of Edinburgh , Session 1877-78. 
527 
the increase in the size of drop, with the increase in the rate of 
dropping, is due to the attraction of the solid tearing more of the 
root of the drop in low than in high rates is put to a crucial test by 
an experiment in which mercury drops from a wide glass tube so 
arranged that the tube only acts as a support for a column of liquid 
from the end of which the drops fall. In this case there is no solid 
to reclaim by adhesion any of the drop, and yet there is the same 
increase in size as the rate increases. The author accounts for the 
increase as follows : — 1. The rupture of the neck of a drop is not 
an instantaneous process, but lasts for a short time, and during that 
time liquid is flowing into the drop through the neck, and the faster 
the flow the greater is the increment of the drop during rupture. 
2. When the rate is high the breaking neck has a longer life-time, 
as the stump follows after the full drop as in the beginning of the 
formation of a stream. Briefly stated, the quicker the rate the larger 
the drop, because more liquid flows into the drop after the rupture 
has commenced, and the longer does that flow continue. The 
author calls a drop when it begins to break a “normal ” drop ; 
and to find its weight he determines the decrease of weight with 
decrease of rate, and reduces the latter to zero when the weight of a 
normal drop is found. Apparatus is shown by which experiments 
were carried out, and inaccuracies eliminated. The normal drop is 
found to weigh 0 4130 grm., and as the width of the neck is found 
to be 3*395 mm., this gives a breaking strain of 0*0456 grm. per 
square millimeter for mercury at 1 6° C. 
4. Note on Vector Conditions of Integrability. By 
Professor Tait. 
(1.) The relation 
dtr = uqdpq ~ 1 
ensures that the tensor of d<r shall always be u times that of dp 
Hence, if p be the common vector of three series of surfaces which 
together cut space into cubes, <r possesses the same property. (See 
§ 6 of my paper On Orthogonal Isothermal Surfaces, Trans. B.S.E., 
1873-4. In what follows this paper will be referred to as O.) 
We may suppose the tensor of q to be any constant, unity suppose. 
Then, from 
4 A 
VOL. IX. 
T? 2 =l, 
