170 APPENDIX IV P> ; only the head, expressed in millimeters of water, corresponding to the friction loss per second of air at 0° and 760 mm passing through a brick-lined flue with a velocity of 1 m per second, the sectional area of the flue corresponding to the equation -~= 1.293. According to the computations of the author, 0.016 may be taken as the value of the coefficient m with sufficient precision for the computations met with in metallurgy. The verification of this coefficient was made by using it in computations upon Cowper and Massick and Crook hot-blast stoves. The formula (A) may be used for all cases in which a current of gases is flowing through mains or flues. 1. If the current of flowing gas is subdivided into a number of channels or streams of equal area, the friction loss in each of these secondary channels is 8 Q in which S , = ~ and n CO «.=-; n being the number of secondary channels or flues. 2. If the cross-sectional areas of these secondary channels or flues are not equal (as, for example, in the gas and air flues of an open-hearth furnace), the values B=SL and co in the formula (A), for the parts located between the point where the gaseous currents separate and the point where the secondary flues join comprise, respectively, the entire surface touched by the gases in passing and the sum of the average areas of all the channels or flues through which the gases pass. 3. If the gas in motion does not fill the furnace to its full height, the depth of the gaseous stream is computed by the formula for the inverted weir. The value given to the perimeter of the channel should be based upon the depth of the stream of gases. As the. lower stream of the gas in motion slides on top of the immobile layer of the same gas in the bottom portion of the flue, it is necessary to take account of the frictional resistance by considering the entire perimeter of the flowing stream of gases, including the " free lower surface " of the stream, and the cross- sectional area of the stream as determined by the depth of the stream in the flue.