Mechanics of Luminosity. 261 



Hence A^ _ cotan 2 'a f 



A cotan 2 a ' 



therefore rotanV 



E , = . 24 cotana 



cotan^a 



In our case 



a = 36°30', E=4'7, and £=5^, 



so that 



^, __. 4 '7 cotanV AAnflAO cotanV 

 E' = 0*24^^ — i-Tq7m =0-00203 2tt(>1 cm. g. sec. cal. 



55bcotan 2 36J cotan^ooj to 



Coefficient of Total emission of 1 #t\ sodium in absolute 

 measure. 



25. In order to test, in the first place, the dependence of 

 the emission of light upon the quantity of sodium chloride 

 contained in the unit volume, two solutions of sodium chloride 

 were scattered into a flame in the mode described by Herr 

 Ebert, exactly in the same way. They contained in 1 cub. 

 centim. respectively 



(a) M = 0-0304 gr. sodium, (b) M x = 0*0132 gr.' sodium. 

 Their density was nearly unity. 



A portion of the flame was placed opposite to the slit, which 

 appeared uniform in the whole section. Its diameter is 

 2 cub. centim. 



The readings a on the photometer and the corresponding 

 cotanV were for 



(a) a! = 31°, cotanV =2*770, 



(b) a^ = 42°, cotan 2 a/ = 1-233. 

 Therefore, very nearly, 



M : M x = cotanV : cotanV/, 

 viz. :— . 0304 . 0-0132 = 2-770 : 1*233. 



The brightness therefore increases nearly proportionally to 

 the quantity of salt present, which is also what Herr Gouy* 

 has found. 



For solutions of sodium carbonate, which contain in the 

 unit volume the same quantities of sodium as the above 

 sodium chloride solutions, the same brightnesses were found. 



26. We will now calculate the quantity of sodium which 

 in the first of these solutions yields the observed brightness, 

 and the corresponding quantity of energy. 



2100 cub. centim. of gas-mixture pass through the burner 

 per minute f- The velocity at this point is, therefore, 



* Ann. de Chem. et de Phys. [5] xviii. p. 5 (1879). 

 t Cf. also H. Ebert, Wied. Ann. xxxiv. p. 83 (1888). 



