430 REPORT — 1856. 



to detect the fact of ineflSciency, and it will then be for the professional 

 engineer to detect and remedy the cause thereof. The annunciation of the 

 formula, or the mercantile rule above referred to, is as follows : — Multiply 

 the cube of the speed, expressed in knots or nautical miles per hour (V^), 

 by the cube root of the square of the displacement (Df ), and divide by the 

 consumption of coals, expressed in cwts. per day of 24 hours, the resultant 

 numeral coefficient (C) will indicate the dynamic or locomotive efficiency 

 of the vessel ; and such is the variable condition of steam-ships in present 

 use, that the coefficient has been found to be as low in some cases as 120, 

 whilst in other cases it has reached the number 250. The pecuniary value 

 of gold is determined by assay ; and in like manner the contract price to be 

 paid for a steam-ship should, in some measure, be regulated by the coefficient, 

 based on the mutual relation of displacement, speed, and coals, which may 

 be realized on trial of the ship ; for example, multiply the contract price by 

 the numeral coefficient that may be actually realized, and divide by the 

 coefficient that may be regarded as the par measure of dynamic efficiency, 

 according as the vessels maybe painted or sheathed with copper. Contracts 

 based on this principle would constitute a check upon the production of 

 inefficient ships, and award a premium on the construction of ships of superior 

 merit. 



The approximate trustworthiness of the formula (^~j — j~ — — ^1 being 



conceded, we now have the means of pursuing our exposition of the extent 

 to which any definite diflference of type or falling off in the working condition 

 of a ship will affect the amount of prime cost expenses incurred in the con- 

 veyance of merchandise by steam-ships. Suppose, for example, that we 

 have ships whose coefficients of dynamic duty or index numbers (C) deduced 



from the formula f . . . ^ — =C j are respectively 250 and 166, which num- 

 bers correspond with 1000 and 664, if the unit of marine engine-power be 

 taken at 4 ind. h.p., as is the case in the tabular calculations given in Ather- 

 ton's ' Steam-ship Capability,' and are coefficients of dynamic duty not 

 unusual as between different steam-ships in actual practice ; in evidence of 

 which, confirmatory of the official records whence L ..se numbers are taken, 

 I may refer to a tabular statement of steam-ship trials recently supplied to 

 me by one of our most experienced firms (engineers and shipbuilders), by 

 which statement it appears, that, adopting the formula referred to, the index 

 numbers or coefficients of dynamic duty of eight steam-ships varied from 251 

 to 149, thus showing that the difference of constructive types now assumed 

 as the base of calculation for this exposition, is not an exaggeration, but such 

 as is common in practice. In the first place, referring to ' Steam-ship Capa- 

 bility,' 2nd edit, page 78, we will expose the difference of power (ind. h.p.) 

 which would be required by two vessels. A and B, of the respective types 

 or working conditions of service indicated by the coefficients above referred 

 to (namely 250 and 166), supposing the vessels to be each of 2500 tons load 

 displacement. The vessel A will be propelled at 8 knots, 10 knots, and 12 

 knots per hour, by 376 ind. h.p., 736 ind.h.p., and 1272 ind. h.p, ; but the vessel 

 B will require, to attain the same rate of speed, 568 ind, h.p,, 1112 ind.h.p., 

 and 1920 ind. h.p. Thus the ship B requires, in consequence of her infe- 

 riority of working condition, or type of construction, an increase of power of 

 no less than 50 per cent, in order to attain the same rate of speed as ship A ; 

 and, be it observed, that these assumed coefficients are within the range of 

 ordinary difference between one ship and another. 



We will now show the sacrifice which such a difference of type produces 



