travelling, the plane of polarisation is rotated in the same direction as that in which the hands of a clock appear to move when we look at the face, the rotation is said to be right-handed or positive; if the rotation takes place in the opposite direction, it is said to be left-handed or negative.

The rotation in some samples of quartz is to the right, and in others to the left, the amount of the rotation produced by equal thicknesses being the same in both cases. Some liquids, such as turpentine, are also optically active, as well as solutions of some substances such as sugar and quinine.

The rotation varies very nearly inversely as the square of the wavelength, so that, if white light is used, when the analysing Nicol is set to extinguish light of any given wave-length, the light of the other wavelengths will be transmitted. If the transmitted light is examined by means of a spectroscope, the spectrum will be seen crossed by a dark band corresponding to the position of the light which has been intercepted by the analyser.

In the case of a solution of an active substance in an inactive solvent, the rotation is proportional to the quantity of the substance present in the solution. If a is the rotation produced at any given temperature for light of a given colour by a length 1, expressed in decimetres, of a solution containing grams of the active substance in one cubic centimetre of the solution, the quantity a/lr is called the specific rotation of the substance at the given temperature and for the given-coloured light.

412. Connection between Optical Activity and Chemical and Physical Nature. We have mentioned in the previous section that some samples of quartz rotate the plane of polarisation to the right and some to the left. It is found that this difference in their optical behaviour, exhibited by different specimens of quartz, is connected with a difference in their crystalline form. Thus the ordinary form of a quartz crystal is a six-sided prism topped by a six-sided pyramid. The alternate solid angles where two pyramid faces meet two faces of the prism are, however, often bevelled off by small secondary faces or facets which are inclined to the main faces. In any given crystal, these facets all appear to slope towards the right or towards the left when the crystal is held with the pyramid uppermost. When they slope towards the right, the specimen rotates the plane of polarisation to the right, and vice versa. A similar result was obtained by Pasteur with reference to the double racemate of sodium and ammonium.

Of amorphous bodies which exhibit optical activity, with the exception of one or two very little-known compounds containing nitrogen, it is found that they are not only all compounds of carbon, but that in every case one or more of the carbon atoms has its valency satisfied by four different atoms or radicals, which fact is generally expressed by saying that these bodies contain one or more asymmetrical carbon atoms.

There also exists in every case a twin substance, or isomer, which has the same composition but which rotates the plane of polarisation in the opposite direction. If the substance contains only one asymmetrical carbon atom, the rotation produced by the isomers are equal and opposite. Thus in the case of tartaric acid there is a dextro-tartaric acid which rotates the plane of polarisation to the right, and a levo-tartaric acid which rotates it to the left, and finally, in many reactions an inactive tartaric acid is produced. Pasteur has, however, shown by certain processes which only affect the dextro acid and not the levo, that this inactive acid consists of an equi-molecular mixture of the dextro and levo acids.

413. Use of Optical Rotation to Estimate Sugar-Saccharimetry. Cane sugar being an optically active substance, if we measure the rotation produced by a known length of a solution of this substance, we can calculate from the specific rotation the quantity of sugar contained in the solution.

If the solution contains not only the dextro-rotatory cane sugar but also the levo-rotary levulose, after determining the rotation produced by the mixture, the cane sugar is converted into levulose by acting on the solution by means of hydrochloric acid, and then the rotation is again determined. The change in the rotation will give the quantity of cane sugar in the original solution.

BOOK V

MAGNETISM AND ELECTRICITY

PART I-MAGNETISM

CHAPTER I

MAGNETS AND MAGNETIC FIELDS

414. The Loadstone.-It was known to the ancients that certain ores of iron possess the property of attracting to themselves and retaining small particles of iron. This property was exhibited in a marked degree by some of the ores which came from a place in Asia Minor called Magnesia, and hence the ores which exhibited this property were called magnetic stones. All the phenomena connected with the properties of such magnetic stones, or magnets as they are now called, are referred to as magnetic phenomena, and the branch of physics dealing with this subject is called magnetism. The loadstone consists of equivalent proportions of the two oxides of iron, FeO, Fe¿О3.

If a natural magnet, as a loadstone is often called, be dipped in iron filings, the filings will be found to adhere to the magnet in very characteristic tufts; these tufts are not uniformly distributed over the surface, but are much more marked at some parts of the surface, chiefly projecting corners, than at others.

415. Artificial Magnets. In addition to the loadstone, there are other bodies which exhibit magnetic properties; chief among these are bars of hard steel which have been treated in a manner which we shall consider in detail in a subsequent section. Such a bar of steel is called an artificial magnet, but since we shall be dealing with artificial magnets exclusively we shall in future term it a magnet, and when it is dipped in iron filings it attracts them and forms tufts, but these tufts are almost exclusively confined to the two ends of the bar. The ends of the magnet where the power of attracting iron filings seems to be situated are called the poles of the magnet.

Another fundamental property of a magnet which also was known, at any rate to the Chinese, long ago is that when a magnet is suspended or

pivoted so that it can turn freely about a vertical axis, it will set itself in a definite direction, which is very nearly parallel to the meridian, that is, it sets itself in the north and south direction. It is found that it is always the same end of any given magnet that points towards the north pole, and hence this pole of the magnet is called the north-seeking pole, or simply the north pole, while the other pole is called the south-seeking pole, or south pole. The fact that we are able in this way to distinguish the two poles of a magnet shows that there must be some difference between the two poles.

416. Magnetic Attraction and Repulsion.-If a magnet is suspended by a fine thread, or pivoted on a point, so that it can turn freely in a horizontal plane, then, as we have already said, it will set itself in a direction which, in the absence of any disturbing force due to other magnetic causes, will be very nearly due north and south. If under these circumstances the north pole of another magnet is brought near the north pole of the suspended magnet, this latter will be repelled. If, however, the south pole of the magnet is brought near the north pole of the suspended magnet, this pole will be attracted. In this way we may verify the following general law: Two poles of similar name repel one another, while two poles of different name attract one another.

This gives us a ready means of ascertaining which pole of a magnet is the north pole; for we have only to bring one of the poles near the north pole of a suspended or pivoted magnet, such as a compass-needle, when, if the north pole of the compass-needle is repelled, we know that the pole of the other magnet must be a north pole.

417. Permanent and Temporary Magnetism.-If a bar of soft iron is dipped into iron filings, or is suspended so as to be able to rotate, it will neither attract the filings nor will it set itself in the north and south direction, in fact it is not a magnet. If, however, a magnet is brought near one end of the bar of soft iron and the other end is then dipped in iron filings, it will now attract the filings, forming tufts in the same way as a magnet does. If the magnet is now removed, the iron at once loses its power of attracting the filings. We thus see that, in addition to the permanent magnetism exhibited by a steel magnet, we have temporary magnetism induced in a bar of soft iron when it is in the neighbourhood of a magnet. Other substances besides soft iron possess the property of acquiring temporary magnetism, though to a much smaller degree than in the case of iron. Such a body is called a magnetic body, while a body, such as a piece of hard steel, which is permanently magnetised is called a magnet.

If an unmagnetised piece of steel is brought near a magnet it will become magnetised, as did the piece of soft iron under the same conditions; on the removal of the magnet the steel will, however, not lose its magnetism but will have become a permanent magnet. This difference between the behaviour of steel and soft iron is referred to as being due to

the superior coercive power of the steel. We shall return to this subject

in a future section.

Magnets are made in many different shapes, according to the purpose for which they are intended. The two commonest shapes are a straight bar of which the section is either a rectangle or a circle, such a magnet being called a bar magnet, while the other form would be derived from a bar magnet by bending it round in the form of a horse-shoe, so that the north and south poles are brought near together; such a magnet is called a horse-shoe magnet. Other special forms of magnets we shall consider when dealing with the instruments in which they are used.

418. Magnetic Lines of Force.-We have seen that a magnet is capable of exerting a force on another magnet, even when they are separated by some distance, so that the space surrounding a magnet possesses some properties, due to the presence of the magnet, which it does not possess when the magnet is not present. We therefore say that a magnet is surrounded by a magnetic field of force, for in the space considered magnetic forces are brought into play.

If a small compass-needle is brought within the field of force of a magnet it will set itself at each point in a definite direction. If lines are drawn so that they are everywhere in the direction in which a compassneedle would set itself under the influence of the magnet, these curves are called the lines of force of the field of force of the magnet, or, more shortly, the lines of force of the magnet.

When a small pivoted compass-needle is placed in the neighbourhood of a magnet both its poles will be acted on by the two poles of the magnet. Thus the north pole of the needle will be attracted by the south pole of the magnet and repelled by the north pole, while the south pole of the needle will be attracted by the north pole of the magnet and repelled by the south pole. The needle will therefore set itself in such a direction that these four forces will have no resultant moment round the pivot about which the needle can turn. Hence the resultant of all four forces must have no moment round the pivot (§ 73).

Let NS (Fig. 397) be the magnet and sn the needle in its position of equilibrium under the nfluence of NS. Then the forces acting on the needle are along SA, SB, NC, ND. If the length of the needle is sufficiently small the two forces sa and nc are parallel and equal and opposite, for the points n and s may be taken as at the same distance from N. In the same way the two forces SB and D are equal and opposite. Hence the resultant SR is parallel to the resultant R'. Therefore if these two resultants are not to have a couple about the pivot of the needle K, they must both act in a direction passing through K, that is, the line joining the poles of the needle must be parallel to the resultant force acting on a magnetic pole placed at the point K. Hence the direction of the line of force at any point represents the direction of the resultant magnetic force due to the action of the two poles of the magnet.