328 



MR. P. W. BARLOW ON THE LAWS WHICH GOVERN 



sistance of a steam vessel with that of the paddles, a calculation which the preceding 

 investigations and experiments have enabled me to arrive at with considerable ac- 

 curacy. Having obtained, through the kindness of O. Lang, jun. Esq. (to whom I 

 have been highly indebted for many of the preceding data), the sectional immersed 

 area of several of the vessels, I have made the calculations, and obtained the results 

 given in the annexed Table. These have been made in the following manner. 



Let V = the velocity of the wheel, v that of the vessel, s its sectional area im- 

 mersed, and a the area of a paddle whose action is horizontal, and effect equal to 

 that of all the paddles. The resistance being as the square of the velocity, (V — v^ a, 

 will express the resistance on the paddle, and t^^ s would be the resistance of the vessel 

 if it were a plane surface ; but the real resistance being (V — v)- a, the fraction of the 



resistance compared with a plane will be 



(V-vfa 



V* s 



The value of a has been obtained by knowing the depth of immersion, so as to 

 ascertain the angle at which the centre of pressure entered the water, and thence the 

 number of times the whole effective action exceeds that of the vertical paddle ; this 

 multiplied into the area of the paddle, gives the whole surface above denoted by a. 



In the following Table is given the effective pressure exerted by the engine in every 

 experiment where the dip or immersion of the paddle was known ; but the comparison 

 of the resistance of the vessel with a plane, is of course limited to those experiments 

 only in which the area of the immersed section could be ascertained. 



Table V. 



