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XV. — On the Thermal Energy of Molecular Vortices. By W. J. Macquorn 

 Rankine, C.E., LL.D., F.R.SS. L. & E., &c. 



(Read 31st May 1869.) 



§ 1. Object of this Paper. — In a paper on the Mechanical Action of Heat, 

 which I sent to the Royal Society of Edinburgh in December 1849, and which 

 was read in February 1850, it was shown, that if sensible or thermometric heat 

 consists in the motion of molecular vortices supposed to be arranged in a par- 

 ticular way, and combined in a particular way with oscillatory movements, the 

 principles of thermodynamics, and various relations between heat and elasticity, 

 are arrived at by applying the laws of dynamics to that hypothesis.* The object 

 of the present paper is to show how the general equation of thermodynamics, and 

 other propositions, are deduced from the hypothesis of molecular vortices, when 

 freed from all special suppositions as to the figure and arrangement of the vor- 

 tices, and the properties of the matter that moves in them, and reduced to the 

 following form : — That thermometric heat consists in a motion of the particles of 

 bodies in circulating streams, with a velocity either constant or fluctuating periodi- 

 cally. This, of course, implies that the forces acting amongst those particles are 

 capable of transmitting that motion. 



§ 2. Steady and Periodical Component Motions. — A vortex, in the most 

 general sense of the word, is a stream or current which circulates within a limited 

 space. Conceive a closed vessel of any figure and volume to be filled with 

 vortices, or circulating streams, the mean velocity of circulation in each such 

 stream being the same ; and let the velocities of the moving particles be either 

 constant or periodic. How complex soever those motions may be, they may be 

 resolved into the following component motions; — a motion of steady circulation 

 with the uniform velocity already mentioned as the mean velocity ; and a motion 

 consisting in periodical fluctuations of velocity. Those two component motions 

 may be called respectively the steady circulation and the disturbance. 



§ 3. Mean Pressure due to Centrifugal Force. — Let an elementary circu- 

 lating stream— that is, a circulating stream of indefinitely small sectional area — 

 be supposed to flow round and round in an endless tube with the uniform velocity 

 w; let p denote the density of the stream; da- the sectional area. Consider two 

 cross sections of the stream at which the directions of motion of the particles are 



* Transactions of the Royal Society of Edinburgh, 1850, vol. xx. 

 VOL. XXV. PART II. 7 E 



