366 Mr. A. M. Worthiiigton. [June 16, 



is in no way inconsistent with the variation just noticed, for the angle 

 at which the liquid leaves the tube is practically indeterminate at the 

 sharp edge of the glass where the liquid can select and attach itself to 

 some elementary portion inclined at the required angle. But this 

 constancy of the real angle of contact accounts for the fact that if a 

 very narrow tube be used, the drop will spread up it on the outside 

 before separating. As soon as the angle between the extreme element 

 of the curve and the vertical side of the tube is equal to this definite 

 angle of contact the spread will take place. 



It will be noticed, especially with wide tubes, that the base of the 

 drop suffers but little change after a certain point. 



The concavity, however, of the upper portion is seen to deepen before 

 the liquid separates, but the drop remains suspended after this deepen- 

 ing has begun. 



It is very difficult to tell precisely where separation takes place, since 

 it is accomplished generally with great rapidity, but I am inclined to 

 think that it occurs at the place of greatest concavity. 



Sometimes the small secondary drop (observed by Dr. Gruthrie) is 

 seen to follow the main drop. This was very noticeable in the case of 

 water dropping through petroleum, where separation is effected com- 

 paratively slowly. The point at which this small drop is first seen 

 serves, in this case, to determine fairly accurately the place of separa- 

 tion. There can be no doubt that this secondary drop is due to the 

 spontaneous segmentation of the cylindrical neck of liquid, which joins 

 the upper and lower portions up to the last moment before complete 

 separation takes place ; and that it is the same phenomenon that was 

 first observed and explained by Mr. Plateau in his experiments on 

 cylinders of mercury.* 



It is obvious that if drops are extruded in rapid succession there 

 will be a considerable influx of liquid through this residual neck into 

 the lower portion after it has begun to separate, and that the drops 

 which fall will on this score be larger. 



Since, however, the velocity of the inflowing liquid will produce a 

 pressure on the lower portion of the drop, tending to hasten separa- 

 tion, it is to be expected that a definite increase in the rate of influx 

 will produce a greater effect on the size of the drop which falls off 

 when the rate of dropping is slow than when it is fast. 



These considerations go far to explain the results of Dr. Guthrie's 

 experiments on the influence of the rate of dropping on the drop size. 

 It is further evident that an influx of liquid, after separation has 

 begun, only complicates the phenomenon, and that it is from a study 

 of the curve, when the influx is zero, that we are most likely to obtain 

 an insight into the manner and cause of separation. 



* " Statique Experimentale des Liquides." 



