380 Roi/al Society. 



The observations here registered are those of the thermometer at 

 9 A.M., at noon, and at 6 p.m., and the points of the wind, and height 

 of the barometer for each day of the abovementioned years. 



May 5. — A paper was in part read, entitled " On the Optical Phe- 

 nomena of certain Crystals." By Henry Fox Talbot, Esq., F.R.S. 

 See our last Number, p. 288. 



May 12. — The reading of Mr. Talbot's paper was concluded. 



May 19. — A paper was read, entitled, "On the valuation of the 

 mechanical effect of Gradients on a line of Railroad." By Peter 

 Barlow, Esq., F.R.S. 



The exact amountof the influence of ascents and descents occurring 

 in tlie line of a railway on the motion of a load drawn by a locomotive 

 engine having been differently estimated by different persons, the au- 

 thor was induced to investigate the subject. A few observations are 

 premised on the erroneous assumptions which, he conceives, have in 

 general vitiated the results hitherto deduced. The first of these is that 

 the expenditure of power requisite for motion is equal to the resistance 

 to traction ; whereas it must always greatly exceed it. No account, 

 he remarks, has been taken of the pressure of the atmosphere on the 

 piston, which the force of the steam has to overcome before it can be 

 available as a moving power. Another source of error has been that 

 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 ; 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 in passing over 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 ; and con- 

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

 the length of an equivalent horizontal plane ; 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 



