316 MR. p. W. BARLOW ON THE LAWS WHICH GOVERN 



but in consequence of the lower part coming sooner into and continuing longer In 

 action, it must be taken some distance below the centre of gravity. 



It is not easy to determine this by calculation ; but by a comparison of all circum- 

 stances bearing upon this question, I have been induced to make an allowance of 

 one eighth of the paddle on this account. 



It may be proper to observe, that in these wheels there is no relation between the 

 diameter of the polygon and the diameter to the centre of pressure, the paddles being 

 differently hung and differently shaped in the several vessels, particulars it has not 

 been thought necessary to introduce into the Table. The remaining calculated 

 columns will, I believe, be sufficiently understood by the heads, except 1 7 and 1 8, 

 the former of which exhibits the actual pressure in pounds upon the lower or 

 vertical paddle, as due to the velocity given by the experiment, and the latter the 

 portion of the whole power of the engine which is exerted upon it. The formula for 

 column 1 7 (V being the velocity of the centre of pressure, v that of the vessel, a the 

 area of the paddle, 62| the weight of a cubic foot of water in pounds, and 64 J = 4 g, 



g denoting the force of gravity,) will be \-^^i-) X 62j x a, the pressure upon a sur- 

 face moving in a fluid at the velocity (V — v), being equal to the weight of a column 

 of water whose base is the area of the surface, and altitude the height, through which 

 a body must fall to acquire that velocity. This pressure being overcome at a velocity 

 V, the above result, when multiplied by V, will express the power expended upon the 

 vertical paddles ; and this number, divided by the whole power of the engine, gives 

 the decimal part of the whole power consumed by the vertical paddle given in co- 

 lumn 18. In estimating the part of the power of the engine exerted in any case, the 

 number of strokes made in a minute is compared with the actual number of strokes 

 which ought to be made for the engine to perform its full duty, assuming, as usual, 

 33000 lbs. raised one foot high per minute to denote the power of one horse. 



