Now the actuating force is equal to _f_, and is represented by the difference of pressure at the two ends of the pipe, _i.e._, the initial pressure, viz., that at the place whence gas is distributed or issues from a larger pipe will be greater by the quantity _f_ than the terminal pressure, viz., that at the far end of the pipe where it branches or narrows to a pipe or pipes of smaller size, or terminates in a burner. The terminal pressure in the case of service-pipes must be settled, as mentioned in Chapter II., broadly according to the pressure at which the burners in use work best, and this is very different in the case of flat-flame burners for coal-gas and burners for acetylene. The most suitable pressure for acetylene burners will be referred to later, but may be taken as equal to p_0 inches head of water. Then, calling the initial pressure (_i.e._, at the inlet head of service-pipe) p_1, it follows that p_1 - p_0 = _f_. Now the cross-section of the pipe has an area (pi/4)_d^2_, and if _h_ represents the difference of pressure between the two ends of the pipe per square inch of its area, it follows that _f_ = _h(pi/4)d^2_. But since _f_ has been found above to vary as _ldsv^2_ , it is evident that _h(pi/4)d^2_ varies as _ldsv^2_. Hence _v^2_ varies as _hd/ls_, and putting in some constant M, the value of which must be determined by experiment, this becomes _v^2_ = M_hd/ls_. The value of M deduced from experiments on the friction of coal-gas in pipes was inserted in this equation, and then taking Q = pi/4_d^2v_, it was found that for coal-gas Q = 780(_hd/sl_)^(1/2) This formula, in its usual form, is Q = 1350_d^2_(_hd/sl_)^(1/2) in which _l_ = the length of main in yards instead of in feet. This is known as Pole's formula, and has been generally used for determining the sizes of mains for the supply of coal-gas. For the following reasons, among others, it becomes prudent to revise Pole's formula before employing it for calculations relating to acetylene. First, the friction of the two gases due to the sides of a pipe is very different, the coefficient for coal-gas being 0.003, whereas that of acetylene, according to Ortloff, is 0.0001319. Secondly, the mains and service-pipes required for acetylene are smaller, _cateria paribus_, than those needed for coal-gas. Thirdly, the observed specific gravity of acetylene is 0.91, that of air being unity, whereas the density of coal-gas is about 0.40; and therefore, in the absence of direct information, it would be better to base calculations respecting acetylene on data relating to the flow of air in pipes rather than upon such as are applicable to coal-gas. Bernat has endeavoured to take these and similar considerations into account, and has given the following formula for determining the sizes of pipes required for the distribution of acetylene: Q = 0.001253_d^2_(_hd/sl_)^(1/2)