In Fig. 6 it should be pointed out that the surface A B may be either the horizontal surface of a liquid at rest (and considered the limiting surface of a bubble of infinite radius), or, equally important, the surface A B may be considered the surface of a bubble of small diameter within the body of a liquid. This bubble may have a radius of one foot or one inch or one thousandth of an inch, and the action of the sulphide particles with reference to the bubble will be just the same as it is with reference to the free surface of a liquid. If the bubble has a radius of, say, onetenth of an inch, and the blende particle a mean diameter considerably less, the bubble will rise by its buoyancy to the surface of the liquid, and carry up with it the blende particle adhering to the surface A B of the bubble. If then, instead of only one blende particle, we mix slightly acidified water with crushed ore and a little oil, and release in the whole body of the pulp a large number of minute gas bubbles, we will have the above described sequence of events taking place in innumerable instances, and these innumerable bubbles will rise to the surface of the liquid and rest there in the form of a froth, carrying with them the sulphide particles, while the gangue in the meantime has exercised its preferential adhesion for the water and become wetted, and remains within the body of the liquid and sinks to the bottom of the vessel. The bubbles may be bubbles of air introduced by violent agitation of the pulp, or air bubbles released from solution in the liquid by subjecting the liquid to a vacuum, or air bubbles dissolved in the liquid at super- atmospheric pressure, followed by a release of pressure, or they may be carbonic- acid gas bubbles released by the chemical reaction of sulphuric acid on carbonates, or in several other ways.

In Fig. 7 it will be seen that near C there is a point where the air, the liquid, and the solid all meet in a common point, this point being the trace of a line perpendicular to the plane of the drawing. The angle E C D is made up on one side with the solid and the other side with a tangent drawn somewhere on the curve C F. It is certain that a study of the curve C F, by means of a microscope and screen, would be a profitable line of experimental work. Maxwell says : " The constancy of the angle of contact between the surface of a fluid and a solid was first pointed out by Dr. Young." It is difficult to say where this tangent should be drawn. From a consideration of the forces acting near the region of mutual contact between a solid, a liquid, and a gas, it seems most reasonable to assume that there is no definite point where one could draw a tangent, but that the curve C F is a continuous curve, the functions of which are : (1) The force of surface tension of the liquid ; (2) the force of surface activity or adhesiveness between the solid and the liquid : (3) the force of adhesiveness between the solid and the gas ; (4) the force of adhesiveness between the gas and the liquid ; (5) the force of gravity ; (6) temperature ; (7) pressure ; (8) shape of the solid surface ; (9) composition of the solid ; (10) composition of the liquid ; (n) composition of the gas ; and others.

The methods of measuring what are termed contact angles are shown in Fig. 8, a piece of mineral having one plane surface, generally a cleavage plane, being immersed in a liquid surface as at A, and then turned through an angle, a, to a position like B. As the piece of mineral turns, the curved surface of the liquid in the neighbourhood of the line of mutual solid-liquid-gas contact flattens until it is horizontal, and the angle 180 - a is said to be the angle of the contact. This angle is a definite angle under fixed conditions.

H. Livingstone Sulman, in Bulletin No. 79, Trans. I.M. & M.. speaking of the angle 180- a, announced that "a study of a series of observations on various substances showed a series of curiously discrepant readings, which on further research proved to be due to the existence of a variable range of the contact angle between liquids and solids, though of constant magnitude of variation for each substance. This hysteresis appears to be intimately connected with the ability of a given solid to condense upon itself gas films, and when submerged in a liquid to determine the attachment of a gas when generated. It follows that this angular hysteresis reaches its highest value for minerals that are the most susceptible of flotation. Besides roughly quantifying the gas-condensing power due to the surface energy of solids, it brings us somewhat closer to an explanation of the efficiency of acidification. Whereas the angular hysteresis of silica in plain water may exceed 30, thus indicating that substance to have a definite power to occlude gas and float, it drops to from 4 to o in water acidulated with sulphuric acid." Sulman has here announced a discovery of the first magnitude, and places in the hands of the physicist a clue to many puzzling questions.