The forces with which we are dealing are feeble in magnitude when compared with, say, the force of gravitation. It should be emphasized, however, that although these forces acting at the surface of substances are to our conception feeble, they act continuously at all surfaces ; and although we cannot increase the unit force, we do have it in our power to increase enormously the units of surface, and thereby we can bring the nett resultant work of these forces up to an effective sum.

There are two ways in which the surfaces involved can be increased. A cube of ore 2.1544 feet on each edge contains 10 cubic feet. If this ore is a definite mixture of quartz, blende, galena, etc., it will weigh just a ton. The cube will have a total surface area of about 28 square feet, or roughly 4,000 square inches. If this cube of ore is crushed to 4O-mesh it is certain, on reasonable assumptions, that the superficial area of the ton of ore is increased to more than 30,000,000 square inches, an increase in area of several thousand times the original.

The De Bavay process uses the surface film of the liquid at rest as the transporting agent, and therefore does not get the advantage of the second method of increasing the surface factor, which is advantageously made use of by Elmore, Minerals Separation, and Potter-Delprat. This second method of increasing the effective surface is by creating a froth of bubbles, each bubble of which acts as previously described. It is no unusual sight to see on the flotation boxes of the Potter-Delprat and Minerals Separation processes two inches of froth composed of a compact arrangement of bubbles and sulphides. By determining, roughly, the size of the bubbles and the distance apart, it is safe to say thai? the available liquid surface is increased from 20 square feet on the free surface of the liquid in a box to 2,000 square feet when the surface of all the bubbles is counted. In both the case of the mineral and the liquid it is obvious that only a small portion of the surface is used for the work of flotation.

As before stated, the surface tension of water has been determined to be a force of 81 dynes per square centimetre, acting at the surface, to resist penetration of the surface. If we assume that the force tending to make finely divided sulphides penetrate the surface is the force of gravity, then each gramme of sulphides is impelled to penetrate the surface by a force of 981 dynes, and therefore one square centimetre of the surface will hold up 81 -* 981 = 82.6 milligrammes of ore.

Leaving out of account the enhancement of this force of surface tension by the admixture of oil and acid and other means, the following table will show that this force is adequate for the work required of it. The efficiency of the utilisation of the force is in all four cases very low.

Referring to the last two columns, in the case of Minerals Separation, Elmore, and Potter-Delpart, it will be seen that they have increased their theoretical capacity per hour, based on the surface area of the boxes, to several times more actual working capacity be means of marking of froth. The varibles in the problem are so many that it is not safe to attempt more than to roughly quantify to force available, but it is certain that the force available in many time as large as is necessary for the work to be done. This pharse of the project is an interesting one for research and speculation, and will, no doubt, receive critical study.