228 EIGHTH REPORT 1838. 



In the first two experiments, with the gross load of 15'6 

 tons, no acceleration is apparent in the descent. In the first 

 the velocity fluctuated between 100 yards in 6 and 100 yards in 

 7 seconds, the mean being 100 yards in 6*48 seconds. In the 

 second experiment the limits of the varying observed speed are 

 more narrow, being 100 yards in G^^ seconds and 100 yards in 

 7 seconds, the mean being 100 yards in 6*61 seconds. The 

 mean result of these two experiments is 100 yards in 6'55 se- 

 conds, or 45 "8 feet per second. 



In the last three experiments a slight acceleration is apparent 

 in the first thousand yards of the descent, but the subsequent 

 variations of speed are too minute and irregular to be ascribed 

 to anything save the casual inequalities of the rails and the in- 

 evitable errors of observation. 



The time of moving down the last thousand yards in the third 

 experiment was 61 seconds, in the fourth 60 seconds, and in 

 the fifth 61 seconds. We cannot, therefore, be far from the 

 truth if we assume that the train loaded, as in these experi- 

 ments, with 18-05 tons gross would continue to descend a plane 

 falling 1 in 96 with the velocity of 1000 yards in 60f seconds, 

 or 49*45 feet per second. 



Thus, then, it appears that the uniform velocities attained by 

 the same train of coaches loaded with 15'6 tons and 18*05 tons 

 was 45'8 and 49"45 feet per second respectively. 



It will be evident from the formula (25.) that if the resistance 

 of the air vary in the ratio of the square of the velocity within 

 the limits of the experiments, tlie gross weights of the same 

 train differently loaded ought to be in the ratio of the squares 

 of the uniform velocities attained by it in descending the same 

 plane, the effect of the wind being supposed to bear an incon- 

 siderable proportion to the whole resistance at this speed. For 

 let M and M' be the two loads and V and V the two uniform 

 velocities, we shall then have 



In the present ease 



M^ _ 15-60 

 M' ~ 18-05 



= 0-864 



V'^ (49-45)2 



