glass body, a solid bit of glass, which occupies 10 mm.; hence, it is obvious that when the trough is charged with a liquid, the light will pass through 1 mm. in the lower half and 11 mm. in the upper half of the trough. In other words, light passing through the upper part will be weakened in the proportion to the lower as 10 is to 1; it will pass through 1 mm. of the lower half and 11 mm. of the upper half. This trough is so adjusted before the divided slit of the spectroscope that the light passing through the one half slit is wholly derived from the upper half of the trough, and that passing through the other half slit is wholly derived from the lower half.

Before the trough is placed in position both slits are opened an equal width, and the light adjusted until an exactly equal illumination is obtained. On now adjusting the trough the illumination will, of course, be unequal.

A complete revolution of the micrometer screw is equal to 100 divisions, and supposing that to make the light equal, the one micrometer screw has to be turned down to 30, then, as the intensity of the light falling through the 1 mm. is to be considered as equal to 1, the unabsorbed light is in the proportion of 30 to 100, or as 0·3 to 1. The light passing through the 1 mm. being equal to 1, and the light passing through the solution to 0.3, then the extinction coefficient is equal to the reciprocal or arithmetical complement of the logarithm of 0.3, or e log 0·3.

If a table of logarithms be consulted, the logarithm of 0.3 will be found to be 1-47712; if the last figure in the decimal portion be subtracted from 10, and the remainder from 9, and the index or characteristic be diminished by 1, this gives the arithmetical complement-that is, 0.52288, which is the extinction coefficient. The extinction coefficient being known, the absorption proportion must be obtained, and this is known if the concentration is known, for

If c = the concentration expressed as grammes per cubic centimetre. e the coefficient extinction.

A = the absorption proportion.

If the absorption proportion is known, the concentration unknown, all that the experimenter has to do is, for one or more definite regions of the spectrum, to work out the extinction coefficient, multiply this by the absorption proportion for that particular region of the spectrum, and the result equals the grms. per c.c.—that is,

c = e A.

In other words, once the absorption proportion for various regions of the spectrum is known, it is easy to ascertain the percentage composition. The more regions of the spectrum investigated, of course, the more accurate is likely to be the determination.

As an example, let us take the absorption spectrum of permanganate. For wave lengths, 680-7 to 650, Krüss found that a solution containing 0.001 grm. per cc. gave a coefficient extinction of 0.47238; and for a concentration of 0.00025 per cc. a coefficient extinction of 0.11351.

Therefore, dividing c by e in each case, for the one we get as the absorption proportion 0-002116, for the other 0-002202, the mean of which is 0.002159.

In the region embraced between the wave lengths 596-4 and 582.8, for solutions containing respectively 0.00025 grm. and 0.000125 grm. per cc., Krüss found the coefficient extinction to be 0.40561 and 0·16242; the mean of the results of

c divided by e is 0.006845;

and so on for various portions of the spectrum. For example, if it were desired to ascertain the strength of a solution of potassic permanganate, the unknown solution would be diluted until, from its colour, it was judged to be somewhere near the strength of the solution whose absorption proportion was known and several extinction coefficients obtained. Thus, in the present instance, supposing for the wave lengths 680.7 to 650·1 an extinction coefficient of 0.47238, and for the wave lengths 613-2 to 5964 a coefficient extinction of 1.08093 was obtained, the absorption proportion for the respective wave lengths being known to be 0·00215 and 0.0009186, we should have—

[ex A = c.]

(1) 0·47238 × 0.002159 = .00102

(2) 1·08093 × 0.0009186·00124

giving a mean value of 0·0011, the real value in this case being in a cc. 001; a nearer approximation could be made to the true value by more determinations.

For every coloured substance there are special regions of the spectrum most suitable for quantitative estimation, and it is necessary in ascertaining the "absorption proportion" to measure carefully the proportions of the spectrum observed; for example, Krüss finds that the most suitable regions for the quantitative estimation of potassic permanganate solution are

as shown in the following table, which also gives the absorption for those regions:

If oxygen is to be determined by permanganate, then the absorption, in terms of oxygen, is for the wave lengths given-0.00004833, 0·00005699, and 0.00008296.

Three solutions of permanganate gave the following strengths, as estimated by the spectral method, using alone the three regions mentioned; 0·00189 grm., 0.00218 grm., and 0.00228 grm. per cc., while titration with sodic thiosulphate gave 0-00191, 0.00217, and 0.00229, thus proving the great accuracy and convenience of the method.

As before mentioned, any spectroscope with an accurate scale may be used, but Krüss has invented an instrument which has some special advantages; it is called the "Universal Spectral Apparatus," and is represented in fig. 14.

S is the double slit before described, and is carried by the collimator, A; the edges of the slits are of platinum, and both edges open equally; B is a tube carrying the ordinary photographic scale, the image of which can be thrown on the prism; the 100 on the scale is made to coincide with the sodium line, D. The prism is contained in D; two prisms are supplied with the apparatus, one a flint-glass prism with a refracting angle of 60° and a dispersion extending from A to H2 = 4° 30', the other a Rutherford prism with a dispersion from A to H2 of 8° to 11°. The first is used for qualitative work, and in cases where good illumination is preferred; the second when a long spectrum is necessary. C is the telescope, and the eyepiece contains cross threads, this piece carries the special measuring apparatus, which is represented in detail in the figure. This measuring apparatus is accessory to the scale, already mentioned, carried by B, which, for most purposes, is all that is necessary; but for fine measurements the micrometer arrangements, 71, 1, and T2 la are useful.

2

The lower milled head micrometer screw has its circumference, r1, divided into 100 divisions; it moves the telescope round the axis, V, and the cross threads of the telescope being made to coincide with any line or band, by means of the scale, i1, and the divided circle, r1, a measurement expressed by four figures, can be made. Similarly the upper milled head works a micrometer screw, and is supplied with a similar scale, l2r2 This upper screw moves the cross threads, and by its aid very fine measurements may be made; k is a vertical slit in a shutter, and its use is to shut out all other parts of the spectrum save that under observation.

Whoever uses the double slit for the first time will experience some difficulty in educating his eye to appreciate small differences in the upper and lower half of the strip of colour. The main errors of observation are due to placing the eye in such a position that more of the one slit is seen than the other. It is essential to success for the two portions observed to be nearly

equal. The double slit can also be used as a colorimeter; that is to say, by the use of a reflecting prism and two fairly equal lights, the illumination by a little management is made equal and then the light from the one solution, whose value is known, is caused to pass through the one slit, and the other rays from the second source of illumination are made to pass through the solution of unknown concentration through the other slit. Then by widening or narrowing the one slit the light is equalised.

In a similar way the colour of two samples of water can be appreciated; or a sample of water can be compared with distilled water. For this purpose a stratum of from 10 to 20 cc.

is necessary.

In making comparative colorimetric observations by the aid of the double slit, the solutions by suitable dilution should be made approximately equal, for equality produced by a moderate narrowing or widening the slit gives the best results.

gif

T

§ 57. Photography.-The introduction of dry plates and the general simplification of photography will, in a very little time, make its practice general in all the larger laboratories for purposes of registration. In important analyses, likely to entail evidence in the higher courts of justice, it might be useful (and will always be possible) to photograph certain analytical results. In the quantitative determination of mixtures of starches, a microphotograph of the mixed starch and the "imitation" mixtures, renders the counting of the number of starches in the field a very easy operation. Similarly, if a measurement of any object be required, a micro-photograph having been taken, and next a photograph of the stage micrometer with the same powers, the object may be measured more easily than in the ordinary way. It is also most useful for the analyst to have by him, in this way, a series of "picture records" for reference. Stein's photographic microscope,* when the object is not to make pretty pictures, nor to use high

Fig. 15.

Das Licht im Dienste wissenschaftlicher Forschung. Von Dr. Th. Stein, Leipzic, 1877.