DIFFEItENCES OF LEVEL. 255 



is approximately accurate in most cases that occur, and a trigono- 

 metrical determination 1 of the error is consequently superfluous. 

 In water, with the refractive index -f , each difference of level is 

 therefore diminished by a quarter of its real magnitude i.e., reduced 

 to f . (Accurate calculation gives with an angle of incidence 

 of 18 instead of f the somewhat smaller value '7395.) 



There is, moreover, a simple method of eliminating this source of 

 error : we replace the layer of air between the objective and the 

 cover-glass by water; the measurements will then agree exactly 

 with the true values. 



1 If D is the real and d the apparent difference of level, a the angle of 

 incidence, and d the (larger) angle of refraction, we get 



cos d sin a 



~~ sin d cos a ' ' 

 and sin (a'- a) 



