168 Dr.W. F. Magie <mt/ie 



of the object-glass was fastened a small piece of white paper, 

 the images of which, reflected at the under surface of the 

 lens and at the surface of the bubble, could be observed by 

 the microscope. The paper was illuminated by the rays from 

 a gas-flame or an incandescent electric lamp, concentrated by 

 a lens and reflected upon the paper by a mirror. The mirror 

 was a glass plate, silvered on the front surface, backed with 

 black paper, and pierced with a small hole through which the 

 reflected images were observed. Light was thus largely ex- 

 cluded from the interior of the bubble. The cathetometer 

 was furnished with a micrometer-screw reading directly to 

 hundredths of a millimetre. To make a measurement of k a 

 bubble was formed under the lens, and observations were 

 suspended until the liquid film had evaporated from the 

 centre of the lens under the microscope. Five settings were 

 then made on the sharply focused image of the paper re- 

 flected at the under surface of the lens, and five settings on 

 the image reflected at the bottom of the bubble. The dis- 

 tance between the two positions, determined from the means 

 of these settings, is the distance A — N of formula III. which 

 follows. To form a new bubble, most of the air contained in 

 the one already measured was removed with the pipette, yet 

 not so much that the liquid again wetted the portion of the lens 

 under the microscope. The bubble was then enlarged by the 

 introduction of more air. In this way the delay occasioned 

 by waiting for the evaporation from the lens' surface was 

 avoided, and an accuracy in the settings obtained which was 

 not possible when the reflexions were observed before the 

 reflecting portion of the lens became dry. 



Calculation of k from Measurements, — If the measurements 

 described were made upon a bubble formed under a plane 

 glass plate, it can easily be shown that the measured distance 

 A — N would be the desired distance k. Since, however, 

 the bubble is formed under a lens, three corrections are 

 necessary : — 



1. The first of these arises from the fact that in the first 

 observation the rays from the object pass through the thick 

 lens, are reflected at a convex surface, and pass out through 

 the lens. If we express by 



A, the distance from the object to the lens in the first 



observation, 

 e, the thickness of the lens at its centre, 

 n, the index of refraction of the glass, and by 

 /, a distance such that (n — l)/=R, the radius of curvature 



of the concave face of the lens, 



