52 Eev. T. Pelham Dale on the Upper Limit 



which gives us 



sin(7r — ^)_ n sin^ 

 rfr—0 " 1-n ' "d 



Now since sin (tt— ^) is equally a solution of the equation, 

 a sin ^= sin md, it is probable therefore that this solution may 

 have a physical meaning. 



It was noticed in my former paper that, of the substances 

 for which data were at hand, selenium alone had its upper 

 limit within the visible spectrum. Accordingly a fresh cal- 

 culation of the values of 0jc, v, and Xjc were made and the 

 results given below (Table I.). 



It will be seen from the table that the limiting wave-length 

 which is transmissible is X,= 5295'7. This is a little below 

 Xrj w'hich is 5269"13. It was of great interest to observe how 

 far this purely theoretical result would be supported by obser- 

 vation. As neither temperature nor specific gravity of spe- 

 cimen were given, and the indices of refraction to the third 

 place of decimals only, it Avas evident that, as a preliminary 

 experiment, all that could be sought for was a general 

 agreement. 



With this in view I had a Browning amateur spectroscope- 

 eyepiece fitted to my microscope, an old instrument constructed 

 many years ago by Troughton and Sims. After a few trials 

 I succeeded in obtaining a tolerably uniform film of selenium 

 mounted as an ordinaiy microscope-slide. The film when 

 cold was quite transparent, and transmitted a deep ruby tint. 

 This film was found under the spectroscope to transmit rays 

 nearly to the line D, Another and thinner slide was prepared. 

 Under the microscope the thinner portions were found to be 

 of a more orange tint, due to a spectrum reaching to the 

 beginning of the green. Even in brilliant sunlight no sen- 

 sible extension beyond this took place. In parts of the film 

 were holes. If these were in the field they appeared as 

 spectra extending to the violet end, but with sharp well- 

 defined sides, showing apparently that a very thin film was 

 effective to stop all the upper rays. Thus, then, the agree- 

 ment of theory and observation seems as satisfactory as could 

 be anticipated, considering both the data and instrumental 

 means employed. 



The examination of sulphur gave similar results. Here the 

 limiting wave-length lies beyond the visible spectrum. A 

 film of melted sulphur transmits yellow light. This film 

 darkens rapidly as the temperature rises, and when the sul- 

 phur begins to boil, it, as is well known, assumes a brownish 

 tint. Examined under the spectro-microscoj)e, it is seen that 



