48 APPENDIX. 



DEDUCTIONS FROM THE TABULAR NUMBERS. 



The amount of resistance on the vertical paddle, and proportion of the power of the engine 

 expended upon them, will be found to differ considerably in the different cases given in the 

 table, and might, if unexplained, throw an appearance of doubt upon the accuracy of the 

 experiments. These discrepancies are evidently attributable to the result depending upon 

 the square of the difference of two velocities ; so that the slightest inaccuracy in either of the 

 observations is greatly magnified. There is no doubt, however, with so many experiments 

 made at different times and under different circumstances, that the means obtained in the 

 table are sufficiently near the truth for all practical purposes. 



In examining column 18, a striking difference is seen in the proportion of the power of the 

 engine expended on the vertical paddle in Morgan's wheel and in the common wheels, the 

 mean of the former being -546, and of the latter '151 and -197. The difference arises from 

 the nature of the action : in the new wheel the vertical position is the most effective in propelling 

 the vessel, and in the common wheels the least so , a fact which, although little known among 

 the projectors of paddle wheels, and even among engineers, who are constantly witnessing 

 their daily performance, it is very essential should be understood before any calculation or 

 judgment can be formed of the construction and proportion of wheels best adapted to steam 

 vessels, under the different circumstances and various kinds of duties in which they are 

 employed : we beg therefore to call the attention of the reader particularly to this point. 



The difference of action which caused this unexpected result will be understood by exa- 

 mining Fig. 5., which exhibits the positions of each paddle, at equal intervals of time, in a 

 vessel in motion : it will there be seen, that the progress made through the water bv the 

 radiating paddle, while passing the vertical position, is considerably less than in the preceding 

 equal interval of time. After first entering the water, and as the resistance opposed varies as 

 the square of the velocity or space passed through, it is evident that the resistance in passing 

 from A to B will greatly exceed that of passing from B to C ; and it may be readily demon- 

 strated, that in ordinary cases it exceeds it so much, that the portion of it which when 

 resolved is in a horizontal direction, or effective in propelling the vessel, is greater than the 

 whole action at the vertical position, although this latter is attended with no loss from oblique 

 action. This effect will be illustrated very clearly by assuming the extreme case of the 

 paddle wheel being immersed to the axle : here the floats will enter the water at the whole 

 velocity of the wheel ; but this velocity will diminish until they arrive at the vertical position, 

 when it will be only the difference of the velocity of the wheel and vessel, which is generally 

 not more than one quarter of the whole. 



On the contrary, if we examine the position of the vertically acting paddles of the new wheel 

 in the same equal intervals of time, we find that the space B C, in passing the vertical posi- 

 tion or bottom of tlie arc, greatly exceeds that of the preceding interval of time A B : in fact, 

 the motion of the vertical paddle in entering the water is scarcely perceptible, but it gradually 

 increases until it has passed the bottom of the arc ; and hence arises one of the greatest 

 advantages of this construction of wheel, by totally avoiding the shock or blow on the paddle 

 entering the water, which is experienced in the common construction, and which is not only 

 injurious to the engine and unpleasant to the passengers, but. productive of a serious loss of 

 power, particularly at sea, or when the vessel is deeply immersed. 



