391 



the statical and dynamical effects of friction have been confounded to- 

 gether ; whereas they are the same in amount only when the body is 

 put in motion by gravity ; but not when it is urged down an inclined 

 plane by an extraneous force. In the latter case these effects are no 

 longer comparable ; friction being a force which, in an infinitely small 

 time, is proportional to the velocity, while that of gravity is constant 

 at all velocities j or, in other words, the retardation from friction is pro- 

 portional to the space described, while that from gravity has reference 

 only to the time of acting, whatever space the body may pass over in 

 that time. It is an error to assume that the mechanical power of the 

 plane is equivalent to a reduction of so much friction ; for the friction 

 down the inclined plane is the same as on a horizontal plane of the 

 same length, rejecting the trifling difference of pressure ; and the 

 whole retardation inpassingover the plane, or the whole force required 

 to overcome it, is the same at all velocities, and by whatever force the 

 motion is produced ; but the assisting force from gravity is quite inde- 

 pendent of the space or of the velocity. 



In the investigations which the author has prosecuted in this paper, 

 he assumes that equal quantities of steam are produced in the same 

 time at all velocities ; and he adopts for his other data, those given by 

 Mr. Pambour in his Treatise of Locomotive Engines. He deduces a 

 formula from which, the speed on a level being given, we may compute 

 the relative and absolute times of a train ascending a plane j and con- 

 sequently also the ratio of the forces expended in the two cases ; or 

 the length of an equivalent horizontal plane 5 that is, of one which 

 will require the same time and power to be passed over by the loco- 

 motive engine as the ascending plane. 



The next objects of inquiry relate to the descent of trains on an in- 

 clined plane, and comprise two cases : the first, that when the power 

 of the engine is continued without abatement ; 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 velocity, 

 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 5 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 j 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 as 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 



