180 comets' tails, the corona, and the aurora. 



comets' tails. 



The (single new principle introduced ])y Arrhenius arises in connec- 

 tion with the problem of comets' tails. ^' Astronomers have always felt 

 that the phenomena exhibited by these .strange oljjects could onl}" be 

 accounted for b}^ making the sun the seat of a violent radial repulsive 

 force, but were entirely at a loss to account for this repulsion. So long 

 as light was supposed to consist of myriads of corpuscles discharged 

 with a speed of 186,000 miles per second, it was eas}^ with Kepler, to 

 regard the corpuscles as carrying with them in their rush the materials 

 vaporized from the comet by the heat of the sun. But the establish- 

 ment of the wave theory of light put an end to this idea. Thus 

 Newcomb .says (Popular A.stronomy): "If light were an emission of 

 material particles, as Newton su})posed it to be, this view would have 

 some plausibility. But light is now conceived to consist of vibrations 

 in a ethereal medium; and there is no known way in which they could 

 exert any propelling force on inatter!" 



Now, Arrhenius points out that according to the electro-magnetic 

 theory of light a ray of light does exert a pressure on any surface on 

 which it impinges. Maxwell not only proved this in his original pub- 

 lication of the theory in 1873, but showed how to calculate its value.* 

 With the known constants of solar radiation he found that sunlight at 

 the surface of the earth should exert a pressure of 0.592x10"^*^ grams 

 on eveiy square centimeter. This is too small a force to be detected, 

 though it has been looked for,'" 



« Thi.s principle was first suggested as an explanation of comets' tails by P. Lebedew 

 in 1891 ( Wied. Ann., 45, p. 292), where it is pointed out that Maxwell's formula can 

 only be applied strictly to a perfectly absorbing black body wlio.se dimensions are 

 small compared with the wave length of the incident light. 



?' Maxwell's formula was deduced on thermodynamical grounds V)y Bartoli (1876; 

 see also Exner's Repert. d. Phys., 21, p. 198, 1885), Boltzmann (Wied. Ann., 22, pp. 

 81, 291; and 31, p. i;)9, 1884), and Galitzine (Wied. Ann., 47, p. 479). 



'Until the appearance of Arrhenius's papers (Phys. Zeitschrift, Nov. 10 and 17, 

 1900) all attempts to detect the pressure of light experimentally had failed, since the 

 effect to be looked fur liad ))een masked by convection and radiometric effects of 

 much greater magnitude in the high vacua employed. But immediately afterwards 

 it was successfidly measured ))y Lebedew (Drude, Ann., (5, p. 433, 1901) and by E. F. 

 Nichols and Ci. F. Hull (Physical Review, Nov., 1901, p. 397), employing different 

 methods, but in both cases reaching results which accord with the calculated values 

 within the limits of error of the observations. 



Arrhenius applied the formula) for comparatively large and perfectly absorbing 

 spheres to jjarticles ranging down to molecrular dimensions which could not be 

 regarded as absorbing. K. Schwarzschild (Miinch. Ber.. 31, pp. 293-338, 1901), 

 employing Spherical Harmonic Series, has given a complete mathematical discus- 

 sion of the problem for perfectly reflecting spheres of any size. He finds that the 

 pressure reaches a maximum when the diameter of the particle is one-third of a 

 wave length, and then falls off rapidly; but that this maxinmm pres.-ure (about 

 18 times the value of the solar gravitation) is all that is required for Arrhenius's 

 tlu'iiiy. In fact, the agreement with the numbers (luoted from Bredichin in the 

 text, in ignorance of !8cliwarzschild's analysis, is curiously exact. 



