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 that their colour depends on the gas in which they are formed, being gold-colour in air and nitrogen, rose-colour in hydrogen, yellowish rose in oxygen, and greenish gray in carbonic acid.

The colour of the luminosity due to positive rays is not in general the same as that due to anode rays; the difference is exceptionally well marked in helium, where the cathode ray luminosity is blue while that due to the positive rays is red. The luminosity produced when the rays strike against solids is also quite distinct. The cathode rays make the body emit a continuous spectrum, while the spectrum produced by the positive rays often shows bright lines. Thus lithium chloride under cathode rays gives out a steely blue light and the spectrum is continuous, while under the positive rays the salt gives out a brilliant red light and the spectrum shows the red helium line. It is remarkable that the lines on the spectra of the alkali metals are much more easily produced when the positive rays fall on the oxide of the metal than when they fall on the metal itself. Thus when the positive rays fall on a pool of the liquid alloy of sodium and potassium the specks of oxide on the surface shine with a bright yellow light while the untarnished part of the surface is quite dark.

W. Wien (Wied. Ann. 65, p. 445) measured the values of e/m for the particles forming the positive rays. Other measurements have been made by Ewers (Wied. Ann. 69, p. 167) and J. J. Thomson (Phil. Mag. 13, p. 561). The differences between the values of e/m for the cathode and positive rays are very remarkable. For cathode rays whose velocity does not approach that of light, e/m is always equal to 1.7✕108, while for the positive rays the greatest value of this quantity yet observed is 104, which is also the value of e/m for the hydrogen ions in the electrolysis of dilute solutions. In some experiments made by J. J. Thomson (Phil. Mag., 14, p. 359) it was found that when the pressure of the gas was not too low the bright spot produced by the impact of a pencil of these rays on a phosphorescent screen is deflected by electric and magnetic forces into a continuous band extending on both sides of the undeflected position. The portion on one side is in general much fainter than that on the other. The direction of this deflection shows that it is produced by particles charged with negative electricity, while the brighter band is due to particles charged with positive electricity. The negatively electrified particles which produce the band c.c are not corpuscles, for from the electric and magnetic deflections we can find the value of e/m. As this proves to be equal to 104, we see that the mass of the carrier of the negative charge is comparable with that of an atom, and so very much greater than that of a corpuscle. At very low pressures part of the phosphorescence disappears, while the upper portion breaks up into two patches (fig. 27). For one of these the maximum value of e/m is 104 and for the other 5✕103. At low pressures the appearance of the patches and the values of e/m are the same whether the tube is filled originally with air, hydrogen or helium. In some of the experiments the tube was exhausted until the pressure was too low to allow the discharge to pass. A very small quantity of the gas under investigation was then admitted into the tube, just sufficient to allow the discharge to pass, and the deflection of the phosphorescent patch measured. The following gases were admitted into the tube, air, carbonic oxide, oxygen, hydrogen, helium, argon and neon, but whatever the gas the appearance of the phosphorescence was the same; in every case there were two patches, for one of which e/m = 104 and for the other e/m = 5✕103. In helium at higher pressures another patch was observed, for which e/m = 2.5✕108. The continuous band into which the phosphorescent spot is drawn out when the pressure is not exceedingly low, which involves the existence of particles for which the mean value of e/m varies from zero to 104, can be explained as follows. The rays on their way to the phosphorescent screen have to pass through gas which is ionized by the passage through it of the positive rays; this gas will therefore contain free corpuscles. The particles which constitute the rays start with a charge of positive electricity. Some of these particles in their journey through the gas attract a corpuscle whose negative charge neutralizes the positive charge on the particle. The particles when in this neutral state may be ionized by collision and reacquire a positive charge, or by attracting another particle may become negatively charged, and this process may be repeated several times on their journey to the phosphorescent screen. Thus some of the particles, instead of being positively charged for the whole of the time they are exposed to the electric and magnetic forces, may be for a part of that time without a charge or even have a negative charge. The deflection of a particle is proportional to the average value of its charge whilst under the influence of the deflecting forces. Thus if a particle is without a charge for a part of the time, its deflection will be less than that of a particle which has retained its positive charge for the whole of its journey, while the few particles which have a negative charge for a longer time than they have a positive will be deflected in the opposite direction to the main portion and will produce the tail (fig. 27).

A similar explanation will apply to the positive rays discovered by Villard (Comptes rendus, 143, p. 674) and J. J. Thomson (Phil. Mag. 13, p. 359), which travel in the opposite direction to the rays we have been considering, i.e. they travel away from the cathode and in the direction of the cathode’s rays; these rays are sometimes called “retrograde” rays. These as far as has been observed have always the same maximum value of e/m, i.e. 104, and there are a considerable number of negative ones always mixed with them. The maximum velocity of both the positive and retrograde rays is about 2✕108 cm./sec. and varies very little with the potential difference between the electrodes in the tube in which they are produced (J. J. Thomson, Phil. Mag., Dec. 1909).

The positive rays show, when the pressure is not very low, the line spectrum of the gas through which they pass. An exceedingly valuable set of observations on this point have been made by Stark and his pupils (Physik. Zeit. 6, p. 892; Ann. der Phys. 21, pp. 40, 457). Stark has shown that in many gases, notably hydrogen, the spectrum shows the Doppler effect, and he has been able to calculate in this way the velocity of the positive rays.

Anode Rays.—Gehrcke and Reichenhein (Ann. der Phys. 25, p. 861) have found that when the anode consists of a mixture of sodium and lithium chloride raised to a high temperature either by the discharge itself or by an independent heating circuit, very conspicuous rays come from the anode when the pressure of the gas in the discharge tube is very low, and a large coil is used to produce the discharge. The determination of e/m for these rays showed that they are positively charged atoms of sodium or lithium, moving with very considerable velocity; in some of Gehrcke’s experiments the maximum velocity was as great as 1.8✕107 cm./sec. though the average was about 107 cm./sec. These velocities are less than those of the positive rays whose maximum velocity is about 2✕108 cm./sec.

CONDUCTION OF HEAT. The mathematical theory of conduction of heat was developed early in the 19th century by Fourier and other workers, and was brought to so high a pitch of excellence that little has remained for later writers to add to this department of the. subject. In fact, for a considerable period, the term “theory of heat” was practically synonymous with the mathematical treatment of a conduction. But later experimental researches have shown that the simple assumption of constant coefficients of conductivity and emissivity, on which the mathematical theory is based, is in many respects inadequate, and the special mathematical methods developed by J. B. J. Fourier need not be considered in detail here, as they are in many cases of mathematical rather than physical interest. The main object of