MOSSOTTI ON FRAUNIIOFER'S RETICULAR SPECTRA. 441 



2. In the communication which I made to the third Scientific 

 Association which was held at Florence, I have given the for- 

 mula which expresses the refractive index in function of the 

 lengths of the waves. If this formula be extended, by carrying 

 out the approximation to the fourth power of the lengths of the 

 waves, it may be represented by the following function : — 



v='+"(^y+<i°)' (>•' 



In this formula V signifies the velocity of the propagation of 

 the light in the refracting medium, taken as unity in vacuo or in 



the air; z^ therefore corresponds to the index of refraction; Kq 



indicates in the air the length of the waves of a single ray of a 

 gi\'en colour, and A the same for a ray of any colour; i, h, k are 

 three constant coefficients, dependent upon the nature of the 

 medium, and which may be experimentally determined for every 

 refracting substance. 



3. To carry out this determination in the present instance, we 

 shall have recourse to a known formula, which Fraunhofer also 

 made use of. If <$ = 26° 24' 30" denote the refracting angle of 

 the prism, ^ = 1 7° 21' 8" the angle of refraction of the ray of the 

 colour situated at the line D, and .r the angular distance in the 

 spectrum between the line D and the line which runs through 

 the colour corresponding to the length X, we have 



I _ sin 1 (4> + ^^ + A') 

 V sin i (p 



If this value of the index of refraction be made equal to the one 

 above, we obtain the equation 



sm i (p 



(xf-K^f- 



The value of the first member may be calculated for each of 

 the principal bands by means of the magnitudes previously 

 given ; thus if, in the second member, we substitute for A^and A 

 the corresponding values of the length of the waves which have 

 been already given, we obtain an equal number of equations, 

 from which the values of the constants i, h, k may be deduced, 

 ajjplying, if thought necessary, the method of least squares. 



'] o cdcct this determination more conveniently, the above 



