Philadelphia Paper - Discussion on Steel Rails. Virginia Meeting

to same extent, the assumptions tinderlying Dr. Ilu?ley's con alusions. These amrrmptions are: that 'the loss of metal per million tons of trafffc, depends, first upon the circrtnistances under which the rail is worn; secondly, upon the proportions of its various constituents, ancl that the anlorlnt of loss is afEect~d by eacb constitnent in a cer tain ratio, so that if the circunlstances were the same for all tlie mils, the wear per nliilion tons might he upproxi91ately expre~sed by an equation of the form I + Cc + Pp + SR + Mm = R, io wtlioh I is an unknown valne, dependi~.rg on the quantity of iron (and other ingre dients not determined) in the rail, and assumed to be constant for all the rails ; c, p, s, and m are the experimentally determined quan tities of carhon, phosphorus, sulphur, and manganese, as tabulater1 in YIates VT and VII of Dr. Dudley's paper; and R is the experirnen tdlly dcterlnincd wear per million tons; while C, P, S, and M are onknown wfficients. In other words, it is assunled that the differ ence in wear is proportional to a difference in c, p, s, or m, and that the effects of a change in the amonnt of either are independent of the amount of the rest-—within the experinlental limit5 of the problem. It is also assr~med that sulphar, copper, and other ingredients, not determined, are qually present in all the rails, or at least {lo not affect the wear, since I is taken as constant. Dr. Dudley tacitly assumes the coefficient6 C, P, S, and M to be positive; and assigns certain valries to them, by means of which he redom t.he equation to the form I + Pa: = R, x being equal to cc + Es +Mm i Pp, or tjje uanjbe,. of so-called phosphorus units in the rail. But we do not have R directly given under constant circumstances. The varying weights (per engine, car, or train) and the varying epds, we must neglect for lack of data, and assume that in these rwpects the rails examined have been treated srlbstantially alike. But there remain the varying conditions as to track, which mnst he elirninsted. Dr. Dudley gives six clrlsses, four of which contain 8 rails each, and two 16 rails each. Beginning with the 6~st (tangent grade), take the mean of the figures expressing wear for that clam; and continaing tliis process through the other five, we obtain six expressions in quantity of loss 'by wear, which we assome tc, represent, in their differences, the varying conditions of the trarli, with respect to grade and direction. We now take the mean of these moans (giving double weight to the gmiip containing 16 ohwrvafieras). This general rnean is the 10 of metal per million tons of trafio for a rail of avorage constitution under mean ciroumstances.