170 Dr. W. F. Magie on the 



was determined to be 3742 millim. The value of A is 14' 6 3 

 millim., and the value of N is found from it when A— N has 

 been measured. From these quantities the first correction 

 was computed once for all to be 0*160 millim. The second 

 correction varies with each value of h ; it may be calculated by 

 the use of the approximate value for h obtained by omitting 

 the second correction. Its value differs for different liquids, 

 but varies so little for any one liquid that, after it has been 

 calculated for one bubble, it may be estimated for the others. 

 It usually amounts to between 0*03 and 0*04 millim. For 

 the third correction a table was prepared giving the heights 

 of the arcs for a series of values of chords such as those 

 ordinarily obtained in the experiments, and the corrections 

 were obtained by interpolation. This correction was the 

 one of most importance, its values ranging from 0*3 millim. 

 to 0'7 millim. 



In the computation of a 2 from the value of k thus obtained, 

 the value of eo, the angle made by the surface of the bubble 

 with the horizontal plane passing through the circle of con- 

 tact, was assumed to be zero, although strictly it should have 

 been taken to be the angle made with that plane by the lens' 

 surface at the circle of contact. The cosine of that angle 

 was so nearly equal to unity that the slight difference was 

 neglected. 



Results. 



The results obtained by the use of the above described 

 methods of measurement are presented in the following 

 tables. The first column contains the values of q, expressed 

 in divisions of the eyepiece-micrometer. One division 

 of this micrometer was found, by comparison with a Roger's 

 stage-micrometer, to be equal to 0"02658 millim. The 

 second column contains the values of A — N in millimetres, 

 A and N being each positions determined by the mean of 

 five settings of the micrometer-screw of the cathetometer. 

 The third column contains the computed values of k; the 

 fourth the semidiameters of the bubbles in millimetres; the 

 fifth and sixth the values of a 2 , computed from q and from k 

 respectively. The constant of diameter given is the length 

 to be subtracted from the measured semidiameters to obtain 

 the semichords used in the computation of the third correc- 

 tion for k. The temperatures of the liquid and of the air just 

 above the liquid are also given sufficiently often to indicate 

 their values during a set of observations. The temperatures 

 are put together in brackets, the upper one being the tempe- 

 rature of the liquid. 



