pass the spark through a solution of the subtance to be examined, and for this purpose the following apparatus can be constructed out of the ordinary apparatus of the laboratory (fig. 10).

A Woulfe's bottle is fitted with two good india-rubber corks. In the one a stout glass rod is placed, bent at right angles, serving as a support for a glass tube, through which the wire of the negative pole projects; the other neck carries a little test

t

tube with the wire, g, which comes up through the cork, and the test-tube supports a still smaller one, capable of holding a very small quantity of the liquid to be examined; the wire is fused into the bottom of this tube, and terminates a little below the mouth. Over the wire there is a minute tube, somewhat funnel-shaped at the end, which prevents the spark flying to the side of the test-tube; in the larger tube there is a little mercury to ensure contact. One effect of this arrangement is that the lower pole has always a thin film of the liquid over its surface, and on passing the current the spark volatilises the substances in solution, and their characteristic spectra are easily observed.

Fig. 10.

QUANTITATIVE ESTIMATION OF COLOURING-MATTERS. $56a. (1) The Polarising Colorimeter.-The simplest method is to imitate the solution of colouring-matter, the strength of which is unknown, by diluting a stronger solution of known strength and placing the two solutions in two glass cylinders of equal bore; accurately match the colours by pouring some of the solution of the stronger shade out until the colours are equal, then the colouring matter is proportional to the depth or height of the liquids. The results with practice are in many cases fairly correct. A beautiful and more accurate method of colorimetry is made by the aid of a special apparatus-viz., the "polarisation colorimeter;" this, in its most improved form, consists of two graduated cylinders, A and B, having at the bottom a white reflecting surface, C, which throws the light equally through the two cylinders (fig. 11). Above the cylinder, A, is a prism, D, of Iceland spar, the so-called "glans air prism.' The prism is cut in the direction cd, and both halves again joined together. The surfaces, a d, cb, and bd, are polished;

m and n are diaphragms, admitting the rays of light thrown up from C. The ordinary ray passing from A is reflected at the surface, cd, while the extraordinary ray, a, passes on to the Nicol. The rays of light passing through B into the Iceland spar half prism, E, divide into extraordinary and ordinary rays; the extraordinary rays pass through

the prism, the ordinary are reflected from the polished surface, ef, are again reflected by the surface, cd, and pass on to the Nicol, forming the bundle, B. The Nicol prism thus receives ordinary rays from B and extraordinary rays from A. The Nicol prism can be rotated on its axis, and the amount of rotation measured by a divided circle.

There will be two points, in one of which the extraordinary rays will vanish, and in the other, 90° from the former, the ordinary ray will vanish. Let these points be 0° and 90°. If both rays come with equal clearness from D, then at 45°-that is, exactly between 0° and 90°-the two fields will be equally clear.

f

C

E

a

A

Fig. 11. The polarising colorimeter.

The clearness of the ray, a-that is, the extraordinary ray-is at 0° = 0, at 90° = 1; the other ray, the ordinary, ẞ, is exactly the reverse-that is, at zero it is equal to 1, at 90° it is equal to 0°. The angle, , measured by the rotation of the Nicol with regard to the ray, a, is proportional to the square of the sine, that of the ray, ß, is proportional to the square of the cosine.

=

If both rays are equal in intensity, then for any angle, ; aß sin2 : cos2 p tan2 1. The simplest method of using the polarisation colorimeter is always to fill the cylinders, so that the liquid of known concentration stands at the same height as the liquid of unknown concentration. The Nicol is turned until both fields are of precisely equal brightness, and the angle, 4, being read the cylinders are now reversed-that is, the cylinder A is put in the place of B, and the cylinder B in place of A, and the angle, ', again read; then the calculation is very easy, denoting the concentration of the one liquid as c, the other as c', and the angle as p.

tan
c = c'
tan o'

An improvement, even on this method, is the introduction of a quartz plate between the Nicol and D; the quartz plate has a thickness of 3.75 mm., and consists of one-half of right-handed, the other of left-handed quartz. The result of this is that the eye sees four fields, the ray ẞ dividing into two and the ray a dividing into two.

The Nicol being at 0°, or at 90°, the fields, B1 and B2, are of an equal colour as well as those of a1 and a2, at a point between the two angles; a1 and 62 are of an equal yellow colour, while 31 and 2 are of a blue colour.

If in the cylinders, A and B, are placed solutions of a colouring material of different concentration, the one known, the other not, both fields lying to the right have a different degree of clearness to the fields lying to the left; and since two solutions of a substance of different concentration show a different spectrum, in this case the field a1 is differently coloured to the field 2, and 31 differently coloured to a2.

By diminishing the height of the stronger liquid, by letting a little flow out of the tap, after a few trials not only the adjacent fields have the same brightness, but also the same colour.

If the Nicol is placed at 45°, and the height of one or the other fluid be decreased by means of opening the tap, then the concentration of the unknown liquid is given by the equation :

Krüss gives examples of the accuracy of the determinations of various substances by this method, as follows:

* Kolorimetrie u. Quantitative Spektralanalyse, von Dr. G. Krüss and Dr. H. Krüss. Hamburg and Leipzig, 1890.

The small error appears generally to be in excess, and, no doubt, a correction factor could be got out for any solution. An improved form of colorimeter has also been invented by Hugo Krüss,* called "colori

meter with the LumnerBrodhuns prism." The essential part of the instrument is the Lumner-Brodhuns prism (see A, fig. 12); the one part of the prism is an ordinary reflecting prism, but the other part has a polished plane surface, gr; but from e to g and from r to s the section is that of a portion of a circle.

The other prisms have the shape shown in fig. 12, and the path of the rays of light is indicated by the dotted lines. The effect of the arrangement is that the eye, looking through the lens on to the surface ergs, sees an elliptic spot, which, if the light coming from the two cylinders is unequal, is surrounded by a field of a different tone with a sharply

Fig. 12. Colorimeter with the Lumner
Brodhuns prism.

*Kolorimeter mit Lumner Brodhunschen Prismen -paare v. Hugo Krüss. Zeit. f. anorgan. Chemie, v.

defined line; but if the light is equal in intensity, then the line of demarcation vanishes, and the spot is of the same shade and hue as that of the surrounding field. This colorimeter is stated to be of great delicacy and accuracy.

Colorimetry is applicable to the estimation of ammonia, nitrites, nitrates, copper, permanganate, and solutions generally, either coloured in themselves or striking colours with reagents.

§ 56b. (2) Quantitative Spectroscopy.—Quantitative estimations by the spectroscope may be made by an appliance, the invention of Karl Vierordt,* known as the "double slit;" instead of a

single slit, the slit is divided into two halves, as shown in fig. 13, each half of the slit can be opened at a different degree, and the width to which they are respectively opened, accurately estimated by means of the divisions on the milled heads of the respective micrometer screws, i and i. Both of these slits correspond to two spectra, as seen through the observation tube. If the light is properly placed and both slits equal in breadth, the illumination

of both spectra will be equal; on the other hand, if one slit is open of a greater width than the other more light will pass through. If in front of one half of the slit is placed a liquid which absorbs the light more or less, in order to make the illumination, say, of the brightest part of the spectrum equal to the other spectrum illuminated directly by the source of light, the two slits will have to be of a different width, the one having to be narrowed or the other widened, and by reading from the milled heads the width of the slit a basis for calculation of the concentration of the solution is obtained by determining what is called the "extinction coefficient."

The following is the method of obtaining the extinction coefficient of a solution :-A small glass trough, with parallel sides, is taken, the walls of the trough being exactly 11 mm. from each other; the lower half of this glass trough is occupied by a Schulz's

*Die Anwendung des Spectral-apparates zur Photometrie der Absorptionsspectren u. zur quantitativen chemischen Analyse. Tübingen, 1873.