by the mixing pipette d into the blood cell e; the cell is then just filled with water, and the blood and water thoroughly mixed by the handle of c being used as a stirrer. The cover glass is then adjusted, when a small bubble should form, a clear sign that the cell has not been overfilled. The cell is then placed by the side of the standard gradations, and the eye quickly recognises its approximate position on the scale. The camera tube provided with the instrument will more accurately define it. Artificial light should be used.

If it is proved that the blood solution is matched in depth of colour by one of the standard grades, the observation is at an end; but if the tint is higher than one grade, but lower than another, the blood cell is placed opposite to the former, and riders (not shown in the illustration) are added to complete the observation. The standard gradations are marked in percentages, 100 per cent. being taken as normal.

'Worth' of the Corpuscles.-If the percentage of hæmoglobin is 100, and the percentage number of corpuscles is 100 also, then the quotient

100
100

= : 1 is taken as the normal. This varies in health from 0.95 to 1.05 in men, and from 0.9 to 1 in women. This quotient has been termed the 'worth' of the corpuscle.

Specific Gravity of Blood.-Of the numerous methods introduced for taking the specific gravity of fresh blood, that of Hammerschlag is the simplest. A drop of blood from the finger is placed in a mixture of chloroform and benzene. If the drop falls, add chloroform till it just begins to rise; if the drop rises, add benzene till it just begins to fall. The fluid will then be of the same specific gravity as the blood. Take the specific gravity of the mixture in the usual way with an accurate hydrometer.

Schmalz's capillary pycnometer is more accurate.

POLARISATION OF LIGHT

If an object, such as a black dot on a piece of white paper, be looked at through a crystal of Iceland spar, two black dots will be seen; and if the crystal be rotated, one black dot will move round the other, which remains stationary. That is, each ray of light entering such a crystal is split into two rays, which travel through the crystal with different velocities, and consequently one is more refracted than the other. One ray travels just as it would through glass; this is the ordinary ray, the ray which gives the stationary image; the other ray gives the movable image when the crystal is rotated; the ordinary laws of refraction do not apply to it, and it is called the extraordinary ray. Both rays are of equal brilliancy. In one direction, however, that of the optic axis of the crystal, a ray of light is transmitted without double refraction.

Ordinary light, according to the wave theory, is due to vibrations occurring in all planes transversely to the direction of the propagation of the wave. Light is said to be plane polarised when the vibrations take place all in one plane. The two rays produced by double refraction are both polarised, one in one plane, the other in a plane at right angles to this one. Doubly refract

ing bodies are called anisotropous; singly refracting bodies, isotropous. The effect of polarisation may be very roughly illustrated by a model.

If a string be stretched as in the figure, and then touched with the finger, it can be made to vibrate, and the vibrations will be free to occur from above down, or from side to side, or in any intermediate position. If, however, a disc with a vertical slit be placed on the course of the string, the vibrations will all be obliged to take place in a vertical plane, any side to side movement being stopped by the edges of the slit (fig. 69).

1

FIG 69.

Light can be polarised not only by the action of crystals, but by reflection from a surface at an angle which varies for different substances (glass 54° 35', water 52° 45', diamond 68°, quartz 57° 32', &c.). It is also found that certain non-crystalline substances, like muscle, cilia, &c., are doubly refracting.

Nicol's Prism is the polariser usually employed in polariscopes; it consists of a rhombohedron of Iceland spar divided into two by a section through its obtuse angles. The cut surfaces are polished and cemented together in their former position with Canada balsam. By this means the

ordinary ray is totally reflected through the Canada balsam; the extraordinary ray passes on and emerges in a direction parallel to the entering ray. In this polarised ray there is nothing to render its peculiar condition visible to the naked eye; but if the eye is aided by a second Nicol's prism, which is called the analyser, it is possible to detect the fact that it is polarised.

This may be again illustrated by reference to our model (fig. 70).

Suppose that the string is made to vibrate, and that the waves travel in the direction of the arrow. From the fixed point c to the disc a, the string

1 Such a model is, of course, imperfect; it does not, for instance, represent the splitting of the ray into two, and moreover the polarisation takes place on each side of the slit; whereas, in regard to light, it is only the rays on one side of a polariser, viz. those that have passed through it, which are polarised.

is theoretically free to vibrate in any plane; but after passing through the vertical slit in a, the vibrations must all be vertical also; if a second similar disc b be placed further on, the vibrations will also pass on freely to the other extremity of the string d, if as in the figure (fig. 70) the slit in b be also placed vertically. If, however, b is so placed that its slit is horizontal (fig. 71) the vibrations will be extinguished on reaching b, and the string between b and d will be motionless.

c here represents a source of light; the vibrations of the string represent the undulations which by the Nicol's prism a are polarised so as to occur in one plane only; if the second Nicol's prism or the analyser b is parallel to the first, the vibrations will pass on to the eye, which is represented by d; but if the planes of the two nicols are at right angles, the vibrations allowed to pass through the first are extinguished by the second, and so no light reaches the eye. In intermediate positions, b will allow only some of the light to pass through it. It must be clearly understood that a Nicol's prism contains no actual slits, but the arrangement of its molecules is such that their action on the particles of æther may be compared to the action of slits in a diaphragm to vibrations of more tangible materials than æther.

The Polarising Microscope consists of an ordinary microscope with certain additions; below the stage is the polarising nicol; in the eye-piece is the analysing nicol; the eye-piece is so arranged that it can be rotated; thus the directions of the two nicols can be made parallel, and then the field is bright; or crossed, and then the field is dark. The stage of the microscope is arranged so that it can also be rotated.

ray

The polarising microscope is used to detect doubly-refracting substances. Let the two nicols be crossed, so that the field is dark; interpose between the two, that is, place upon the stage of the microscope a doubly-refracting plate of which the principal plane is parallel to the first prism or polariser; the from the first prism is unaffected by the plate, but will be extinguished by the second; the field therefore still remains dark. If the plate is parallel to the second nicol the field is also dark; but in any intermediate position the light will be transmitted by the second nicol. In other words, if between two crossed nicols, which consequently appear dark, a substance be interposed which in certain positions causes the darkness to give place to illumination, that substance is doubly refractive. How this takes place may be explained as follows:

Let NN1 (fig. 72) represent the direction of the principal plane of the first nicol, and N,N, that of the second. They are at right angles, and so The imperfection of the model has been explained in the preceding footnote.

the ray transmitted by the first will be extinguished by the second. Let PP represent the principal plane of the interposed doubly-refractive plate. The extraordinary ray transmitted by N,N, vibrates in the plane N,N,, and falls obliquely on the plate PP; it is by this plate itself split into two rays, an ordinary and an extraordinary one, at right angles to one another, one vibrating in the plane PP, the other in the plane P1P1. These two rays meet the second nicol, which can only transmit vibrations in the plane N,N,. The vibrations in PP can be resolved into a vibration in N,N, and a vibration in N,N,; the former is extinguished, the latter transmitted. Similarly the vibration in P1P1 can be resolved into two sub-rays in N,N, and N,N, respectively, the

latter only being transmitted. The N2

illumination is thus due to two sub-rays, one of the vibrations in PP, the other of those in P1P1 which have been made to vibrate in N2N2.

P

N

N1

FIG. 72.

Р

Na

Now, although these two subrays vibrate in the same plane, they are of different velocities; hence the phases of the vibrations do not coincide, and thus the phenomena of interference are obtained. If we have two sets of vibrations fused, the crest of one wave may coincide with the crest of the other, in this case the wave will be higher; or the crest of one may coincide with the hollow of the other, that is, the undulation would be extinguished; in other intermediate cases, the movement would be interfered with, either helped or hindered, more or less. Interference in the case of many kinds of doubly-refracting substances (Iceland spar is in this an exception) shows itself in the extinction of certain rays of the white light, and the light seen through the second nicol is white light minus the extinguished rays; those extinguished and those transmitted will together form white light, and are thus complementary. Moreover, the rays extinguished in one position of the plate will be transmitted in one at right angles and vice versa; thus a crystal showing these phenomena of pleochromatism, as it is termed, will transmit one colour in one position, and the complementary colour in a position at right angles to the first; blue and yellow, and red and green, are the pairs of colours most frequently seen in this way.

Rotation of the Plane of Polarisation.-Certain crystals such as those of quartz, and certain fluids such as the essence of turpentine, aniseed, &c., and solutions of certain substances like sugar and albumin, have the power of rotating the plane of polarised light to the right or left. The polarisation of light that is produced by a quartz crystal is different from that produced by a rhombohedron of Iceland spar. The light that passes through the latter is plane polarised; the light that passes through the former (quartz) is circularly polarised, i.e. the two sub-rays are made up of vibrations

Q

which occur not in a plane, but are curved. The two rays are circularly polarised in opposite directions, one describing circles to the left, the other to the right; these unite on issuing from the quartz plate; and the net result is a plane polarised ray with the plane rotated to right or left according as the right circularly polarised ray or the left proceeded through the quartz with the greater velocity. There are two kinds of quartz, one which rotates the plane to the right (dextro-rotatory), the other to the left (lævo-rotatory).

Gordon explains this by the following mechanical illustration. Ordinary light may be represented by a wheel travelling in the direction of its axle, and the vibrations composing it executed along any or all of its spokes (a). If the vibrations all take place in the same direction, i.e. along one spoke, and the spoke opposite to it (b), the light is said to be plane polarised. The two spokes as they travel along in the direction of the arrow will trace out a plane (see fig. 73) between b and b'. If this polarised beam be made to

travel now through a solution of sugar, the net result is that the plane so traced out is twisted or rotated; the two spokes, as in bb', do not trace out a plane, but we must consider that they rotate as they travel along, as though guided by a spiral or screw thread cut on the axis, so that after a certain distance the vibrations take place as in b"; later in b''', and so on. This effect on polarised light is due to the molecules in solution, and the amount of rotation will depend on the strength of the solution, and on the length of the column of the solution through which the light passes, or, in the case of a quartz plate, on its thickness.

If a plate of quartz be interposed between two nicols, the light will not be extinguished in any position of the prisms, but will pass through various colours as rotation is continued. The rotation produced for different kinds of light being different, white light is split into its various constituent colours; and the angle of rotation that causes each colour to disappear is constant for a given thickness of quartz plate, being least for the red and greatest for the violet. These facts are made use of in the construction of polarimeters. Polarimeters are instruments for determining the strength of solutions of sugar, albumin, &c., by the direction and amount of rotation they produce on the plane of polarised light. They are often called saccharimeters, as they are specially useful in the estimation of sugar.

POLARIMETERS

Soleil's Saccharimeter. This instrument (see fig. 74) consists of a Nicol's prism, d, called the polariser: this polarises the light entering it, and the polarised beam then passes through a quartz plate (b infig. 74), 3·75 mm ̧