376 
ME. LOUIS VESSUT KING ON THE SCATTERING AND 
The same remark applies to the case where the scattering is due to small particles of 
dust since these partake, to some extent at least, of the molecular agitation of the gas 
in which they are held in suspension. 
The intensity of radiation at any point is measured by the amount of energy 
crossing unit area of a surface normal to the direction of the radiation in unit time. 
Unpolarized radiation of intensity E falls on an element Si' of a gas of density p and 
containing N molecules per unit volume. The intensity of the scattered radiation in 
a direction 6 with the incident radiation and at a distance r from Sv we denote by 
( 7 ', 0) (5r, so that I(r, is the energy contained in a small solid angle So} 
crossing a spherical surface at distance i' in unit time. 
The expression for I (O, 0) is of the form 
I(O,0) = m(6)E.(1) 
where p.{0) depends on the direction 0 and is proportional to the number N of 
molecules per unit volume, i.e., pl{6) is also proportional to the density p. 
If /.to ( 0 ), No, po refer to values of p. (0), N, p under determinate conditions of pressure 
and temperature we have 
m(6)//«o(0) = N/Nq = pIpo .( 2 ) 
p{0) may be expressed in terms of the optical properties of the medium : the results 
of Rayleigh,"^ and Kelvin t worked out on various hypotheses of the molecule and of 
the gether agree in giving rise to the expression, 
/.(0) = i7r2(/i2_i)2x-^(i + cos^0)/N.(3) 
where n is the refractive index of the gas and X the wave-length of The incident 
radiation. 
ScHUSTEnj has recently obtained this result from general considerations indepen¬ 
dently of any particular theory. 
Since u—1 and N are both proportional to the density of the gas we notice that 
p{6) is also proportional to the density, as already stated. 
T Formula (3) shows that the intensity of the scattered radiation is twice as great 
in the direction of the incident radiation as it is in a direction at right angles. 
Considerable simplification in the analysis is obtained by employing the mean value of 
p ( 0 ) over a spherical surface. Thus, writing 
Airp = j /X ( 0 ) dw .( 4 ) 
( 3 ) gives 
p^ .(5l 
* Rayleigh, ‘Phil. Mag.,’ XLL, p. 107; ‘ Collected Works,’ vol. L, p. 87. 
t Kelvin, ‘Baltimore Lectures’ (1904), p. 311. 
X ScHiTSTEE, ‘Theory of Optics,’ 2iid ed. (1909), p. 325. 
