152 



APPENDIX. 



Log. 9 R 3 a. = 3-91463 

 36 R a? a. = 3-73247 

 32 R 3 a sin. 0= 3-87904 

 7 R 3 k sin. /3 = 3-44084 

 12 a 2 A sin. /3= 2-89070 

 2 k 3 sin. /3 = 2-55625 



Log. 39 fl 2 a sin. a = 4-05838 



6 a 3 sin. a = 2-46125 



9/Z 3 /8 = 3-77117 



12 Ra* /3 = 3-11189 



24 Rakft = 3-63477 



8 A 2 sin. /3 = 2*93646 













 



9 R 3 a = 8215-4 



36 R a 1 a = 5401-0 



32 R 2 a sin. /3 = 7569-0 



7 R 3 k sin. /S = 2759-6 



12 a 2 & sin. /3 = 777'5 



2 A 3 sin. /9 = 360-0 



Sum of positive terms = 25082-5 



979-5 



Log. 979-5 



7T 2 Rn 3 w b m 

 " 178200000 x 2y 



H.P. 



2-99100 

 - 1-30853 



2-29953 



H.P. 



= 199-31. 



In this example the ratio of the effective to the total power is only 0-443, which shows that 

 the principle of vertical paddles is in this case fallacious. We do not think it necessary here 

 to enter into the practical objections that may be raised against this wheel, but proceed at 

 once to the next kind that claims our attention, which is, 



2. Oldham's Paddle Wheel. 



The principle of this wheel will be perfectly understood by conceiving the axis of the 

 excentric in Buchanan's to revolve round the main shaft in the same direction as the latter, 

 and with half its angular velocity. This is effected by fixing a spur wheel on the shaft close 

 to the vessel's side ; another on an independent axis fixed to the vessel's side, working in the 

 former ; a third on the same axis as the second, and fixed to it, but of a different size ; and a 

 fourth fixed to the excentric, or guiding frame, concentrically with the main shaft, working 

 in the third ; the dimensions of all being so proportioned that the last shall make one revolu- 

 tion to every two of the first. It follows from this, that as each paddle-crank or lever must 

 of necessity be constantly parallel to the imaginary line which joins the two centres, and as 



