516 MEMOIR OF DANIEL TKEADWELL. 



as the resistance fronj elevating this load 4,J feet. AVe have likewise the mean draft of the load used 



iu Xos. 1 and 3. 



Xos. 1 and 3, 119.4 + 110.3= 114. S lb., mean of both. 



From this take 21.0 lb., being the quantity due to elevating the load, and we have 9.3.2 lb. for tlie re- 

 sistance from all other sources. Then, if we reject experiment No. 4, as not made under the same 

 circumstances with the others, we have the mean draft in 



Nos. 2 and 5, 91. G + 77.1 = 84.3 lb., mean of both. 



From this take 18.9 lb., being the quantitj- due to elevating the load, and we have 65.4 lb. for the re- 

 sistance from all other sources. Then, if we divide the loads iu both cases by the resistance from these 

 sources we have results as follows : — 



m%'> = 1G9 7, and ijV.fo = 212.2. 



Tliat is, in Xos. 1 and 3 the resistance reduced to a level railway was yjo^ths of the load. Or they 

 give one ton of 2,240 lb. drawn by 13.2 lb., and in Nos. 2 and 5 the resistance reduced to a level was 

 ^^S^ds of the load, or one ton of 2,240 lb. drawn by 10.55 lb. In experiments Nos. 1 and 3, a part of 

 the load, namely, that of apparatus car, was carried upon gudgeons of 1 J inches diameter. Let us then, 

 to ascertain if the resistance was in proportion to the diameters of the gudgeons of the cars on which it 

 rested in each set of experiments, multiply the load carried by the diameters of the gudgeons. Thus : 



Xos. 1 and 3, 4,670 X H = 8,756 

 11,150 X 3 = 33,4.50 



42,206 

 Xos. 2 and 5, 13,880 X IJ = 26,025 



We have the proportion, 26 023 : 42,206 : : 65.4 : 101.8. 



But we have found that the resistances reduced for a level were as 65.4 : 93.2. The resistance, therefore, 

 does not follow the exact proportion of the size of the axles or the gudgeons, although it approaches 

 somewhat near to that ratio. It must be evident, however, that a part of the resistance is produced be- 

 tween the wheels and the rails. Some force is destroyed by the motion of the rails in the chairs, and 

 there is, moreover, some resistance from the passage of the load through the air. If we take the force 

 of traction required to overcome all these resistances as equal to ^^ih part of the load, we have for the 

 friction of the gudgeons in 



Xos. 1 and 3, the load 15,820 -^ 600 = 26.3 



Xos. 2 and 5, the load 13,880 -^ 600 = 23.1 



and the traction for a level in 



Xos. 1 and 3, 93 2 - 26.3 = 60.9 

 Xos. 2 and 5, 65.4 — 23. 1 = 42.3 



Tliat is, the resistance from friction, at the gudgeons alone, in Nos. 1 and 3 was 66.90 lb. and in Nos. 2 

 and 5 it was 42.3 lb. Then, taking the loads in both cases multiplied by the diameters of the gudgeons, 

 wc have the proportion 26,025 : 42,206 : : 42.3 : 68.9, which accords very nearly with the experiments. It 

 is said that the cars and wheels now used upon the Worcester road, if mounted upon larger gudgeons, 

 will be strong enough to carry much larger loads than three tons, to which they are now limited. This 

 raises the question whether, considering this greater weight of load in connection with the weight of the 

 cars, it will not be good economy to use the large gudgeons carrying these greater loads ? Let us exam- 

 ine this question. 



Suppose a car alone to weigh 2,600 lb., and that we load it with 6,000 lb., the actual resistance 

 will be found as follows, for gudgeons of IJ-inch diameter: 2.600 -f- 6.000 = 8,600 -=- 212.2 = 40.5 lb. 

 For carrying loads upon cars with 3-iuch gudgeons, loaded with double the above weight, we have 



