It is necessary to have a means of comparing the work of a tube mill or other crushing machines grinding to various sizes so that the most effective range may be determined and the successive stages of crushing may be proportioned to give the maximum efficiency for each machine. For this purpose we must use a mathematical formula which will contain the necessary elements and which is consistent with practical experience. While the problem appears at first sight an easy one, the more it is studied the more complex it becomes, by reason of certain factors which cannot be determined with accuracy.

The problem is to determine the amount of work done in crushing ore, work being the overcoming of resistance through space, represented by the formula, work = distance X resistance. The work done in crushing particles of rock to smaller dimensions varies in proportion to the surface exposed in crushing or to the ratio of the original to the final diameters. This is known as the Rittinger theory.

Opposed to this we have what is known as Kick's law which states that "the energy required for producing analogous changes of configuration of geometrically similar bodies of equal technological state varies as the volumes or weights of these bodies." While personally I favor the Rittinger hypothesis, both theories have their advocates. In most of the cases I have worked out the two methods give nearly the same results. I quote from a recent article by O. A. Gates1 who is the originator of the crushing surface diagram method of computing crushing efficiencies based on the Rittinger theory:

"Some 2 years ago there was published in your columns a note on the rock-crushing tests then being conducted at McGill University, the preliminary results of which indicated that Stadler's theory of Kick's law was correct. Recently the secretary of the Canadian Mining Institute called my attention to an editorial in their October Bulletin referring to my paper presented in the September Bulletin of the American Institute of Mining Engineers, but more particularly giving preliminary conclusions on the work that has been done at McGill up to date. The editorial concludes thus:

Nearly 200 tests have been made at McGill during the past 2 years and we understand that each series will demonstrate convincingly the fallaciousness of expressing power in terms of "energy units,"as proposed by Mr. Stadler in accordance with Kick's law. Rittinger's hypothesis, on the other hand, is supported in so satisfactory a degree by the results obtained by actual experiment as to appear quite dependable. It seems probable, therefore, that the investigations made at McGill and Purdue universities will result in terminating the long standing controversy between the supporters of respectively Rittinger and Stadler; while if, as now seems likely, it will conduce to the definite establishment of a correct basis for calculating the efficiency of rock-crushing machines, a work of great utility, by reason of its practical value to millmen, will have been accomplished."