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CANE SUGAR.contact, its width should be as small as possible. The width of the trashturner is determined by what may be called the vertical angle of the mill, i.e.,the apex of the triangle formed by joining the centre of the rollers; thelarger this angle, the wider the trash turner. In actual practice, verticalangles lying between 75° and 90° are met with, a very general angle beingabout 82°-84°. In addition to a small vertical angle diminishing the widthof the trash turner, the component of the downward pressure exertedvertically on the top roller, on the line joining the centres of two rollers, isgreater. There is a limit, however, to decrease in the vertical angle since, asthis narrows, the space available for the shaft of the lower rollers becomesless. By the employment of the best material, mills with small shafts ofsufficient strength and narrow trash turners can be made.A very large number of curves has been suggested for the trash turner,in all of which the personal equation of their originators appears very largely.On certain mathematical grounds it can be shown that the correct curve is alogarithmic spiral, the construction to obtain which is given below. Themethod which appeals most to the writer is one of trial and error:—indicatingthe engine with different settings, and adopting that setting which isfound to absorb least power. Another essentially practical method is to adoptthat curve into which an old trash plate has been worn. It must be borne inmind, however, that the proper curve and setting is dependent amongst otherthings on the nature of the canes ground, particularly on the amount of fibreand on its mechanical structure and resistance to compression, so that asetting satisfactory with one lot of canes may be the reverse with another;continual watchfulness on the part of the engineer is called for here.The efforts of engineers have been directed largely in late years towardsdiminishing the width of the trash turner, and towards obtaining at the sametime a small apex to the mill; all the departures from conventionalityinstanced above have had this point in view.Bergmans' Theory of the Trash Turner 3 .—The followingmathematical treatment of the trash turner was published in 1889, byR. P. Bergmans and is here reproduced:—The duty of the trash turner in sugar mills is to direct the crushed canefrom the first cylinder pair (one and two) to the second (two and three).The crushed cane must be so guided that cylinder S can take the feedwithout stopping the working of the plant.Let T1 represent the speed with which the crushed cane leaves thefirst cylinder pair and T2 that of the bagasse leaving the second cylinder pair(see Fig. 114); then must always T1 = T2 and it hence follows that thepassage of the bagasse over the trash turner must be uniform.184