y − 3z + u = 0, 2x + 2y = 0, x + z = 1;
so that
y = −x, z = 1 − x, u = 3 − 2x.
Accordingly
| M ∝ | Ta | ( | T | )x−1. |
| g | gσa² |
Since x is undetermined, all that we can conclude is that M is of the form
| M ∝ | Ta | ·F( | T | ), (1) |
| g | gσa² |
where F denotes an arbitrary function.
Dynamical similarity requires that T/gσa² be constant; or, if g be supposed to be so, that a² varies as T/σ. If this condition be satisfied, the mass (or weight) of the drop is proportional to T and to a.
If Tate’s law be true, that ceteris paribus M varies as a, it follows from (1) that F is constant. For all fluids and for all similar tubes similarly wetted, the weight of a drop would then be proportional not only to the diameter of the tube, but also to the superficial tension, and it would be independent of the density.