254 THEORY OF MICROSCOPIC OBSERVATION. 



VI. 



DIFFERENCES OF LEVEL. 



SINCE only those objects can be distinctly seen through the Micro- 

 scope which lie exactly in the plane of adjustment, it is possible to 

 ascertain the distance of two object-points in the direction of the 

 optic axis, by measuring the difference of level of the corresponding 

 planes of adjustment with the help of a second Microscope placed 

 horizontally, or by a micrometer screw constructed for this purpose. 

 In this latter method there must be taken into account a source of 

 error which influences to a very considerable extent the results of 

 the measurement in cases where the objects are immersed in a solid 

 or liquid medium for instance, in water. If we determine the 

 tube-displacement which is necessary in order to bring into the 

 plane of adjustment the two given object-points alternately, the 

 amount of the displacement will always be considerably less than 

 the actual difference of level. We get for instance, as focal length 

 of a spherical air-bubble in water *98 1*04 (the radius taken as 

 unity), whilst, in reality, it amounts for the central rays to about T3. 

 This error is due to the fact that the passage of the pencils from 

 water into air (the cover-glass not here coming into account) pro- 

 duces with the microscope the same effect as with the naked eye 

 that is, a body situated in water is apparently raised, and, taken 

 absolutely, the more so the deeper it lies. The virtual image of an 

 air-bubble is therefore raised to a greater degree than its centre, the 

 focal length being consequently shortened ; and for the same reason 

 in general the vertical distance of the two points is lessened. The 

 amount of this diminution depends, of course, upon the angle of in- 

 cidence of the effective rays, and is for small values (as long as the 



arcs are in the same ratio as the sines) expressed by 1 , where n 



denotes the refractive index. Since, then, the incident cones of light 

 are refracted in the objective as if they consisted of rays of definite 

 mean inclination, and as this inclination does not exceed 12 18 

 in the higher powers we have examined, the above expression 



