in which the symbols refer to the same quantities as before, but the constant is calculated on the basis of Q being stated in cubic metres, l in metres, and d and h in millimetres. It will be seen that the equation has precisely the same shape as Pole's formula for coal-gas, but that the constant is different. The difference is not only due to one formula referring to quantities stated on the metric and the other to the same quantities stated on the English system of measures, but depends partly on allowance having been made for the different physical properties of the two gases. Thus Bernat's formula, when merely transposed from the metric system of measures to the English (_i.e._, Q being cubic feet per hour, _l_ feet, and _d_ and _h_ inches) becomes Q = 1313.5_d^2_(_hd/sl_)^(1/2) or, more simply, Q = 1313.4(_hd^5/sl_)^(1/2) But since the density of commercially-made acetylene is practically the same in all cases, and not variable as is the density of coal-gas, its value, viz., 0.91, may be brought into the constant, and the formula then becomes Q = 1376.9(_hd^5/l_)^(1/2) Bernat's formula was for some time generally accepted as the most trustworthy for pipes supplying acetylene, and the last equation gives it in its simplest form, though a convenient transposition is d = 0.05552(Q^2_l/h_)^(1/5) Bernat's formula, however, has now been generally superseded by one given by Morel, which has been found to be more in accordance with the actual results observed in the practical distribution of acetylene. Morel's formula is D = 1.155(Q^2_l/h_)^(1/5) in which D = the diameter of the pipe in centimetres, Q = the number of cubic metres of gas passing per hour, _l_ = the length of pipe in metres, and _h_ = the loss of pressure between the two ends of the pipe in millimetres. On converting tins formula into terms of the English system of measures (_i.e._, _l_ feet, Q cubic feet, and _h_ and _d_ inches) it becomes (i) d = 0.045122(Q^2_l/h_)^(1/5) At first sight this formula does not appear to differ greatly from Bernat's, the only change being that the constant is 0.045122 instead of 0.05552, but the effect of this change is very great--for instance, other factors remaining unaltered, the value of Q by Morel's formula will be 1.68 times as much as by Bernat's formula. Transformations of Morel's formula which may sometimes be more convenient to apply than (i) are: (ii) Q = 2312.2(_hd^5/l_)^(1/2) (iii) _h_ = 0.000000187011(Q^2_l/d^5_) and (iv) _l_ = 5,346,340(_hd^5_/Q^2) In order to avoid as far as possible expenditure of time and labour in repeating calculations, tables have been drawn up by the authors from Morel's formulæ which will serve to give the requisite information as to the proper sizes of pipes to be used in those cases which are likely to be met with in ordinary practice. These tables are given at the end of this chapter.