on a new Friction Sledge for stopping Raihcay Trains. 223 



A and /x. A few trials soon convinced me that fx was not a constant, and that 

 equation (3) did not represent the experiments ; this result might have been 

 foreseen, as the loss of motion arising from the shock of imperfectly elastic 

 bodies was neglected in finding equation (3). I could not discover any di- 

 rect method of introducing the loss of motion due to the shock, and therefore 

 sought to modify equation (3) by experiment, so as to make it represent what 

 actually occurred in each trial. After many failures I was induced to assume 



K being a constant. Introducing this value of jx into (3), and dividing by -/.?, 

 we obtain 



—^^A + Kseci-T-. (4) 



vs vs 



I hope to be able to show that this equation represents faithfully the whole 

 series of experiments, and that, too, with a degree of accuracy which seems to 

 prove that it is the true expression of the facts which were observed. 



The numerical values of the constants in the above equations were deter- 

 mined with care, and are as follows : 



00'= 22-5 feet, sin /= 0146, sin i = -050; 

 0'X= 11-25 feet, cos / = 999, cos i = '998. 



The force down the inclined plane, allowing 10 lbs. per ton for friction, resist- 

 ance of air, &c., is consequently, 



/= -4651 ft. 



The original measurements and calculated results are all given in the fol- 

 lowing tables, in which I have not suppressed a single experiment, although one 

 of them is undoubtedly erroneous. The evidence on which I was induced to 

 adopt the form (4) is completely given, and an opportunity thus ofiered for 

 another interpretation of the experiments, although the accuracy with which 

 equation (4) represents the results seems to preclude the possibility of an 

 interpretation differing much from that which is here given. 



