300 OF STEAM NAVIGATION. [SECT. x. 



V. Consequently, when tan. a = 1, the power is to the effect as 3 to 2, as in the 

 ordinary paddle wheel ; but if tan. a = 1'5, the power and effect are equal : on the 

 contrary, if tan. a = '5, or the angle C A B is about 26, the power is to the effect 

 as 3 : 1. 



Now a little more than one revolution of the spiral would produce this effect, and 

 a second revolution at the same angle could have very little action, because the 

 water would have acquired all the velocity the spiral could communicate. If it be 

 continued, it should therefore be made with a decreasing angle. 



627. In practice the size corresponding to these effects is every thing ; our 

 next object must therefore be to ascertain it. Taking an angle of 60 for the angle 

 CAB, tan. a = 1*732, and sin. a = '866. The effect is in this case, 



1-732 , j* (2 x -8662 + -866) = 0-73 * x- ; 



but JT .r 2 is the area of the end of the cylinder, therefore each foot of surface of the 

 end of the cylinder will act with a force of 0'73 Ibs. for one foot per second. The 

 length of the cylinder would be 2 ic x tan. a = 10 - 8 times its radius, or 5'4 times 

 its diameter. The power required for this effect is, 



3 x- (2 x -866* + -866) _ .g g7 ^ ^ 

 8 



or 0'887 Ibs. for each foot of area of the end of the cylinder, for one foot per 

 second. 



When a = 40, the effective force is only 0'4368 Ibs. per foot, and the power to 

 each foot must be '64 Ibs. The power therefore decreases nearly in the same ratio 

 as the length. 



These calculations are sufficient to show that this method may be used with 

 considerable advantage, the action being under water, and the projection from the 

 side not so great as paddle wheels ; while the smoothness and the uniformity of the 

 motion are circumstances much in its favour. On the other hand, the mode of 

 communicating motion and the resistance the parts will offer that are applied for 

 that purpose, are objections ; for the present I shall therefore content myself with 

 recommending it to the notice of my readers. 



PADDLE WHEELS. 



628. The next inquiry is to ascertain the effect of paddle wheels. Of these 

 the commonest species are plain boards, called paddle boards, fixed to the arms of 

 a wheel ; these arms are as thin as is consistent with strength, and are connected 

 by one or more thin iron rings, to act as braces in giving them firmness ; they are 



