316 Mr. J. L. Woodbridge on Turbines. 



in No. 3. The momentum is mv, and the force will be mvco, 

 which acts in the direction na, and being resolved gives 

 along the vane, 

 — mvco normal to the vane. 



No. 5. In passing from a f to d f the increase of cop will be 



codp in a time dt, and the reaction will be mco -=£, in a direction 



tangential to the motion of the wheel but backwards, and its 

 components will be 



mco -j- cos 7 along the vane, 



— mco -j- sin 7 normal to the vane. 



No. 6. In passing from a' to d', cop will be changed in 

 direction by the angle a'Od'=— = — -, and the rate of 



angular change will be 



cot 7 dp 



~p~'dt' 

 and the momentum will be 



mcop ; 

 hence the reaction will be 



mco cot 7 -~, 

 at 



which acts radially inward, and its components are 

 -mw cos y~ along the vane, 



—mco cot y cos y ~ normal to the vane. 

 No. 7. By moving from a' to d\ v will be increased by an 



amount -7- dp, in the time dt, and the reaction will be m A 



dp dp dt 



which acts backward along the vane, and its components are 

 f p . J along the vane, 

 normal to the vane. 



No. 8. In passing from a 1 to d f , v is changed in direction 

 by two amounts :— 1st, the angle 7 changes an amount 



—j- dp, and 2nd, the radius changes in direction an amount 



— m 



