But if k represent the fraction of the light lost by absorp tion and reflexion at the faces of the vessel, we have

To eliminate the effects of the vessel the experiment should be repeated with the vessel filled with water or some other fluid for which the absorption is small; the difference between the two results will give the absorption due to the thickness used of the absorbing medium.

Of course in all cases four positions of the Nicol can be found in which the two spectra will appear to have the same intensity. At least two of these positions—which are not at opposite ends of the same diameter-should be observed and the mean taken. In this manner the index error of the pointer or circle will be eliminated.

For success in the experiments it is necessary that the sources of light should be steady throughout. In the experiments recorded below two argand gas-burners with groundglass globes were used. The apparatus and burners must remain fixed, relatively to each other, during the observations.1

Dr. Lea has recently suggested another method of using the instrument to compare the concentration of solutions of the same substance of different strengths.

A cell is employed with parallel faces, the distance between which can be varied at pleasure. A standard solution of known strength is taken and placed in a cell of known thickness; let 1 be the concentration, that is, the

1 See Proc. Cam. Phil. Soc., vol. iv. Part VI. (Glazebrook on a Spectro-photometer).

quantity of absorbing matter in a unit of volume, m, the thickness of this solution. The apparatus is adjusted until the intensity in the two images examined is the same. The other solution of the same medium is put in the adjustable cell, which is then placed in the instrument, the standard being removed, and the thickness is adjusted, without altering the Nicols, until the two images are again of the same intensity, whence, if c be the concentration, m the thickness, we can shew that

cm = c1m1;

:. c=c1m1/m

.. (1) and from this c can be found, for all the other quantities are known.

We may arrive at equation (1) from the following simple considerations. If c be the concentration, cm will be proportional to the quantity of absorbing material through which the light passes. If, then, we suppose that with the same absorbent the loss of light depends only on the quantity of absorbing matter through which the light passes, since in the two cases the loss of light is the same, we must have

or

cm = c1m1,

c = c1m1/m.
Experiments.

(1) Determine by observations in the red, green, and blue parts of the spectrum the proportion of light lost by passing through the given solution.

(2) Determine by observations in the red, green, and blue the ratio of the concentration of the two solutions.

Enter results thus :

(1.) Solution of sulphate of copper 1 cm. in thickness.

(2.) Two solutions of sulphate of copper examined. Standard solution, 10 per cent., 1 cm. in thickness.

Thickness of experimental solution giving the same absorption observed, each mean of five observations.

The colour box is an arrangement for mixing in known proportions the colours from different parts of the spectrum and comparing the compound colour thus produced with some standard colour or with a mixture of colours from some other parts of the spectrum.

Maxwell's colour box is the most complete form of the apparatus, but it is somewhat too complicated for an elementary course of experiments.

We proceed to describe a modification of it, devised by Lord Rayleigh, to mix two spectrum colours together and compare them with a third. This colour box is essentially the spectro-photometer, described in the last section, with the two Nicols F and G removed. Between the lens L and the mirror K is placed a double-image prism of small angle, rendered nearly achromatic for the ordinary rays by means of a glass prism cemented to it. This prism, as well as the mirror K, is capable of adjustment about an axis normal to the bottom of the box. The prism thus forms two images of the slit, the apparent distance between which depends on the angle at which the light falls on the prism; this distance can therefore be varied by turning the prism round its axis.

The light coming from these two images falls on the direct-vision spectroscope ss', and two spectra are thus formed in the focal plane QR. These two spectra overlap, so that at any point, such as B, we have two colours mixed, one from each spectrum. The amount of overlapping

and therefore the particular colours which are mixed at each point, depend on the position of the double-image prism, and, by adjusting this, can be varied within certain limits.

Moreover, on passing through the double image prism the light from each slit is polarised, and the planes of polarisation in the two beams are at right angles. We will suppose that the one is horizontal, the other vertical. Thus, in the two overlapping spectra the light in one spectrum is polarised horizontally, in the other vertically. For one position of the analysing prism the whole of one spectrum is quenched, for another position at right angles to this the whole of the second spectrum is quenched. The proportion of light, then, which reaches the eye when the two spectra are viewed, depends on the position of the analyser, and can be varied by turning this round. Thus, by rotating the analyser we can obtain the colour formed by the mixture of two spectrum colours in any desired proportions, and at the same time the proportions can be calculated by noting the position of the pointer attached to the analyser. For if we call A and B the two colours, and suppose that when the pointer reads o° the whole of the light from a and none of that from B passes through, and when it reads 90° all the light from B and none from A is transmitted, while a, ß denote the maximum brightnesses of the two as they would reach the eye if the Nicol H were removed, then when the pointer reads 0° we shall have

The standard light will be that in the lower part of the field, which comes from the slit c, after reflexion at the mirror K. This light being almost unpolarised the reflexions and refractions it undergoes slightly polarise itis only slightly affected in intensity by the motion of the analyser. By adjusting the tap of the gas-burner we can alter its intensity, and by turning the mirror K we can bring any desired portion of the spectrum to the point B.

The instrument was designed to shew that a pure yellow, such as that near the D line, could be matched by a mixture of red and green in proper proportions, and to measure those proportions. It is arranged, therefore, in such a way that the red of one spectrum and the green of the other overlap in the upper half of the field at B, while the yellow of the light from c is visible at the same time in the lower half.

Experiment.-Determine the proportions of red and green light required to match the given yellow.

Captain Abney has recently shewn how, by a modification of Rumford's photometer, the luminous intensity at each point of the spectrum may be compared with that from a given source.

For this purpose a pure spectrum of the given source is produced on a screen. This may be done as in chap. xiv., fig. 34.

It is preferable, however, to use two lenses in such a way that the light from the slit s, (fig. xxxiii), which is placed at the principal focus of the first lens, falls as a parallel beam on the prism P. After refraction through it, parallel rays of each different colour fall on the lens L2, and are brought by it to a focus on the screen D D. In this screen there is a second slit (s), through which rays of only one refrangibility pass. These rays fall on a third lens (L3) arranged so as to produce on a white screen at F E an image of the nearer face of the