Royal Society. 381 



of the engine is continued without ahatement ; and the second, that 

 when the steam is wholly excluded, and the train is urged in its de- 

 scent by gravity alone. The author arrives at the conclusions, that 

 in the first of these cases, when the declivity is one in 139, the velocityt 

 on becoming uniform, will be double that in a horizontal plane : and 

 that for a declivity of one in 695, the uniform velocity of descent will 

 be one fifth greater than on the horizontal plane ; and this, he ob- 

 serves, is perhaps the greatest additional velocity which it would be 

 prudent to admit. A plane of one in 695 is therefore the steepest de- 

 clivity that ought to be descended with the steam-valve fully open ; 

 all planes with a declivity between this and that of one in 139 require 

 to have the admission of steam regulated so as to modify the speed, 

 and adjust it to considerations of safety ; and lastly, all planes of a 

 greater slope than this last require, in descending them, the application 

 of the brake. 



A paper was also read, entitled, " On the application of Glass us a 

 substitute for metal balance-springs in Chronometers." By Messrs. 

 Arnold and Dent. Communicated by Francis Beaufort, Esq., Captain 

 R.N., F.R.S., Hydrographer to the Admiralty. 



In their endeavours to determine and reduce the errors arising: from 

 the expansions of the balance-spring of chronometers consequent on 

 variations of temperature, the authors came to the conclusion that 

 there exist certain physical defects in the substances employed for its 

 construction, beyond the most perfect mechanical form that can be 

 given to it, which interfere with the regularity of its agencv : so that 

 however exquisite may be its workmanship, and however complete its 

 power of maintaining a perfect figure when in difiFerent degrees of 

 tension, yet the imperfect distribution of its component parts may give 

 rise to great incorrectness in its performance. Hence the balance- 

 spring not only should be made of a substance most highly elastic, 

 but its elasticity should not be given to it by any mechanical or che- 

 mical process : as a body in motion, it should be the lightest possible ; 

 and, as far as the case admits of, it should be free from atmospheric 

 influence. Glass suggested itself as the only material possessing, in 

 the greatest degree, all these desirable properties. Its fragility, al- 

 though apparently a great objection to its employment, was found, on 

 trial, to constitute no obstacle whatever ; for it was found to possess 

 a greater elastic force than steel itself, and thus to admit of greater 

 amplitude in the arc of vibration. 



It was first proposed to ascertain how far a glass balance-spring 

 would sustain low temperatures ; and it was found by experiment that 

 it resisted completely the efl^'ects of a cold as great as that of + 1 2° of 

 Fahrenheit's thermometer ; thus satisfactorily removing any objection 

 which might be brought against its use from its supposed fragility in 

 these low temperatures. The next object of solicitude was to deter- 

 mine whether it would withstand the shock arising from the discharge 

 of cannon in the vicinity; and its power of resisting concussions of 

 tills nature wns fully established by experiments made with this view 

 on board H.M.S. Excellent at Portsmouth. 



. On comparing the performance of glass balance-springs with me- 

 tallic ones, when the temperatures were raised from 32"^ to 100", it 



