816 SUMMABY OF CURBENT RESEABOHES RELATING TO 



if the value of r be accurately known, it becomes easy to find the value 

 of n : 



n — 1 = r i 



\p p 



/'I 1\ 

 « = ! + »• ) . . . a. 



\^ p / 



But as in practice it is difScult to determine the exact value of r, it is 

 better to find, not the absolute refractive index of the liquid, but that 

 relative to a substance the refractive power of which is already known, for 

 example, glass or water. 



Let n' be the index of refraction of the comparing substance, and p" the 

 distance to which in this case the objective is moved from the micrometer ; 

 the formula then becomes 



from which 



p p" r ' 



n n" ^rt n" ' 



p p p p 



By substituting the value of r in the equation a we get 



But 



\p p / 



\p p"/ 



\p p 



n = I + (n' - 1) ^ — I 



p p — p 



"Where the value of n', that is the refractive index of the liquid used for 

 comparison, is known, and the other values, that is, the distances between 

 the objective and the object, it becomes sufficiently easy to make the 

 required calculation. 



Instead of measuring these distances, it is possible and more convenient 

 to calculate them. In the three cases before us let us suppose these to 

 be g g' g" : then when the optical arrangement remains the same, there is 

 a constant relation between these and the focal length of 



gp = gp' = g" p" . . . y. 



In the equation /8 the values oi p p' p" may be expressed in functions of 

 g g' g" taken from equation y. 



