ON PADDLE WHEELS. 131 



Thus a power of 88'23 horses is sufficient, if applied immediately to the vessel; but 151-66 

 horse powers are required to be applied to the wheels to produce the same propelling effect, 

 the proportion of the effective to the total power being as 0-582 to 1. This shows the loss of 

 power at deep immersions to be very great, even without considering the effects of the shock and 

 back water: it amounts in the above example to more than 63 h. p., or about 41-8 per cent, 

 of the whole power transmitted to the wheels. 



It is obvious, that at light immersions, when the upper edge of the float is never under 

 water, all the terms in which /3 or sin. /3 enters as a factor disappear, and only one-half of the 

 number of terms remain ; and even if the float is immersed a few inches above its upper edge 

 at the middle of the stroke, the amount of those terms is so small, that they may be neglected 



15 7 

 without causing any material error in the result. For example, if a= rand p= r, the 



16 8 



error is about one per cent.; but if p=a, then the error is only about one-third per cent. 

 Thus, the diameter of the wheel being 20 ft., the depth of the floats 2 ft., and their greatest 

 immersion 2 ft. 6 in., or 6 inches above their upper edge, the resistance would not be more 

 than one per cent, less than if the floats were made 2 ft. 6 in. in depth, so as to reach the 

 surface of the water. We here suppose the radius of the rolling circle to be 7 ft. ; if it were 

 only 6 ft. the error would be a little more considerable, but not much, for if the immersion 

 were 3 ft. and the radius of the rolling circle 6 ft., the error would not exceed 2 per cent. 



If we calculate the power of the ' Phoenix ' from the data which we possess, which coincide 

 exactly with those given in Mr. Barlow's tables, except in the diameter of the wheels, which 

 is 21 ft., and not 20 ft. 4 in. as he has there given it, we shall find but 110 h. p. for the power 

 of the engines, or not much more than one-half of the nominal power. It is however very 

 probable that there were some slight errors in the observations ; for the dip of the floats is 

 measured before starting, when it is generally not the same as when the vessel is in motion : 

 there is a wave on each side of the vessel, travelling along with it, caused by the displacement 

 of the water, and varying in its position according to the form of the bows : this is sometimes 

 situated directly under the paddle shaft, and then naturally increases the dip of the floats. 

 The mean speed may be a little too great, a difference of a few seconds in the time of running 

 a mile making a difference of half a mile an hour in the speed; it is also next to impossible 

 to know the exact mean number of revolutions made by the wheels in a minute without 

 counting the whole number made during the run. If, during the trial of the ' Phoenix,' the 

 immersion of the floats was 2-8 ft. instead of 2- 5 ft., the mean speed 11-23 miles, instead of 

 ir7, and the mean number of revolutions 21 instead of 21, we should find for the power 

 of the engines 203 f h. p., which is about 6 per cent, below their nominal power, and it is 

 probable that the dip of the floats was still more considerable. 



We have been informed by a gentleman who cannot well be mistaken, that no copy of the 

 official account of the mile trials of Her Majesty's steam vessels at Woolwich has hitherto 

 been published, and we know that some of the dimensions in Mr. Barlow's table are incorrect, 

 so that we cannot rely upon the other figures contained in it, although they coincide with a 

 table which we have obtained from another quarter. Wishing to have authentic data to 

 reason upon, we applied to the Lords Commissioners of the Admiralty for permission to 

 obtain a copy of the official returns, but their lordships declined acceding to our request, and 

 no information is to be obtained at Woolwich dock-yard on this subject. We are at a loss to 



