is employed for the purpose, where D is the diameter of the pipe, assumed to be uniform, L the length of the pipe, p1 the pressure at the entrance, p the pressure at the farther end, u the velocity at which the compressed air travels, [Delta] its specific weight, and f(u) the friction per unit of length. In proportion as the air loses pressure its speed increases, while its specific weight diminishes; but the variations in pressure are assumed to be so small that u and [Delta] may be considered constant. As regards the quantity f(u), or the friction per unit of length, the natural law which regulates it is not known, audit can only be expressed by some empirical formula, which, while according sufficiently nearly with the facts, is suited for calculation. For this purpose the binomial formula, au + bu², or the simple formula, b1 u², is generally adopted; a b and b1 being coefficients deduced from experiment. The values, however, which are to be given to these coefficients are not constant, for they vary with the diameter of the pipe, and in particular, contrary to formerly received ideas, they vary according to its internal surface. The uncertainty in this respect is so great that it is not worth while, with a view to accuracy, to relinquish the great convenience which the simple formula, b1 u², offers. It would be better from this point of view to endeavor, as has been suggested, to render this formula more exact by the substitution of a fractional power in the place of the square, rather than to go through the long calculations necessitated by the use of the binomial au + bu². Accordingly, making use of the formula b1 u², the above equation becomes, p1 - p 4L ------- = ---- b1 u²; [Delta] D [TEX: \frac{p_1 - p}{\Delta} = \frac{4L}{D} b_1 u^2] or, introducing the discharge per second, Q, which is the usual figure supplied, and which is connected with the velocity by the relation, Q = ([pi] D² u)/4, we have p1 - p 64 b1 ------- = --------- L Q². [Delta] [pi]² D^5 [TEX: \frac{p_1 - p}{\Delta} = \frac{64 b_1}{\pi^2 D^5} L Q^2] Generally the pressure, p1, at the entrance is known, and the pressure, p, has to be found; it is then from p1 that the values of Q and [Delta] are calculated. In experiments where p1 and p are measured directly, in order to arrive at the value of the coefficient b1, Q and [Delta] would be calculated for the mean pressure ½(p1 + p). The values given to the coefficient b1 vary considerably, because, as stated above, it varies with the diameter, and also with the nature of the material of the pipe. It is generally admitted that it is independent of the pressure, and it is probable that within certain limits of pressure this hypothesis is in accordance with the truth.