Note 38 — Chapter II · ON MAGNITUDE

Let L be the length, S the (wetted) surface, T the tonnage, D the displacement (or volume) of a ship; and let it cross the Atlantic at a speed V. Then, in comparing two ships, similarly constructed but of different magnitudes, we know that L = V2 , S = L2 = V4 , D = T = L3 = V6 ; also R (resistance) = S · V2 = V6 ; H (horse-power) = R · V = V7 ; and the coal (C) necessary for the voyage = H ⁄ V = V6 . That is to say, in ordinary engineering language, to increase the speed across the Atlantic by 1 per cent. the ship’s length must be increased 2 per cent., her tonnage or displacement 6 per cent., her coal-consumpt also 6 per cent., her horse-power, and therefore her boiler-capacity, 7 per cent. Her bunkers, accordingly, keep pace with the enlargement of the ship, but her boilers tend to increase out of proportion to the space available.