140 APPENDIX. 



do not presume to say that a means may not be found to facilitate the operation, so as to 

 render it practicable. 



It is very clear that the desired effect could not be produced by reducing the size of the 

 paddle boards, except inasmuch as the centre of pressure is thereby brought nearer to the 

 axis of the wheel : suppose, for example, that a piece has been cut off from the end of each 

 board ; the consequence will naturally be that the circumferential velocity of the wheel will be 

 increased, until the mean pressure on the floats becomes equal to what it was before they were 

 reduced. The pressure being restored, the horizontal pressure will be so too, but cannot 

 surpass what it was before, since the ratio of the horizontal to the total pressure is independent 

 of the breadth of the floats. The speed of the vessel must therefore remain the same, 

 although the expenditure of fuel is increased in the ratio of the increased velocity of the 

 engines. If, on the other hand, we suppose the floats to be reefed, then the engines will not 

 only move so much faster that the floats shall experience the same resistance, but their 

 velocity will increase until the mean pressure on the floats is to the former mean pressure as 

 the former radius to the centre of pressure is to the new one. The total pressure being thus 

 increased, the horizontal pressure will be so in a greater proportion, because, the angles of 

 the floats being less oblique, the ratio of the horizontal to the total pressure will be greater ; 

 consequently the vessel will go faster. We can only come to this general conclusion at 

 present, as there is no method yet known of finding the precise effect of reefing the floats. 



2. Field's Paddle Wheel. 



This is what Mr. Field calls the Cycloidal Wheel ; but as we do not consider that appellation 

 at all suitable, we prefer that adopted at the head of this chapter, Mr. Field having been, to 

 the best of our knowledge, the first inventor of this variety of paddle wheel. It was tried on 

 the ' Endeavour,' a passage steamer, in the year 1 833, but was abandoned immediately. 



The construction of this wheel is thus explained by Mr. Field in the 'London Journal' for 

 December, 1835 : 



" Each board is divided into several parts, or narrower boards, and arranged in, or nearly, 

 such cycloidal curves, that they all enter the water at the same place in immediate succession, 

 thus avoiding the shock produced by the entrance of the common board, so unpleasant to 

 passengers, injurious to the vessel, and wasteful of the power. As the acting face of each 

 board is radiating, it propels while passing under the centre in the ordinary way, and when it 

 emerges, the water escapes simultaneously from each narrow board, and consequently cannot 

 lop-up." 



Mr. Galloway describes his invention to be exactly the same thing, but goes into geometrical 

 details, which are not mathematically correct. 



Fig. 1. Plate LXXV. is a diagram intended to elucidate the construction of this kind of 

 wheel. Not having any data at the time this plate was engraved, we contented ourselves with 

 the same dimensions as those of the common wheel in Plate LXXIV., and supposing the same 

 performances as with the latter, merely with the view of comparing their modes of action. 

 Each board is divided into four narrow boards, a, b, c, d, respectively, six, seven, eight, and 

 nine inches in depth. Figs. 2 and 4 show the path of one set of boards at the light and load 

 draught, and Figs. 3 and 5 the nodes, enlarged to four times the scale on account of the 

 complication resulting from the number of boards in the set. On inspecting the two latter 



