Principle of the Screw to the Floats ef Paddle-wheels. 251 



the float, as it must be when the only way for it to run off is in 

 the direction of the motion of the float ; hence by this method all 

 the back-water is got rid of; and this is perhaps one of the 

 greatest advantages which this wheel has over the ordinary wheel 

 without feathering floats. 



4. Again, the new wheel will work whether it be only slightly 

 immersed or whether the water rises nearly up to the axis of the 

 wheel ) and it seems to have the greatest advantage over the or- 

 dinary wheel when they are both deeply laden. 



There are other important features which might be pointed 

 out ; but these I have no doubt Dr. Croft will take an oppor- 

 tunity of bringing before the notice of the scientific world ; but 

 I have mentioned these few points to show that it is not unlikely 

 that this invention may lead to our more steady and more rapid 

 onward progress by means of paddle-wheel steamers. 



Two questions still remain : Can sufficient hold on the water 

 be obtained by means of the new floats ? and if so, what power 

 will be necessary to obtain it ? To these questions it is proposed 

 to give a mathematical solution, based on the laws of resistance 

 on surfaces in motion through fluids, which laws, although they 

 are not sufficiently perfect to give absolute results in any par- 

 ticular case, may yet be employed to compare the pressures on 

 two surfaces under similar conditions, and so in this case may be 

 expected to show whether the new wheel is any improvement on 

 the old, either in getting up the same speed with less power, or 

 in getting up a greater speed with engines of the same horse- 

 power. 



Fig. 3. 



Fig. 1. 



By the mathematical theory, the resistance perpendicular to 

 the surface on any part of a surface in motion through a fluid, 

 where the direction of the motion makes an angle a with the 

 perpendicular to the surface, is i^o^ 2 cos 2 «. where p x is the 



S3 



