AIR-BUBBLES IN WATER. 



191 



of cases to a searching discussion based upon mathematical 

 developments. 1 The phenomena of refraction and reflexion which 

 determine the microscopic image of given objects are first dis- 

 cussed; then the effects of light depending upon interference, 

 which were formerly called, as far as they were known, diffraction 

 phenomena, the origin of which may be of a very different kind. 

 Finally, a short consideration is devoted to oblique illumination 

 and to the appearances presented by objects in motion. 



I. 



SPHERICAL AND CYLINDRICAL OBJECTS. 

 1. AIR-BUBBLES IN WATER. 



LET A B (Fig. 104) be the vertical section of an air-bubble freely 

 floating in water, and there- 

 fore spherical, and M N 

 the plane of adjustment of S^ 

 the Microscope ; then any 

 point P in this plane is 

 illuminated in the micro- 

 scopic image by the rays 

 which, after their passage 

 through the air-bubble, seem 

 to come from this point, and 

 are directed towards the eye 

 by the refraction in the 

 Microscope. The inclination 

 of these rays to the perpen- 

 dicular cannot be greater 

 than half the angle of aper- 

 ture of the objective. If 

 this latter is assumed to be 

 60, then the ray reaches its maximum at 30. Similarly, the 



1 Harting (" Das Mikroskop," 2nd ed. ii. p. 31) expresses the opinion with 

 regard to these developments, that it is possible to explain the real point in 

 question less tediously. We do not for a moment say that Harting is alone in 

 holding this opinion. But in our view, and others certainly agree with us, it 

 is important here as elsewhere to understand the phenomena we observe, and to 



