178 Dr. W. F. Magie on the 



differences from which the existence of a contact-angle is 

 inferred. 



The variations in single readings of the value of q arise 

 partly from the fact that the image of the slit is not all in focus 

 at once, and spreads out at the ends. It is sometimes difficult 

 to avoid setting on a wrong portion of the image, especially 

 after the field has been illuminated to enable the eyepiece- 

 micrometer to be read. The proper illumination of the pointer 

 also offers difficulties, which may result in some cases in 

 faulty focusing and consequent errors of setting. The read- 

 ings of k are made uncertain from the adaptability of the eye. 

 The faintness of the reflected images makes it impracticable 

 to use the method of determining the focus by the parallax of 

 the image with a spider-line in the eyepiece. In the five 

 settings from which a position was determined, the extreme 

 readings of the micrometer-screw differed usually by three or 

 four hundredths of a millimetre. 



Criterion of the Existence of a Contact-angle. — Although 

 these sources of error, and possibly real differences in the 

 values of a 2 for different bubbles in the same liquid, render 

 the separate results in a series sometimes widely discrepant, 

 and the small number of results included in the mean seems to 

 make the ordinary rules for obtaining the probable error 

 scarcely applicable, yet I have thought it worth while to ap- 

 pend to the means their probable errors. I think that the 

 probability of constant errors of importance is slight, and the 

 accuracy of the observations sufficient to warrant the belief, 

 when the results by the two methods differ by more than the 

 sums of their probable errors, that the difference is a real one. 

 In all cases but that of alcohol, the difference, when it exists, 

 is such that the result by the " k " method is less than that by 

 the "<?" method. In these cases I have concluded that the 

 observations indicate a finite contact-angle. 



Water. — The results for water point, though doubtfully, 

 toward a finite contact-angle. The difference between the 

 11 q" and " k" values in the first set of observations is very 

 striking. The difference in the second set is much less, but 

 still evident. The large difference in the first set may per- 

 haps be explained by the difference of temperature between 

 the water and the air, as discussed later in this paper. From 

 the second set of observations alone I should hardly be willing 

 to draw the conclusion of a finite contact-angle for water, if 

 it were not that the results of these observations are substan- 

 tiated by those of a number of preliminary measurements. 

 By a modification of the "<?" method, in which "q" was 

 observed by an ordinary cathetometer, I obtained a 2 equal to 



