222 



The Rev. Samuel Haughton's ^ccoM7i< of Experiments made 



to the horizon, i the angle which the axis of the waggon makes with the in- 

 clined plane when the front wheel is at the point Z. The line OY is horizontal ; 

 X is the point of bisection of 00'; and XZ is also horizontal. The velocity of 

 the waggon at 0' is its velocity at the commencement of the shock ; the velocity 

 at is equal (neglecting the friction of the wheels) to its velocity atY; i. e., 

 its velocity at the end of the shock. 



I shall assume that the shock consists of a single blow given at the point Z 

 with the velocity which animates the waggon at the point X. 



If v' represent this velocity, then the velocity of impact actually imparted 



to the sledge will be 



mv 



V = 



m + m 



in denoting the weight of the waggon, 

 m! sledge. 



If V represent the velocity with which the sledge and waggon begin to 

 move, and /x, k^ represent the coeiBcients of friction of rest and motion respec- 

 tively, we easily obtain {neglecting the loss of momentum caused hy imperfect 

 elasticity) the following equations : 



F = V cos i — jx(g cos I — vsini); ( 1 ) 



F==2^s (^cos/-sinJ); (2) 



the first of which expresses the fact, that the momentum with which the sledge 



begins to move is equal to the difference between the original momentum and that 



destroyed by the friction of rest ; the second equation is true on the hypothesis, 



that the friction of motion is a constant retarding force ; eliminating F between 



these equations we obtain 



V = A v^s + fJLU sec i; (3) 



A and u being defined by the following equations : 



A cos i — V{2g [k cos I — sin /]), 



n = g cos / — u sin i. 



Each experiment tried with the Friction Sledge, should give particular 

 values for 5 and v; which, substituted in (3), would afford a relation between 



