ON RAILWAY CONSTANTS. 255 



value in reference to such a subject ; but they may answer a more useful pur- 

 pose when applied to express in a condensed form results between which an 

 analogy has been traced, serving thus as the first steps of a generalization to 

 be completed only by multiplying observations in every possible way. 



On the 11th July, 1839, the eight second class Grand Junction carriages 

 were taken to the planes, extending from Madeley to Crewe. The wind, as be- 

 fore noticed, blew down the plane. The train of eight carriages was thrice 

 discharged over the head of the plane, at a speed varying from 23 to 26 miles 

 per hour. 



Secondly, one half the train, or four carriages, was dismissed over the head 

 of the plane at 40'9 miles per hour ; the other half, or four carriages, was dis- 

 missed at 32*73 miles per hour ; and, lastly, a train of six carriages was dis- 

 missed at the speed of 25*57 miles per hour. 



1. Eight carriages, weighing gross 40*75 tons, dismissed over the top of 

 Madeley plane, 1 in 177, at 23*71 miles per hour, accelerated to 24*79 miles 

 per hour, and varied between 24*79 and 23*54 miles per hour, until reaching 

 the foot. See Table, No. IX. 



2. Same train dismissed at 23*37 miles per hour, accelerated to 28*21, and 

 varied between 28*21 and 25*77 miles per hour, until reaching the foot. See 

 Table, No. X. 



3. Same train dismissed at 26*39 miles per hour, accelerated to 27*05 miles 

 per hour, and varied between 27*05 and 25*17 miles per hour, until reaching 

 the foot. See Table, No. XI. 



In the first case the maximum speed was attained at post No. 40 ; in the 

 second case at post No. 48 ; in the third case at post No. 52. Let us com- 

 pare the times of descent from post No. 40, for instance, to post No. at the 

 foot of the plane, and deduce from thence the average uniform speed over that 

 distance of 4000 yards. The times were respectively, 



5 min. 39*25 seconds = 24*1 miles per hour. 

 5 . . . 8*25 ... = 26*4 

 5 . . . 18*50 ... = 25*6 

 The mean of the whole is 25*4 miles per hour. 



The circumstance of the speed having ceased to accelerate and having be- 

 come uniform, renders unnecessaiy any calculation of the amount of resistance ; 

 for it has been already shown that, in the case of uniform motion, the coefli- 

 cient of gravity is equal to the coeflScient of resistance. The fraction j-fy in 

 this instance then represents the coefficient of resistance ; in other words, 

 12*65 lbs. per ton was the mean resistance encountered by the train of eight car- 

 riages, tvhen moving at the mean velocity of25'4f iniles per hour. 



Upon reaching the foot of the 177 plane, the trains passed on to a plane of 

 1 in 265, extending from the post numbered to that numbered 54. The ob- 

 servations of its motion afford the means of ascertaining the resistance at a 

 slower uniform velocity. 



1. Eight carriages entered upon the 1 in 265 plane at 24*06 miles per hour ; 

 their motion was gradually retarded to 19*83 miles, over a space of about 3000 

 yards, and finally became uniform over the remaining distance. 



2. Same carriages entered the plane at 25*76 miles per hour ; their motion 

 was retarded to 20*20 miles, over a space of 3000 yards, and finally became 

 uniform, or nearly so over the remaining distance. 



3. Same carriages entered the plane at 25*57 miles per hour ; their motion 

 was retarded to 19*02, over a space of 3500 yards, and finally became nearly 



; uniform. 



