WHEN making comparisons of the efficiencies of different grinding and crushing machines it is desirable to be able to estimate the work actually done in crushing the ore from a given size of feed to a given size of product, the screen analysis of both feed and product being determined. Messrs. Klug and Taylor, in a paper on this subject, published in the monthly journal of the Chamber of Mines of WA, 31st January, 1906, have described a method adopted by them in calculations made in connection with a series of trials of grinding pans. Their methOd is based upon the assumption that if a quantity Q of material consisting of particles of average diameter x be crushed down until the average diameter of the particles is y, then the work done in grinding is proportional to Q x. There is no theoretical basis for this assumption that the writer is aware of, and it does not appear to satisfy the fundamental conditions necessary. If the material be further crushed until the diameter 2 becomes Z, the additional work done is measured. The work done in crushing from diameter x to diameter Z in one operation is proportional to Q x:, and therefore we ought to have zx2 y2 x2 Q-+Q-=Q-. y2 Z2 Z2But these expressions are not in general equal to one another. In other words, according to the theory underlying this method, if we crush from diameter x to diameter y, and then from diameter...