We may, by a well-known theorem, write the result as a **coefficient** of z w in the expansion of 1 - z n+1.

The value of the angular **coefficient** d(pv)/dp is evidently (b - c), which expresses the defect of the actual volume v from the ideal volume Re/p. Differentiating equation (17) at constant pressure to find dv/do, and observing that dcldO= - nc/O, we find by substitution in (is) the following simple expression for the cooling effect do/dp in terms of c and b, Sdo/dp= (n+I)c - b..

This **coefficient** is sometimes called the " angular **coefficient**," and may be regarded as a measure of the deviations from Boyle's law, 'which may be most simply expressed at moderate pressures by formulating the variation of the angular **coefficient** with temperature.

This, with a knowledge of the temperature of the screw or scale and its **coefficient** of expansion, would enable the change of screw-value to be determined at any instant.

Less accurate formulae are =p W/(W - W 2), the factor involving the density of the air, and the **coefficient** of the expansion of the solid being disregarded, and 0 =W/(W - W 1), in which the density of water is taken as unity.