finding the Refractive Index of a Liquid. 469 



Second case. — When the liquid is not homogeneous (fig. 2). 



Fig. 2. 



Aj • Aa Aq 



• » 





* r 



* * 



* ' ' 



The liquid is supposed to have the same density at the same 

 depth, which must be the case if it is at rest. The path of 

 the axis of the pencil of light from any point on the scale 

 which enters the telescope must be a curve. 



Suppose P 1? P 2 , P 3 various points on the vertical scale, and 

 A 1? A 2 , A 3 the corresponding positions of the inclined tele- 

 scope when observing them. Suppose M n M 2 , M 3 are the 

 points where the axis of the pencil cuts the surface of the 

 liquid, and draw P 2 N 2 , P 3 N 3 parallel to the surface. Then it 

 is clear that, since MjAj, M 2 A 2 , M 3 A 3 are parallel, P 2 M 2 is the 

 same curve as NaMi moved horizontally, parallel to itself, 

 through the distance P 2 N 2 or AjAg. P 3 M 3 is the same curve 

 as N 3 Mi moved through the distance P 3 N 3 or K.^K Z . Simi- 

 larly for other points. 



Hence, by taking a number of points on the vertical scale 

 and finding the corresponding positions of the telescope, and 

 then plotting a curve having the vertical distances from the 



