1

The same holds good for the remarkable phenomenon observed in 1825 by Fresnel, which he was inclined to interpret as a repulsion between heated bodies. The essentially similar actions which Crookes 2 observed during weighings in rarefied spaces, as well as the motions observed in the apparatus 3 invented by him, and called the radiometer or light-mill, are to be explained by the same ideas.

The vanes of the little mill, which are black on one side and white on the other, are warmed by radiated heat, or even by light—since a luminous ray is only a heat-ray which is also luminous to the eye-but they are warmed unequally, and the black side the more strongly. If, therefore, a particle of air impinges on a black face it carries off more heat, i.e. flies off with greater speed, than if the collision had been against a white face. The reaction which it exerts on the vane in its rebound is, therefore, greater when it leaves the warmer black face than at the colder white side. Consequently, the mill must so turn that the white side of the vanes precedes.

If we think of the immense speed with which the gaseous molecules move, it seems scarcely necessary to specially prove that the force that results from this unequal heating is really sufficient to bring about this action. But since the proof can be easily given independently of the hypotheses on which the theory of gases rests, we will calculate the magnitude of the energy for a simple case, so chosen that the necessary experimental data are known. Suppose the vanes to be made of aluminium foil of 1 sq. cm. area, and to be blackened with soot on one side, and suppose the heating to be caused, not by a source outside the instrument, but by the glass envelope itself, which we will take to be 1 degree C. warmer than the mill.

4

Lehnebach has observed that glass and sooted surfaces radiate with equal intensity towards a region of rarefied

' Ann. Chim. Phys. 1825 [2] xxix. p. 57; Œuvres Complètes, 1868, ii.

p. 667.

2 Phil. Trans. 1873, clxiii. p. 277.

3 Quarterly Journal of Science, 1875, xii. p. 337.

4 Pogg. Ann. 1874, cli. p. 96.

1

air; according to Kirchhoff's law concerning the emission and absorption of radiant heat, they have therefore equal coefficients of absorption also. Hence the conclusion that the radiation received by the blackened side of the vane from the glass envelope is equal to that which the blackened side of the vane would send out to the glass wall if it were as much the warmer as the glass envelope is.

I have calculated 2 in absolute measure the amount of heat which a warmed black surface radiates to the receiver of an air-pump under which it is placed from the observations made by Stewart and Tait,3 on the heating of a blackened disc of aluminium in a vacuum of 7·6 mm. pressure. I have found the value

h = 0·0017

for the constant of radiation, referred to a millimetre, second, and degree C. as units; with centimetres substituted for millimetres, we have

h = 0·00017,

and this number simply means that the heat radiated in one second by a square centimetre of a blackened surface of aluminium at a temperature 1 degree C. above its environment would suffice to raise 0·00017 gram of water through 1 degree C.-that is, is equal to 0.00017 calorie. From observations by Dulong and Petit, and also by F. Neumann, I found h= 0·00013. Later on Lehnebach found a value which, reduced to 1 degree C., is 0.00015; and, lastly, Kundt and Warburg have obtained h = 0·00014 in the same units. The perfect agreement between these numbers vouches for their correct

h

=

ness.

A vane of the radiometer of 1 sq. cm. area would, therefore, receive on its blackened side a radiation of about 0.00015 calorie in a second if the glass envelope were the

1 Pogg. Ann. 1860, cix. p. 275; Untersuchungen über das Sonnenspectrum, 2nd ed. Berlin 1862, p. 22.

2 Ibid. 1868, cxxxv. p. 285.

3 Proc. Roy. Soc. 1865, xiv. p. 339; Phil. Mag. 1865 [4] xxx. p. 314.

Pogg. Ann. 1875, clvi. p. 208.

warmer by 1 degree. According to Stewart and Tait's observations, the emissivity of a surface of bare aluminium is four times smaller, so that, in accordance with Kirchhoff's law, it seems just to assume that a vane made of aluminium will absorb in the same time only a fourth part of that amount of heat, i.e. about 0.00004 calorie. The difference between the two amounts of heat received, viz. 0.00011 calorie, which is the energy that drives the radiometer, is capable of raising 0·00011 × 425 = 0.05 gram by 1 metre, or 5 grams by 1 cm. [that is, the power is 5 gm. cm. per sec.]. This energy, acting on a vane, would certainly be capable of turning the light-mill round, and, indeed, even if the difference in temperature of the vanes and envelope were 100 or 1,000 times smaller than 1 degree. For with the mill there moves only the rarefied, and therefore light, air which has to overcome at the wall only an external friction, which is very much diminished by the rarefaction.

85. Influence of the Temperature on the Viscosity

Since according to the kinetic theory the friction of gases is to be looked upon as a consequence of the molecular motion, the coefficient of friction must be variable with the temperature if that theory is true; and we may expect, from the reasons given in § 76, that it increases with rise of temperature. Every observer who has investigated the influence of the temperature on the friction has found this expectation justified. Only in respect of the rate of the increase with the temperature have the results of different observers shown differences which were at first hard to explain.

We can only conclude, from the observations of Graham on the flow of gases through tubes, that the friction of gases really increases with the temperature, as the theory requires; we might draw the further conclusion from them that the increase of friction with the temperature is in nearly the same ratio for all gases. Both speak in favour of the theory; for the speed of the molecules, which comes

1 Pogg. Ann. 1866, cxxvii. p. 369.

2 Phil. Trans. 1846 and 1849.

as a factor into the formula for the coefficient of viscosity, increases with the temperature at nearly the same rate for all gases; and it is not unreasonable to expect the same also with respect to the free path.

As a fact, the earlier of the more accurate measures made on the increase of the coefficient of viscosity with the temperature seemed to result in a simple relation to the coefficient of expansion, and therefore to a magnitude which has nearly the same value for all gases. Maxwell1 first drew from his observations that the coefficient of viscosity of air increases in the same ratio as the absolute temperature, and thus proportionally to

1 + ad,

where is the temperature measured from freezing-point, and a is the coefficient of expansion. It was, indeed, proved by the later experiments of other observers 2 that the viscosity, at least of atmospheric air, does not increase with the temperature so rapidly as Maxwell had believed; but it was conclusively shown that it rises more rapidly than the square root of the absolute temperature, i.e. faster than the magnitude

√(1 + ad).

There can therefore be no further doubt that, in the formula for the coefficient of viscosity (§ 78)

not only does the speed 2, which is proportional to that square root, increase with the temperature, but so also does the free path L.

The endeavour was then made at first to express the dependence of the coefficient of viscosity on the temperature by a factor of the form

(1 + ad)",

1 Phil. Trans. 1866, clvi. p. 249; Scientific Papers, ii. p. 1.

20. E. Meyer, Pogg. Ann. 1873, cxlviii. p. 203. Puluj, Wiener Sitzungsber. Abth. 2, 1874, lxix. p. 287; lxx. p. 243; 1876, lxxiii. p. 589. von Obermayer, ibid. Abth. 2, 1875, lxxi. p. 281; 1876, lxxiii. p. 433; Carl's Repert. 1876, xii. p. 13; 1877, xiii. p. 130. Warburg, Pogg. Ann. 1876, clix. p. 403.

and this formula seemed to suit the case of atmospheric air when n was taken equal to . Since the molecular speed alters with the temperature proportionally to √(1 + ad), the molecular free path must then be proportional to

(1 + ad)1.

=

According to the observations of C. Barus', who investigated the flow through capillary tubes within a very wide range of temperature, n both for air and for hydrogen; with this value the formula holds from 0° to 1,300°. For both gases, therefore, the free path would increase proportionally to

(1 + a9)3.

Experiments with other gases showed, on the contrary, that this value for n cannot hold in general. Puluj2 obtained by the oscillation method the value n = 0.92 for carbonic acid, and von Obermayer3 observed with capillary tubes values for NO2, CO2, ethylene and ethyl chloride, which were all nearly equal to 1. Eilhard Wiedemann' found for these gases that the value for n is variable with the temperature, and is the smaller the higher the temperature. S. W. Holman arrived at the same result, and he therefore expressed his results by the usual series of

powers.

O. Schumann6 chose a formula with a double factor of the form

(1 + yd)2 √(1 + ad)

to represent his observations; the square root here expresses the dependence of the molecular speed on the tempera

Bull. of the U. S. Geological Survey, No. 54, Washington 1889; Amer. Journ. of Science, 1888 [3] xxxv. p. 407; Wied. Ann. 1889, xxxvi. p. 358. 2 Wiener Sitzungsber. 1876, lxxiii. Abth. 2, p. 589.

3 Wiener akad. Sitzungsanzeiger, 1876, No. 8; Carl's Repert. 1876, xii.

P. 465.

Arch. d. Sc. Phys. et Nat. 1876, lvi. p. 273.

1899, lxvii. p. 816.

Breitenbach, Wied. Ann.

› Proc. Amer. Acad. Boston. 1877, xii. p. 41; 1885, xxi. p. 1; Phil. Mag. [5] iii. p. 81; xxi. p. 199.

'Ueber die Reibung von Gasen u. Dämpfen u.s.w.' Tübinger Habilitationsschrift; Wied. Ann. 1884, xxiii. p. 353.