462 



Prof. Guthrie on Dropi 



[Recess, 



of the sphere increases from which the drop falls, and, further, that the 

 difference of drop-size hrought about by this cause alone may easily amount 

 to half the largest drop-size. For dispensers of medicine this fact is as im- 

 portant as that pointed out in Part I., where it was shown that the growth- 

 time so materially influenced the drop-size. The lip of a bottle from which 

 a drop falls is usually annuloid. The amount of solid in contact with the 

 dropping liquid is determined by the size of two diameters, one measuring 

 the width of the rim of the neck, the other the thickness of that rim. In 

 most cases the curvature and massing of the solid at the point whence the 

 liquid drops is so irregular as not to admit of any mathematical expression. 



The reason why drops which fall from surfaces of greater curvature are 

 larger than those which fall from surfaces of less curvature is surely 

 this : — In the case of a surface of greater curvature the base of the drop 

 has more nearly its maximum size ; the centre of gravity of the liquid film 

 from which the drop hangs is nearer to the centre of gravity of the hang- 

 ing drop ; the contact between the two is more extensive and intimate ; so 

 that the drop is held for a longer time and therefore grows more. 



On comparing columns 3 and 5 of Table VIII., there does not appear 

 to be any obvious law of connexion between the two ; nor indeed can the 

 numbers of column 4 pretend to such a degree of accuracy as would justify 

 us in attempting to establish one. This is seen on comparing inter se the 

 numbers of column 4. Especially with the spheres of longer radii, there 

 is so much difficulty in getting a uniform wetting of the surface whence 

 the drop falls, and this so materially influences the drop-size, that the 

 numbers found are seen to vary considerably. Greater accord is obtained 

 with spheres of less radii. As we might expect, the same absolute increase 

 in length of radius takes less effect upon the drop-size in the case of longer 

 than in that of shorter radii. The infinite, or at least indefinitely great 

 difference between the radii 1 and 2 produces about the same effect upon 

 the drop-size as the difference of 43 millims. between the radii 2 and 3, 

 and so on. 



The following Table of first differences shows this more strikingly ; — 



rn+i-rn. 





oo 



0-01854 



43- 



0-02189 



22-9 



0-01362 



29-7 



0-03760 



2-4 



0-00732 



3-6 



0-01643 



0-3 



0-00226 



1-2 



0-00575 



2-5 



0-00965 



0-4 



0-00479 



The relation exhibited in this Table supports the supposition that the 

 size of the drop varies inversely as the contents of a figure bounded below 

 by a circular horizontal plane of constant diameter (less than that of the 



