102 Dr. C. V. Barton on the Scattering and 



The actual density of mercury vapour was equivalent to* 

 one molecule in a volume X 3 , or 6*07 x 10 13 molecules per c.c; 

 and thus (63) implies that at any instant only about one in 

 9000 (one in 3000) of them are effective resonators : the 

 molecules being of type I. (type II.). This agrees with 

 Wood's qualitative conclusion. 



56. There are, however, some further considerations which 

 should not be lost sight of, and which seem to indicate that 

 one in 9000 (or one in 3000) is an under-estimate. In the 

 first place the secondary diffuse radiation, though effectively 

 restricted to an extremely narrow range of frequency, is far 

 from homogeneous in regard to its absorbability by mercury 

 vapour ; and tbat which is excited well within the mass of 

 vapour is due to a primary beam in which the more absorbable 

 frequencies have already been selectively weakened. It is 

 thus less absorbable than that excited where the primary 

 beam first enters. Since the scattered radiation has to> 

 traverse some thickness of mercury vapour before escaping 

 through the quartz window at the side of the vessel, it follows 

 that the diffuse brightness along the track of the primary 

 beam will appear more uniform than it should, thus leading 

 to an under-estimate of the primary absorption. At the 

 same time the deviation of the general course of absorption 

 from a simple exponential law will be rendered less con- 

 spicuous ; though Wood has already suspected from his 

 measurements that such deviation exists. 



57. In the next place, the energy removed from the 

 primary beam takes the form of secondary radiations which 

 in turn are found to excite tertiary radiations and so on; and 

 thus along the course of the primary beam the falling off in 

 the total radiation available for exciting the resonant mole- 

 cules is less rapid than the extinction of the primary beam 

 itself. 



58. Incidentally it should be remarked that, when the 

 highest homogeneousness in the radiation from a resonance 

 lamp is desired, the total thickness of vapour traversed by 

 incident and scattered radiation should be very moderate ; 

 the scattered energy being then necessarily but a small part 

 of the incident, even in the case of the most effective 

 frequencies. 



59. It is not easy to make satisfactory allowance for the 

 sources of error referred to in §§ 56, 57. From the point of 

 view of theoretical treatment the following slightly modified 

 method seems to have some advantages. A resonance lamp, 

 fulfilling the condition referred to in the last paragraph, is used 

 as a source of radiation, the illuminated object being a small 



