ON FREIGHT AS AFFECTED BY DYNAMIC PROPERTIES. 85 



incurred by ship A, taken as the unit of performance, and which is expressed 

 by £1 per ton. 



20th. — Comparative freight on 100,000 tons of goods, assuming the freight 

 by ship A to be at the rate of £1 per ton of goods conveyed. 



2 1st. — Designations of vessels referred to in the sections. ; 



The table (next page) may be interpreted as follows : — 



Section A. — Freight, as affected (ccsteris paribus) by variations of the 

 size of ship. 



By reference to the table (next page) it will be observed that as the ship's 

 size (column 3) is reduced from 5000 tons displacement to 4000 tons, [the 

 expenses per ton of cargo (column 17) become increased in the ratio of 49 

 to 51, that is, in the ratio of 100 to 104 (column 18), showing an increase 

 of 4 per cent.; or, expressed in money, assuming £1 per ton to be the rate 

 of freight by ship A, of 5000 tons displacement, the rate by ship A,, of 

 4000 tons displacement will be £1 05. 10c?., and by following the table it 

 appears that the rate of freight by ship A^, of 3000 tons, will, as compared 

 with ship A, of 5000, be increased 8 per cent., amounting to £1 \s, 8d. 

 per ton. 



The comparative freight charges on 100,000 tons of goods (column 20) 

 by the vessels A, Aj, A^, respectively would be £100,000, £104,000 and 

 £108,000. 



Thus, in a merely mechanical point of view, and irrespectively of various 

 mercantile and nautical considerations which may limit the size of ships, we 

 see the benefit of performing goods transport service by large vessels in pre- 

 ference to small ones,' provided that adequate cargo be always obtained and 

 that no delay be thereby incurred. But it is to be observed that if the 

 5000-tons ship A, instead of being loaded with its full cargo of 2395 tons, 

 be loaded only with the quantity of cargo (1878 tons) that could be carried 

 by the 4000-tons ship, A,, the freight expenses per ton of cargo would, in 

 this case, be enhanced in the proportion of 63 to 49, that is, in the proportion 

 of 128 to 100, or 28 per cent., or, expressed in monej', in the proportion of 

 £1 4s. lOd. to £1, the same being a higher rate by 24 per cent, than the 

 freight charge at which the 4000-tons ship, Aj, would perform the service. 

 By pursuing the calculations from the data adduced by the table, it will be 

 found that the economic advantage of the 5000-tons ship. A, as compared 

 with the 4000-tons ship. A,, wilt be entirely sacrificed if its cargo be reduced 

 from 2395 tons to 2305 tons, or be only 90 tons, or 3J per cent, deficient 

 of its full load. Also, as compared with the ship A,, of 3000 tons, the 

 advantage of the 5000-tons ship A will be lost if its cargo be reduced from 

 2395 tons to 2218, or be only 117 tons deficient of its full load. 



Hence it appears that the superior economic capabilities of large ships in 

 a mechanical point of view for the conveyance of goods may, in a mercantile 

 point of view, be very soon sacrificed by mismanagement in assigning larger 

 vessels for the discharge of mercantile service than is demanded by the trade, 

 notwithstanding the economic superiority of large ships when promptly and 

 fully loaded. 



Section B. — Freight, as affected {rcBteris paribus) by variations in the 

 constructive type of torm of the hull. 



The relative constructive efficiency of mercantile ships in a purely dynamic 

 point of view, as respects type of form (irrespectively of materials and 

 workmanship), is now generally recognized as being determined by their co- 

 efficients (C^ of dynamic performance, as deduced from actual trial of the 



V^ D2- 

 ships, and calculated by the following formula :j — . .'' =0, which may be 



expressed as follows : — 



