Royal Society. 87^ 



•which was likewise unexpected, is nevertheless a sufficiently obvious 

 consequence of the mechanical conditions of the question. If a given 

 change of direction in the road be made by a curve of large radius, 

 the length of the curve will be proportionably great ; and although 

 the intensity of the resistance to the tractive power, at any point of 

 the curve, will be small in the same proportion as the radius is great, 

 yet the space through which that resistance acts will be great in pro- 

 portion to the radius: these two effects counteract each other; and 

 the result is, that the total absorption of power is the same. On the 

 other hand, if the turn be made by a curve of short radius, the curve 

 itself will be proportionately short ; but the intensity of the resistance 

 will be proportionately great. In this case, a great resistance acts 

 through a short space, and produces an absorption of power to the 

 same extent as before. 



In conclusion, the author arrives at one general and comprehensive 

 formula for the actual amount of mechanical power necessary to work 

 the line in both directions; involving terms expressive, ^r5/, of the 

 ordinary friction of the road ; secondly, of the effect of inclined planes, 

 or gradients, as they have been latterly called ; and, thirdly, of the 

 effect of curves involving changes of direction of the road, the velocity 

 of the transit, and the distance between the rails ; but, for the reason 

 already stated, not comprising the radii of the curves. 



Although the radii of tiie curves do not form a constant element of 

 the estimate of the mechanical power necessary to work the road, 

 nevertheless they are of material consequence, as far as regards the 

 safety of the transit. Although a short curve with a great resistance 

 may be moved over with the same expenditure of mechanical power 

 as a long curve with a long radius, yet, owing to the intensity of the 

 pressure of the flange against the rail, the danger of the trains run- 

 ning oft' the road is increased : hence, although sharp curves cannot 

 be objected to on the score of loss of power, they are yet highly ob- 

 jectionable on the score of danger. 



In the present paper, the author has confined himself to the ana- 

 lytical formulae expressing various mechanical effects of the most 

 general kind ; the coefficients and constants being expressed merely 

 by algebraical symbols; but he states that he has made an extensive se- 

 ries of experiments within the last few years, and has also procured the 

 results of experiments made by others, with a view to determine the 

 mean values of the various constants in the formulae investigated in 

 this paper. He has also, with the same view, made numerous ob- 

 servations in the ordinary course of transit on railways ; and he an- 

 nounces his intention of soon laying before the Society, in another 

 paper, the details of these experiments, and the determination of the 

 mean values of these various constants, without which the present 

 investigation would be attended with little practical knowledge. 



A paper was also read, entitled " Register of the State of the 

 Barometer and Thermometer kept at Tunis, during the years 1829, 

 1H30, 18;ii and 1832." Presented by Sir Thomas Reade, His 

 Majesty's Agent and Consul General at Tunis. Communicated by 

 V. M. koget, M.D., Sec. R.S. 



2 Y2 



