of the French physicist" (Jamin) "but show at the same time that the remarkable reversion of the density at 4°, is not without its influence on the amount of sensitiveness; the change of refractive index between 10° and 5° being 0.0002, whilst that between 5° and 0° is only 0.0001."

They give a table for the values of the index to five places, for A, D, and H at eight temperatures between 0° and 11°.

In 1867 Rühlmann (Pogg. Ann.,' vol. 132, p. 1 and 176) published an account of observations he had made of the refractive index of water at various temperatures; he also used a hollow glass prism and gives the values to five places, for lithium, sodium, and thallium light from 0° to 100°. He states, "Der Brechungsindex des Wassers nimmt stetig ab von 0° bis 80° R., ohne bei dem Dichtigkeitsmaximum irgend eine Abweichung von dem Aenderungsgesetze zu zeigen, mithin die Fortpflanzungsgeschwindigkeit des Lichtes stetig zu."

Lorenz (Wied. Ann.,' vol. 11 [1880], p. 70) made observations by an interference method, on the refractive index of water between the temperatures of 0° and 34°; and Dufet ('Jour. de Physique' (2), vol. 4 [1885], p. 389) determined the index of water at temperatures above 17° by the minimum deviation method and by an interference method, and also calculated from the results obtained by other observers the rate of change of the index with change of tempera

ture.

Ketteler (Wied. Anu.,' vol. 33 [1888], pp. 353 and 506) repeated Rühlmann's determinations for temperatures above 20°, using a total reflection refractometer, but did not make any observations at lower temperatures. More recently still, B. Walter has published ('Wied. Ann.,' vol. xlvi [1892], p. 422) a short account of some determinations of the refractive index of water to five places between 0° and 30° for the D line, made, apparently, with great care by the minimum deviation method.

That the refractive index of water increases with the decrease of temperature until the freezing point is reached, appears to be proved, but as few determinations of the values of the refractive indices of water near its point of maximum density have been published, I have ventured, as the matter is one of considerable theoretical importance, to bring before the Society an account of some determinations I have recently made.

The method employed was the ordinary one, the determination of the angle of minimum deviation for a ray of definite wave-length passing through a hollow glass prism containing water at a known temperature.

The goniometer used was made by Messrs. Troughton and Simms, it has an 8-inch circle divided into 10', and is read by means of two micrometers, directly to 10", and by estimation to single seconds.

The prism was made by Steinheil; the value of its refracting angle, as determined by six independent measurements, 60° 1′ 42′′-0.8".

was

The prism was surrounded by a water-jacket, through which a stream of brine, cooled by a freezing mixture, could be passed.

Openings in the water-jacket allowed the light which had passed through the collimater to reach the prism, and the refracted beam to reach the telescope. The temperature was ascertained by means of a thermometer with its bulb immersed in the water contained in the prism.

The prism was filled with distilled water which had been recently boiled and allowed to cool under reduced pressure.

The determinations were made exclusively with sodium light; it had been originally intended to make observations with lights of different refrangibilities, but it was found that, owing to the brilliancy and constancy of the sodium light, it was not only far easier to make observations with it, but that these observations would certainly be more accurate than those made with light of other refrangibilities.

The prism, not being in actual contact with the water-jacket, cooled very slowly, about four or five hours were usually necessary to reduce its temperature from about 9° to a little above the freezing point.

Owing to the experiments being made at temperatures different from that of the room, and to the temperature of the prism continually, though slowly, altering, it was found impossible to make the determinations by reversing the prism, and then taking half the angle between the two positions of the telescope as the angle of minimum deviation.

Several series of observations were therefore made with the prism in both positions of minimum deviation, and the differences between these readings and those made when the axes of the collimator and telescope were in the same straight line, gave the deviations.

Seven sets of observations were made, and the results are contained in Table I; which gives the deviations for both positions of the prism, and the corresponding refractive indices for the various temperatures.

The angles of deviation differ so little from each other, that any error in the determination of the refracting angle of the prism would not make any difference in the relative values of the indices; it would, of course, affect their absolute values. The probable error

calculated by the ordinary formula 0'674

Σα

✓ from the

n (n-1),

measurements made of the angle of the prism (see above) is ±0.8". A difference of 1" in the value of the refracting angle corresponds to two units in the sixth place in the refractive index; the probable

error in the refractive indices due to the measurement of the refracting angle of the prism is therefore rather less than +0·000002".

A difference of 1" in the value of the angle of minimum deviation

corresponds to 4 units in the sixth place of the refractive index; as the sets of micrometer readings were all fairly concordant, and their probable errors less than 1", the values of the indices were calculated to six places.

The temperatures at which the observations were made not being identical for the two positions of the prism, it was thought that a graphical method, though, from its nature, somewhat "arbitrary," would give a more truthful result than any arithmetical process of taking the means. The results were therefore plotted on paper divided into squares of 1 mm., 0.2° of temperature being represented by 5 mm. on the axis of abscissæ, 0·00001 of refractive index by 4 mm. on that of the ordinates; and a curve drawn in the ordinary way.

Owing to the scale on which the results were plotted, a good deal of "judgment" was necessary in drawing the curve. It was therefore thought desirable also to plot the results on a smaller scale, so far as the ordinates were concerned; this was done, one unit in the fifth place being represented by 2 mm., and another curve drawn. The values of the index for different temperatures, as given by the two curves were compared and were found to agree satisfactorily; and it therefore seemed probable that the curves were really fair representations of the observations.

In the first column of Table II the values of the refractive indices, relative to air, for each degree as deduced from the curves, are given to five places; in the second the values as found by Walter, and in the third and fourth those for sodium light, given by Gladstone and Dale, and Rühlmann.

The values show that the refractive index of water, as was first announced by Jamin, increases continuously up to the freezing point, the rate of increase, however, seems to change about 4°, the temperature of maximum density, as was pointed out by Gladstone and Dale.