ON PADDLE WHEELS. 119 



wheel ; but it does not appear to have answered Mr. Field's expectations at that time, for it 

 did not come into public notice until 1835, when Mr. E. Galloway, ignorant of what had been 

 previously done by Mr. Field, took out a patent for the same arrangement, since which time 

 it has been applied to a considerable number of private steamers and to a few government 

 vessels ; but the experiments hitherto made have not established its superiority over the other 

 kinds of wheel with which it has been compared. 



In order to facilitate the following investigation, we will divide the different kinds of paddle 

 wheels into two classes : 



I. Paddle wheels with fixed floats. 



II. Paddle wheels with feathering floats. 



Before, however, proceeding to the examination of each kind of wheel in particular, 

 we will offer some preliminary observations on the motion and action of paddle wheels in 

 general. 



ON THE MOTION OF PADDLE WHEELS. 



If the paddle wheels of a steam vessel be made to revolve, the vessel being at rest, which is 

 always the case at first starting, any given point of one of the wheels (if of the first class) 

 will describe a circle ; but as soon as the vessel has acquired a certain velocity, its path will be 

 lengthened out into a curve, which has been called a curtate cycloid; this continues to lengthen 

 as the vessel gains velocity, and becomes the common cycloid when the velocity of the vessel is 

 equal to the circumferential velocity of the given point. If the speed of the vessel go on 

 increasing, the given point will describe a curve called a prolate cycloid, 



By circumferential velocity is understood the velocity of any point of the wheel relative to 

 the centre of the shaft, or, in other words, what its absolute velocity would be if, the centre 

 being stationary, the wheel made the same number of revolutions in the same time. 



It is evident that when the vessel has attained her maximum speed, there will be a series 

 of points in each wheel, situated at an equal distance from its axis, which will describe common 

 cycloids : the projection of these points on a plane perpendicular to the axis of the wheel is 

 called the rolling circle. All points situated within the circumference of the rolling circle 

 describe prolate, and all those without the same curtate cycloids. 



To illustrate the motion of paddle wheels, we will refer to Plate LXXIV, where Fig. 1 is a 

 diagram of the common wheel as fitted to Her Majesty's steam vessels 'Phoenix' and 'Sala- 

 mander.' C is the centre of the shaft ; r, r, r, represent the arms ; and A B, A B, A B, the 

 floats. L L is the water line at the light immersion of the ' Phcenix,' and L 1 L 1 at the deep 

 immersion of the ' Salamander.' The extreme radius C A is 10 ft. 6 in.; the depth of the floats 

 2 feet 6 in. ; their breadth 9 ft., 1 and number 16. The floats are here drawn radiating from the 

 centre, which is not strictly the case in practice, as they are generally fixed on one side of the 

 arms of the wheel ; the deviation is, however, so trifling, that it is of no importance. Fig. 2 

 is intended to show the path of one of the floats according to the result of the mile trial of 

 the 'Phcenix' made at Woolwich to ascertain her speed. The number of strokes per minute 



' We have since learned that the breadth of the floats of the ' Salamander's ' wheels is only 8 ft. 9 in. 



