88 REPORT — 18G1. 



Multiply the cube of the speed (V^) by the cube root of the square of the 

 displacement (D|), and divide the product by the indicated horse-power 

 (Ind. h. p.) ; the quotient will be the coefficient (C) of dynamic performance. 



To enter upon the various uses to which this formula is applied would be 

 irrelevant to the matter now under consideration. Suffice it to say that 

 the numeral co-efficient obtained as above set forth affords practically a 

 means by which the mutual relations of displacement, power, and speed 

 of a steam-ship of given type of form, and of which the coefficient is 

 known, may (ccBteris paribus) be deduced, and it affords a criterion indi- 

 cating, whatever be the size of the ship, the constructive adaptation of its 

 type of form for mechanical propulsion, as compared with other types of 

 form tested by the same rule — the condition of the vessels as respects clean- 

 ness of immersed surface, stability, and other essential properties, being 

 assumed to be the same ; and we now proceed to show to what extent, 

 under given conditions, freight per ton of goods conveyed is affected by- 

 variations of type of form, as represented by variations of the coefficient 

 of performance. 



By reference to the table (Section B), it will be observed that as the 

 co-efficient of dynamic performance is reduced from 250 to 150, the ex- 

 penses become increased in the ratio of 100 to 132, or 32 per cent, or, 

 assuming the freight by ship A, of which the coefficient of dynamic per- 

 formance is 250, to be at the rate of £1 per ton of cargo, the charge by 

 ship Bj, of the same size, but of which the coefficient is 200, will be 

 £1 2s., being an increase of 10 per cent.; and the charge by ship B^, of 

 the same size, but of which the coefficient is 150, will be £1 6s. 5d., being 

 an increase of 32 per cent., as compared with the rate of freit(ht by ship 

 A, of which the coefficient is 250. 



The comparative freight charges on 100,000 tons of goods by the vessels 

 A, Bj, B,, respectively, would be £100,000, £110,000. and £132,000. 



Seeing, therefore, that variations of the type of form, as indicated by 

 variations of the coefficient of dynamic performance, even within the limits 

 of 250 and 150, which are of ordinary occurrence in steam-shipping, affect 

 the expenses incidental to the conveyance of mercantile cargo, under the con- 

 ditions referred to, to the extent of 32 per cent,, the coefficient of dynamic 

 performance which a ship may be capable of realizing, being thus (cateris 

 paribus) a criterion of the economic working of the ship with reference to 

 power, becomes a highly important matter for directorial consideration in the 

 purchasing or disposal of steam-ships. 



Section C Freight as affected (cwteris paribus) by variations in the 



working economy of the engines with reference to coal. 



The relative working economy of marine engines as respects the con- 

 sumption of coal per indicated horse-power per hour is evidently an important 

 element for consideration as affecting freight, — to illustrate which, it has been 

 assumed that variations in mercantile practice extend from 2 lbs. per indicated 

 horse-power per hour to 4 lbs. The consumption of so little as 2 lbs. per 

 indicated horse-power per hour is not usually attained, but being now ad- 

 mitted to have been achieved, and such having become a matter of contract 

 stipulation, it may be looked forward to as the probable future consumption 

 on board ship generally, although the ordinary consumption of existing 

 steamers cannot at the present time be rated at less than 4lbs. per indicated 

 horse-power per hour. 



By reference to the table (Section C), it appears that, under the special 

 conditions of the service under consideration (namely vessels of 5000 tons 

 displacement employed on a passage of 3000 nautical miles, and steaming at 



