156 APPENDIX I value of H. It is evident that the following expression will then be obtained: »i * ii 1 from which, according to Eq. (2), 'H-h- h from which and 2VH-h = 0, . (3) - (4) In taking into account this last relationship, Eq. (2) will take the form ^-A, and The actual quantity of gas Q flowing under the inverted weir will be less than the theoretical volume by reason of the frictional and other resistance; therefore these equations will become: <2=?\5 2gH •A,-A, «-\3 2gh^ -A,, (5) (6) in which the coefficients p, and « may not be equal, as, in passing from equations (3) and (4) to the actual flow of the gas, it will be found that the relation between H and h is different from that given in these equations. According to the researches of Bazin, the coefficient M for the flow of water is given by the formula , (7) |^|M= [0.70+0. 185|] [0. in which p is the depth of the channel and E& must not be less than |ff . « E being the distance DD (Fig. 25).