RAILWAY CONSTANTS. 247 



the coach was equal to the gravity on the plane. As the coach 

 descended the next gradient its motion was again gradually re- 

 tarded until the speed became 100 yards in seventeen seconds, 

 but was again accelerated until it became 100 yai'ds in fourteen 

 seconds, these fluctuations being probably due to the varying 

 exposure to the wind. The uniform motion down this gradient 

 may therefore, perhaps, be taken as a mean of the varying mo- 

 tion of the train in descending it. This mean would be 100 

 yards in sixteen seconds, or 12-8 miles per hour. 



If it be assumed that the train of four coaches used in the ex- 

 periments down the Madeley plane, falling 1 in 178, had the same 

 friction as the train of four first-class coaches used in the ex- 

 periments down the Whiston plane (page 224), the proportion 

 in which the whole resistance is in each case due to friction and 

 the air, may be obtained by an easy calculation derived from 

 the formulae 26 and 27 ; making in these the following substi- 

 tutions, 



M = 18, A = — , h' = -L, V = 49-45, V = 31-2, 



' 96 178 ' 



we shall find 



/• 1 1 



409 17043 



In both these experiments the wind was favourable, but its 

 force unascertained, and in the formula from which these values 

 of/ and a have been deduced no allowance has been made for 

 its effect. By comparing the value of/ thus obtained with the 

 value of/ in page 231, it will be seen that the present value is 

 less in amount, as might be expected, from the effect of the wind. 



The resistance per ton due to friction according to this cal- 

 culation would be 5-48 pounds, and the total resistance from 

 friction for the load of eighteen tons would therefore be 98*64 

 pounds. 



Since the entire resistance of this load at twenty-one miles 

 per hour was found by the experiments to be 226'8 pounds per 

 ton, it follows that the total resistance due to the atmosphere 

 was 128" 16 pounds. 



Two objections have been advanced against the method of 

 determining the resistance by moving down inclined planes 

 until a velocity be obtained which renders the resistance equal 

 to the gravitation on the plane. The first is, that the engine 

 not being in front of the train, the flat surface of the foremost 

 carriage is exposed to the air, and that a greater atmospheric 

 resistance is thereby produced than would be produced if the 

 engine were in front of the carriage inasmuch as the engine 



R 2 



