STABILITY^ PROPULSION^ AND SEA-GOING QUALITIES OF SHIPS. 15 



and the heads of the nails well beaten down, to 3-0 for huUs covered 

 with weed and barnacles. 



R is the resistance expressed in kilogrammes, and corresponding to 

 the speed V. 



** Per each ship experimented upon, two trials are sufficient to determine 

 K and Iv'. 



" For the ' Napole'on,' while clean, the copper being oxidized, not greased, 

 I found 



K=l-96, X'=0-44, 



from which I obtain for the general expression for the resistance to the 

 passage of the ship through the Avater, 



R= 1-96S(YH 0-145V')+ 0-440S' ^V. 



A Table previously given shows that during the trial trip of the ' If apole'on ' 

 the values of S and S^ were — 



S between 99 and 100 square metres. 

 S^ between 1580 aud 1610 square metres. 

 * * * * 



" The power needed to obtain this speed is obtained from this calculation 

 by mviltiplying the resistance, so calculated, by the velocity." 



The above remarks are translated from a memoir published by M. Dupuy 

 de Lome on the occasion of his candidature for the French Academy in 

 1865-66. It is reprinted in M. Flachat's ' Navigation a Vapeur Trans- 

 oceanienne,' vol. i. p. 206. 



It may not be out of place to mention, in explanation of M. Dupuy de 

 Lome's remarks about the angle of entrance, that the ai'chitects of the Im- 

 perial Navy avoid the use of the hollow bow. There is at most a slight 

 concavity at the fore -foot. Hence the angle of entrance has a meaning 

 which is sometimes lost in modern English practice. 



M. Bourgois, in his memoir * on the resistance of water, gives formulae 

 which may be grouped under the general form of 



r=b^v^[k,+k,5+K3^], 



B^ being the area of midship section, S the wet surface, and I the breadth 

 extreme. K^, K.,, and K^ are constants which vary with different classes of 

 vessels. 



The dependence of the resistance of ships upon the theory of waves ap- 

 pears to have been first insisted upon by Mr. Scott Russell. That gentle- 

 man seems to have been the first to discover that there was a relation 

 between the length of the ship and the velocity of advantageous propulsion, 

 this relation being taken directly from the theories of the solitary and of 

 the trochoidal waves. We will state his theory of resistance in as few words 

 as possible. 



Scott BusselVs Theory of the Form of Least Resistance. 



A vessel may be divided longitudinally into three portions, bow, straight 

 middlebody (if any), and afterbody. The midship section may be of any 

 shape whatever, the resistance due to it depending on its area and wet 



* Published at Paris, by Arthur Bertrand, s.a. Kee also Sonnet, ' Dictionnaire de.s 

 Mathcmatiqucs Appliquecs,' art. " Ei'sistance des Fluides." 



