192 



APPENDIX. 



Hence, dividing this by the amount expended per minute by one horse's power 

 = 33000 x 1 = 33000, we get, 



a. 

 Horse power expended by both 1 m i* 



wheels / " 275^ J 



o 



In the values of N given in equations (c), (d), (e), restore the value of p by equation () ; 

 assume 



1000 w 



c = 



275 TT 2 ff 

 and we deduce the following general formulae : 



= 1-15291 .... (g), 



by the Engine 

 on the Fluid 

 on the Vessel 



I. HORSES' POWER expended ENTIRE, 





 V / cos. e | V cos. e v cos. ($ e) \ ' 



cS 

 1000 



a, 

 I | 



Vcos. e v cos. 



e)\ 3 d<f> 



by the Engine 



on the Fluid 



on the Vessel 



M, 



vj cos. (<f> e) | Vcos. e t>cos.(c e) \ 2 d<l> 



o * 



II. HORSES' POWER expended HORIZONTALLY, 



a 

 y cos. cos. (< - e) | V cos. e - v cos. (0 - e) j 



..(A) 



cS 

 1000 



x < 



J (V cos. $ v) cos. (0 - e) I V cos. e-v cos. (<f>- e) ] 2 

 o 



a 



v J cos. (0 - e) I V cos. e - v cos. (<f> - e) I *dcf> 



n * 



III. HORSES' POWER expended VERTICALLY, 



by the Engine I c S ,, /* . 



ontheFluid f : = looo" X V Sm ^ ^ ^ ~ 



J 



>'(*) 



o I 



on the Vessel = o 



To effect the integration of these expressions, the mechanical properties of the wheel will give 

 e a function of <f> ; and in this way they will evidently apply to every possible description of 

 wheel. 



By way of examples we shall apply the formulae (A) to Oldham's wheel, the common wheel, 

 and the vertically acting wheel. 



