TRANSACTIONS OF THE SECTIONS. 3 



Therefore the mechanical magnitudes represented in magnitude and direction by 



AB, AC, AE destroy each other's effect (2.) ' 



Complete the parallelogram BE, 



.•.FB=AE=Aa (3.) 



and by the preceding proposition AF represents the magnitude of the resultants of 



AB, AE. 



By (2.) the resultant of AB, AE is equal and opposite to AC ; 



.•.AF=AC=Ba (4.) 



and CAF is a straight line. 



From (3 and 4) Fa is a parallelogram, and because FB || AD, and CAF a straight 

 line, Z nAC= Z BFA. But Z BFA= Z FAE ; .-. ^FAE= Z aAC ; .-. EAa is a 

 straight line. But EA was drawn opposite to the direction of the resultant of AB, 



AC. This direction is therefore the diagonal of the parallelogram BC, 

 The theorem is therefore demonstrated. 



It is clear that this general theorem may be made the common basis of the three 

 sciences of Statics, Kinematics and Dynamics, in the two parts of each which 

 respectively treat of points and bodies of finite magnitude. 



Summary of the Results of the Hypothesis of Molecular Vortices, as applied 

 to the Theory of Elasticity and Heat. By William John Macquorn 

 Rankine, C.E., F.R.S.'E. 



This paper gives a general view of the results of a peculiar mode of conceiving that 

 theory which regards the elasticity connected with heat as the effect of the centri- 

 fugal force of small molecular motions. Each atom of a body is supposed to con- 

 sist of a nucleus enveloped by an elastic atmosphere. The nuclei of the atoms, 

 vibrating independently, or almost independently of their atmospheres, constitute the 

 medium which transmits light and radiant heat. By supposing a small portion of 

 atmosphere to form a load on each nucleus, varying in amount according to the di- 

 rection in which the nucleus vibrates, the phaenomena of double refraction may be 

 explained* (see Philosophical Magazine for June 1851). The total elasticity of a 

 body consists of two parts, one which may be resolved into forces acting along the 

 lines joining the atomic nuclei, and which resists change of figure as well as change 

 of volume ; and another which cannot be so resolved, and which resists change of 

 volume only (see Cambridge and Dubhn Mathematical Journal for February and 

 May 1851). 



Part of this total elasticity is the pressure of the atomic atmospheres at certain 

 surfaces which may be described round each atomic nucleus, and at which the re- 

 sultant of the molecular attractions and repulsions is null. This pressure varies with 

 heat ; that is to say, it is increased by the centrifugal force of the movement of re- 

 volution of the particles of the atomic atmospheres. If v represent the mean velo- 



v" 

 city of that movement, and g the accelerating force of gravity, then Q=— is the 



quantity of heat in unity of weight of the substance. 



Two bodies are said to be at the same temperature when neither tends to commu- 

 nicate heat to the other ; and degrees of temperature are measured by the pressure 

 of a perfect gas at constant volume. Let t represent temperature, as measured from 

 an absolute zero 274°-6 Centigrade, or 494°"28 Fahr. below the temperature of melt- 

 ing ice ; then • 



I 



^m^ where « is a constant, the sam.e for all substances, but varying with the thermo- 

 ^k metric scale ; h is the coefficient of elasticity of the atomic atmosphere, and li a co- 



I 



and Q=(t — x) — , 



* These motions being communicated from the atomic nuclei to their atmospheres, con- 

 stitute that fixed heat which gives rise to increase of elasticity. 



