436 



REPORT — 1856, 



is very important. What other writers have called the efficiency or the ratio 



of the power expended to the work produced, is surely a subject which all 



shipowners ought to be acquainted with. The formula adopted by Mr. 



Atherton for the efficiency or dynamical duty of steam-ships, is, I fear, too 



rough an approximation to be recommended for general adoption, especially 



when a more exact and equally simple formula is at hand, and the one also 



from which Mr. Atherton's adopted formula is no doubt deduced, viz. 



V^x mid. section ^ „, . . ., , x, , p 



. , , =L. ihe power in similar vessels, 1 here take tor granted, 



at present varies as the cube of the velocity. This, I believe, is nearly true, 

 and ought to vary also directly as the immersed midship section. For simi- 

 lar vessels the midship section no doubt varies as displacement raised to 

 the power ^rds ; but scarcely any two vessels are similar (in the mathema- 

 tical sense of the term) ; nor is the same vessel similar to itself when the draft 

 of water varies. 



The following Table, deduced from published statements of some of the 

 ships of the Navy, and also from vessels built by the firm with which I am 

 connected, shows the difficulty there would be in the use of the formula 

 V^ (displacement) f=C, from the (displacement) f having no necessary 

 connexion with the midship section : — 



2 



Comparison between Midship Sections, and (Displ.)^. 



In the ' Fiery Cross,' at different drafts of water, there is a difference of 

 nearly 3 per cent, in the ratio of midship section to (displacement) f , which 

 might affect the coefficient C to the same extent. 



The ' Victoria ' and ' Vulcan ' are two river steamers of nearly the same size 

 and power, yet there is upwards of 5 per cent, of difference in the ratio of 

 midship section to (displacement) f . The formula used by Mr. Atherton 

 is, notwithstanding these remarks, exceedingly useful for commencing the 

 designs of steam-vessels, and may be an approximation sufficiently near for 

 most practical purposes. 



