In the notation of the calculus the relations become - dH/dp (0 const) = odv /do (p const) (4) dH/dv (0 const) =odp/do (v const) The negative sign is prefixed to dH/dp because absorption of heat +dH corresponds to diminution of pressure - dp. The utility of these relations results from the circumstance that the pressure and expansion co efficients are familiar and easily measured, whereas the latent heat of expansion is difficult to determine.
It is to be noticed that each number is the sum of the numbers immediately 35 above and to the left of it; and 35 that the numbers along a line, termed a base, which cuts off an equal number of units along the top row and column are the co efficients in the binomial expansion of (I+x) r - 1, where r represents the number of units cut off.
In the general equation of the second degree the co-efficients of x 2 and y 2 are equal, and of xy zero.
The whole of the deviations when the ship is upright may be expressed nearly by five co-efficients, A.
Expressing this condition we obtain mb = 1/ nc = o as the relation which must hold between the co-efficients of the above equation and the sides of the triangle of reference for the equation to represent a parabola.
., P,,, with which are associated certain co-efficients in1, in2,.