430 Prof. Thomson on the Dynamical Theory of Heat. 



each of the two vessels, and round a portion of the tube contain- 

 ing the small orifice (a stop-cock), has suggested to me a method 

 which appears still simpler, and more suitable for obtaining an ex- 

 cessively delicate test of Mayer's hypothesis for any temperature. 

 It consists merely in dispensing with the two vessels in Joule's 

 apparatus, and substituting for them two long spirals of tube 

 (instead of doing this for only one of the vessels, as Joule does 

 in his third experiment with the same apparatus) ; and in forcing 

 air continuously through the whole. The first spiral portion of 

 the tube, up to a short distance from the orifice, ought to be 

 kept as nearly as possible at the temperature of the atmosphere 

 surrounding the portion containing the orifice, and serves merely 

 to fix the temperature of the entering air. The following inves- 

 tigation shows M'hat conclusions might be drawn by experiment- 

 ing on the thermal phsenomena of any fluid whatever treated in 

 this manner. 



73. Let ji ^^ the uniform pressm-e of the fluid in the first 

 spiral, up to a short distance from the orifice, and let j^' be the 

 pressure a short distance from the orifice on the other side, which 

 vdll be uniform through the second spiral. Let t be tlie con- 

 stant external temperature, and let the air in both spirals be 

 kept as closely as possible at the same temperature. If there 

 be any elevation or depression of temperature of the fluid in 

 passing through the orifice, it may only be after passing through 

 a considerable length of the second spiral that it will again arrive 

 sensibly at the temperature t ; and the spiral must be made at 

 least so long, that the fluid issuing from the open end of it, 

 when accurately tested, may be found not to differ appreciably 

 from the primitive temperature t. 



74. Let H be the total quantity of heat emitted from the 

 portion of the tube containing the orifice, and the second spiral, 

 during the passage of a volume u through the first spiral, or of 

 an equivalent volume %i' through the parts of the second where 

 the temperature is sensibly t. This vdll consist of two parts ; 

 one (positive) the heat produced by the fluid friction, and the 

 other (negative) the heat emitted by that portion of the fluid 

 which passes from one side to the other of the orifice, in virtue 

 of its expansion. To find these two parts, let us first suppose 

 the transference of the fluid to take place without loss of mecha- 

 nical eff'ect in fluid friction, as it would do if, instead of the pai*- 

 tition with a small orifice, there were substituted a moveable 

 piston, and if a volume u of fluid, on the side where the pressure 

 is higher [p), were enclosed between that and another piston, 

 and allowed to slide through the tube till the second piston 

 should take the place of the first, and to expand till its volume 

 should be m'. If we adopt the same notation with reference to 



