272 M. R. Riihlmann on the Alteration produced by Heat 



considerable number of variables, and has certain advantages 

 and disadvantages. 



The most usual method is to take the minimum, and thence to 

 derive the index of refraction from the formula 



. « + S 

 sm 



ii— — 



a 



sm 9 



(if a be the angle of the prism and 8 the least refraction). An- 

 other method, perhaps a little more exact, was first employed, as 

 far as I am aware, for exact measurements by Seebeck, and 

 consists in measuring the angle of the emergent as well as that 

 of the incident ray. In the first place, this method requires, in 

 order to avoid endless complication, that the prism be placed 

 over the centre of the circle of the goniometrical instrument ; it 

 further necessitates the determination of very many angles, 

 whereby its accuracy is partly forfeited. From this instrument, 

 which Seebeck* had already described in 1830, Meyerstein's 

 spectrometer and Babinet's goniometer, in its more perfect form 

 (instruments used for similar purposes), were gradually developed. 

 Van der Willigen used the first of these apparatus in his above- 

 mentioned observations, while Babinet's goniometer was em- 

 ployed by Dutirou and the Vienna physicists Handel and Weiss, 

 who, under Grailich's supervision, obtained the excellent results 

 of their researches on the refractive indices of mixed liquids. 



If the prisms are not in the centre (and it is impossible to 

 place them there in theodolites and most goniometrical instru- 

 ments), correction must be made for the excentric position of the 

 prism. As it was important for me to be able to warm the prism 

 at will, and to combine continual determinations of the refract- 

 ing angle with measurements of the refraction, I chose the fol- 

 lowing plan and arrangement. 



Use was made of the theodolite by Pistor and Martin, the 

 telescope and vertical angle of which could be removed, and 

 which stood in the Physical Cabinet in the University of Leipzig 

 upon a solid stone cylinder about 1 metre in height. Upon 

 this theodolite was placed a table with adjusting feet sup- 

 porting on three points the hollow prism which held the liquids 

 to be examined, and which could be moved on grooves in two 

 directions at right angles to one another. At a distance of about 

 30 centimetres, a Repsold's "universal circle'' was placed upon 

 a firm wooden support, the bent telescope of which was at the 

 same height as the hollow of the prism. At the same height as 



* Observationes circa nexum inter cedent em, &c. Inaugural Dissertation. 

 Berlin, 1830. 



