. 8vo. 1850.

ΤΗ

HE time will come when Hindu antiquaries will search out the history of the revival of algebra in their country, by the agency of its introduction from the West. It will then perhaps appear worthy of note, that one of the earliest native attempts to write algebra in the European form is also an attempt to show that the domain of pure algebra can be extended, without prejudice to the superior facility of the differential calculus and of its equivalents.

The author's method, in general terms, is as follows:-If 4r be a function of the nth degree, which is to be made a maximum or minimum, it is assumed that x2-2+ax2-3+... is a divisor of x-r. The division being made, the identification of the remainder with zero leads to n-2 equations between the n-1 quantities r, a, &c.;

and the quotient, being of the second degree, shows the value of r in terms of a, b, &c., which separates the real from the imaginary roots. This value is the maximum or minimum required, and the equations are then numerous enough to determiner in terms of the coefficients of r. The author applies this method to cases as high as the sixth degree, with quantities of two terms, and then takes various problems in which more variables than one are found.

If it were given to one of our mathematicians to make ma-x¤ a maximum without any use of hypothetical increments added to hypothetical values, that is, without any use of the principle of the differential calculus, he would soon do justice to the ingenuity of the Delhi teacher; and this though he might smile at two pages of algebra substituted for two lines of the higher analysis. But the student of history has seen the use of compelling investigative power to work under restrictions. And the denial of tools of one kind has always been the stimulus to the improvement of others.

XXIV. Proceedings of Learned Societies.

Jan. 15, CH
CHAR

1852.

ROYAL SOCIETY.

[Continued from p. 71.]

HARLES WHEATSTONE, Esq., F.R.S., delivered the Bakerian Lecture, "Contributions to the Physiology of Vision."-Part II. On some remarkable, and hitherto unobserved, phenomena of Binocular Vision.

The first part of these researches was communicated to the Royal Society in 1838, and published in the Philosophical Transactions for that year.

The second part, now presented, commences with an account of some remarkable illusions which occur when the usual relations which subsist between the magnitude of the pictures on the retinæ and the degree of inclination of the optic axes are disturbed. Under the ordinary circumstances of vision, when an object changes its distance from the observer, the magnitude of the pictures on the retinæ increases at the same time that the inclination of the optic axes becomes greater, and vice versa, and the perceived magnitude of the object remains the same. The author wished to ascertain what would take place by causing the optic axes to assume every degree of convergence while the magnitude of the pictures on the retinæ remains the same; and, on the other hand, the phenomena which would be exhibited by maintaining the inclination of the optic axes constant while the magnitude of the pictures on the retinæ continually changes. To effect these purposes, he constructed a modification of his reflecting stereoscope; in this instrument two similar pictures are placed, on moveable arms, each opposite its respective mirror; these arms move round a common centre in such manner that, however they are placed, the reflected images of each picture in the mirrors remains constantly at the same distance from the eye by which

it is viewed; the pictures are also capable of sliding along these arms, so that they may be simultaneously brought nearer to, or removed further from, the mirrors. When the pictures remain at the same distance and the arms are removed round their centre, the reflected images, while their distances from the eyes remain unchanged, are displaced, so that a different inclination of the optic axes is required to cause them to coincide. When the arms remain in the same positions and the pictures are brought simultaneously nearer the mirrors, the reflected images are not displaced, and they always coincide with the same convergence of the optic axes; but the magnitude of the pictures on the retinæ becomes greater as the pictures approach. The experimental results afforded by this apparatus, so far as regards the perception of magnitude, are the following: the pictures being placed at such distances, and the arms moved to such positions, that the binocular image appears of its natural magnitude and its proper distance, on the arms being moved so as to occasion the optic axes to converge less, the image appears larger, and on their being moved so as to cause the optic axes to converge more, the image appears less; thus, while the magnitude of the pictures on the retina remains constantly the same, the perceived magnitude of the object varies, through a very considerable range, with every degree of the convergence of the optic axes. The pictures and arms being again placed so that the magnitude and distance of the object appear the same as usual, and the arms being fixed so that the convergence of the optic axes does not change; while the pictures are brought nearer the mirrors the perceived magnitude of the object increases, and it decreases when they are removed further off; thus, while the inclination of the optic axes remains constant, the perceived magnitude of the object varies with every change in the magnitude of the pictures on the retinæ. After this the author takes into consideration the disturbances produced in our perception of distance under the same circumstances, and concludes that the facts thus experimentally ascertained regarding the perceptions of magnitude and distance, render necessary some modification in the prevalent theory regarding them.

The author next reverts to the stereoscope and its effects. He recommends the original reflecting stereoscope as the most efficient instrument, not only for investigating the phenomena of binocular vision, but also for exhibiting the greatest variety of stereoscopic effects, as it admits of every required adjustment, and pictures of any size may be placed in it. A very portable form of this instrument is then described, and also a refracting stereoscope suited for Daguerreotypes and small pictures not much exceeding the width between the eyes. In the latter instrument the pictures are placed side by side and viewed through two refracting prisms of small angle which displace the pictures laterally, that on the right side towards the left, and that on the left side towards the right, so that they appear to occupy the same place. When the first part of these investigations was published the photographic art was unknown, and the illustrations of the stereoscope were confined to outline