which serves to measure refraction, and we observe the deviation of the luminous rays as in a solid prism, regarding only those which pass through the cavity in which the liquid is enclosed.

Determination of the Ratio of Refraction in Aeriform Substances.

39. THE refraction of the gases is observed in the same way as that of liquids, by introducing them into prismatic vessels, the faces of which are closed by parallel plates of glass; but there are few particular modifications depending on the constitution of these substances.

The gases have much less density than solids or liquids, and their refraction is much less at the same angle. To render it sensible, therefore, we are obliged to increase considerably the refracting angle of the prism in which they are confined. Borda had one constructed with an angle of 145° 7' 28", with a large cylindrical, hollow tube of glass, the two ends of which were cut into a prismatic form, and closed by glasses with parallel faces, carefully luted. The tube was pierced at bottom, and provided with a cock, capable of being attached either to an airpump or to a receiver, by which means a vacuum might be produced within the prism, and the gases under examination intro, duced. We have before said, that for the same substance the refraction is changed by a change of density; but the density of gases varies rapidly with a change of temperature or pressure. To be able to compare the results of different experiments, we must take into account these two elements.

40. To measure the pressure, we attach to the prism a verti Fig. 34. cal tube TV, communicating with its interior, and enclosing a

syphon barometer the open branch of which is long enough to permit the mercury to rise to a level, when a vacuum has been produced in the prism. The height at which the mercury of this barometer is supported by the gas within, determines the pressure. To ascertain the temperature, we might insert into the prism a small thermometer; but it would be necessary to place it in the middle of its capacity, which would intercept the light; on this account it is better to suspend two very sensible thermometers without the prism, and very near it, or even in

contact with its faces. The temperature of these faces, as indicated by the thermometers, may be taken without sensible error for that of the gas and air which touch them within and without; for we know how very easily gases acquire the temperature of surrounding objects. We take every precaution, moreover, that the temperature of the place where our experiments are performed, may vary but little during the experiment, and especially that it may vary very slowly.

This prism is then mounted upon a foot perpendicular to its length, by which it is fixed in a horizontal position. The place of observation and the object which we look at should be chosen in such a manner that this object may lie in the horizontal plane passing through the centre of the prism. We then observe the deviation with a repeating circle, the limb of which is also placed in the same plane, at first by approximation, and afterwards exactly, by the condition that the upper telescope, being turned from the direct object to the refracted image, they shall both be found to be on the same horizontal wire, stretched in the interior of the tube. To verify this horizontal position of the wire, it is well that the signal be placed in one of the faces of some large building which presents in its construction long level lines, by one of which we may be governed. Then the best of all sights is a vertical lightening rod which throws a dark line upon the vault of the heavens.

41. Here as well as in the case of solids and liquids, the method of observation consists always in directing the upper telescope of the circle alternately toward the direct object and the refracted image, in order to measure the angle of deviation. But as the deviation for gaseous substances is always extremely small, even with the large prism here supposed, it is necessary, in order to obtain its value exactly, to multiply our observations, and to take the mean of the results, that opposite errors may balance each other. This is done by a repeating process, founded principally on turning the prism from right to left, and from left to right alternately, so as to admit of our observing the deviation successively with the same telescope in these two positions, as is represented in figure 35.

We naturally attempt first to measure the refraction of atmospheric air. In this case we exhaust the air from the prism by means of the air-pump. This operation does not produce an

absolute vacuum; but when the density of the interior air is very much reduced, so as to support the barometrical column at the height of only a small part of an inch, this height is observed, and account taken of it in our calculations. We have, therefore, a prism void, or nearly void, of air, immersed in the surrounding atmosphere; the luminous rays must consequently, in penetrating it, suffer a deviation, determined by the excess of the refracting power of the exterior air, and this in fact takes place. If the upper telescope of the circle is first directed immediately to the object through the air, when we afterwards come to interpose the prism, the deviation is considerable; this is the effect of the refraction of the air. If the telescope be brought again to the object, by moving the limb, and the prism be then turned half round, the deviation is doubled, and the object twice as much displaced. For example, in our experiments, the prism was placed in one of the chambers of the Luxembourg facing the observatory, whose lightening rods were the points of sight. The turning of the prism carried the wire of the telescope from one side of the building to the other; or, to speak more exactly, the telescope remaining immoveable, the edifice seemed to move to the right and to the left of the wire the whole of this distance. Yet we could perceive no sensible dispersion, though undoubtedly there was one produced; but it was too small to be perceptible.

42. If we would observe the refraction of the air at different densities, the process is the same; we only exhaust the air to the proposed limit, which is indicated by the interior barometer.

When we wish to observe other gases, we must first exhaust the air from the prism as far as possible; observe the density of what remains, and then introduce the gas. This introduction is effected by means of a pneumato-chemical bath of water, or of mercury, if the gas is liable to be dissolved in water. It is necessary that the prism, and the vessel containing the gas, should be connected by a double stop-cock, as in the weighing of gases, in order to avoid the water-bubbles which might make their way into the neck of the instrument.

If we wished to obtain a dry vacuum in the prism, or dry gases, we should place in the glass tube which surmounts it a quantity of caustic potash to absorb the humidity. When this and similar substances act in a void, the absorption is almost

instantaneous; but in the air or in gases, a certain time is necessary for the vapours to be precipitated and to combine with the alkali. If, on the contrary, we wished to observe the refraction of aqueous vapours, it would be necessary to employ every means to moisten the air in the place where we make our observations, by sprinkling water, suspending wet cloths, and especially by raising the temperature; but we must avoid introducing these vapours into the prism, for being deposited upon its faces they would affect the passage of the light.

In all that we have said, we have supposed that the glasses which form the faces of the prism have their two surfaces exactly parallel. When great care is used in their construction this is perhaps nearly true, but it is highly improbable that the condition is ever rigorously fulfilled. But as the refraction of glass is very powerful, while that of the air is feeble, it is easy to see that an error of this kind must very much affect our results. To determine its effect, we open the stop-cock of the prism or even detach the glass tube which surmounts it, in order to give free access to the external air. We then observe the deviation in these circumstances, as we should with the prism void or filled with gas. If the surfaces of the glasses are exactly parallel, the object will not be removed from its place by turning the prism, since the interior and exterior air of the prism will be exactly homogeneous and of equal density; but if we observe any deviation, it will necessarily be produced by a defect of parallelism; and this quantity must be added, with its proper sign, to each of our other observations; for it is with this as with small quantities, of which the partial effects are only to be added to each other to obtain the total effect.

all very

Having now explained every thing which concerns the arrangement of the apparatus and the manner of making the observations, it remains only to determine the ratios of refraction of the air and of gases. This is a simple subject of calculation.†

† For the necessary formulas see Biot's Traité de Physique.

Fig. 36.

Fig. 37.

Of Spherical Lenses.

43. THE methods which we have employed to calculate the deviations of the luminous rays in their passage through prisms terminated by plane faces, may be applied to the general case in which the refracting medium is terminated by any curved surfaces whatever. For here, as in reflection, we may compare the luminous rays to mathematical straight lines, whose refraction for each point of the surface takes place in exactly the same way as it would do in the tangent plane. It is sufficient, therefore, to calculate the positions of this plane for each point of incidence, in order to determine the deviation of the luminous ray; and this calculation is always possible when the form of the surface is given.

In the common applications of optics it is not necessary to make our calculations so general; for in our experiments we make use of spherical glasses only, since there are no other forms which can be exactly and easily executed; it is sufficient, therefore, to analyse and calculate the refractions which these produce. To do this with all possible simplicity, and to comprehend the results indicated by analysis, we must first take a general view of the sort of glasses in question and make ourselves acquainted with their principal properties.

If we imagine a straight line, or axis, drawn through the centres of the two spherical surfaces which terminate such a glass, and that a cutting plane then passes through this axis, we shall have the profile of this glass, which, according to the directions of the curvatures that may be given to the two faces, will necessarily have one of the forms represented in figures 36, 37, 38, 39, 40, 41. These different forms are distinguished by the following names which are generally adopted.

(1.) The double-convex glass. This glass is called a lens, (the Latin word for a lentil, which it resembles in shape,) and the name has been extended to all the other spherical glasses.

(2.) The plano-convex lens. We speak of the concavity or convexity, always, in relation to objects situated without the glass.