ON RAILWAY CONSTANTS. 249 



similar inclined plane to the same point, but which does meet with resistance 

 in its passage, we at once obtain the means of assigning what amount of re- 

 sistance it has suffered. 



Some persons have objected to this method, on the ground that. the results 

 hitherto obtained by it have not always been consistent with each other. 

 Such inconsistencies, however, may be satisfactorily explained, either on the 

 supposition of the data not having been correct, or, what is more probable, 

 from the fact of the existence of unobserved causes of irregularity, such as 

 the influence of favouring or adverse winds, and differences of friction of the 

 carriages. It will hereafter be shown what a remarkable correspondence the 

 motions of the same train exhibit when permitted to descend along the same 

 plane from the same point of elevation, provided the atmosphere be perfectly 

 calm. Such correspondence could only exist under the uniform operation 

 of the same producing cause, and the absence of accidental causes ; and we 

 therefore conceive that no surer test can be applied to determine the mean 

 resistance experienced by a train in moving from one point to another down 

 an uniform inclination, than a comparison between the observed time of its 

 passage and the time it would have occupied if resistance had been altogether 

 removed. 



There are three cases of the motion to which the same formula is equally 

 applicable : — 



1. When the motion is accelerated. 



2. When the motion is uniform. 



3. When the motion is retarded. 



In the first case the coefficient (determined by the inclination of the plane) 

 of gravity is greater than the coefficient of resistance, and therefore the quan- 

 tity which must be added to the coefficient of gravity to represent the coeffi- 

 cient resistance is negative. 



In the second case the coefficient of gravity is equal to the coefficient of 

 resistance, and no correction is required. 



In the third case the coefficient of gravity is less than the coefiicient of 

 resistance, and the addition to the coefficient of gravity is a. positive one. 



In all cases therefore the coefficient of resistance may be found, by adding 

 to the coefficient of gravity a quantity (determined by considerations alluded 

 to in the former Report) which is either negative, or equal to zero, or positive. 



This quantity may be thus obtained : — Multiply the initial velocity (2) in 

 feet per second by the time in seconds (4). From this product subtract the 

 space (in feet) passed over (5), and divide the difference by 16j2 times the 

 square of the time occupied (4). The quotient thus found must be subjected 

 to a slight correction, owing to the rotation of part of the moving mass, which 

 correction may be detei-mined by reference to data Nos. 7, 8, 9, and 10. 



The initial velocity multiplied by the time represents the space which the 

 train would describe were that velocity to remain constant. In the case of 

 imiform motion, the velocity does remain constant, and the product of the 

 two numbers equals the space traversed. Their difference, and consequently 

 the whole quantity dependent upon it, vanishes, and the coefficient of gravity 

 becomes also the coefficient of resistance. 



In accelerated motion the product of the numbers is less than the space 

 traversed, and the quantity to be added to the coefficient of gravity is nega- 

 tive, indicating the amount by which the force of gravity exceeds that of the 

 resistance. On the other hand, when the motion is retarded, the reverse 

 takes place, and the quantity to be added is positive. 



Under the condition of uniform motion we are enabled positively to pro- 

 nounce what is the mean resistance for that particular velocity. When, how- 



