220 Mr. J. J. Waterston on a Difference in the march 



Oct. 1857.] The deviation consists in the elastic force being 



less than the inverse of the density by -^ per atmosphere at 



ordinary temperatures. How the measurement of temperature 

 is likely to be affected by these, we may perhaps appreciate most 

 distinctly by means of a diagram (fig. 5). 



§ 12. Let CQ represent the interval of temperature between 

 the freezing and boiling of water, CD and QP the corre- 

 sponding volumes of air under constant pressure at those tem- 

 peratures. Join PD, and extend it to meet CQ produced in A. 

 We have (PQ-CD) : CD : : CQ : CA, or according to Regnault, 

 0-36706 : 1-00000 : : 100° : 272°-44. 



Suppose the temperature to descend from C to B, the cor- 

 responding volume would be BF if the primary laws of gases 

 were entire. But the deviation, although as yet not perfectly 

 known in a case such as this, points to a lesser volume BE as 

 that which the thermometer would actually exhibit under the 

 influence of the augmented density and diminished temperature, 

 both of which unite in affecting the relation between tension and 

 density, 



§ 13. The locus of the point E is unknown, but it must be 

 curvilinear, as both D and P are to be found in it ; and its cur- 

 vature is convex upwards, showing that between any two points 

 D and P the air-thermometer is in advance of true temperature. 

 As the amount of this difference depends on the degree of cur- 

 vature, it may be worth while to inquire as to its probable 

 maximum between 0° and 100°. Certainty is of course not to 

 be expected, but I think it can be shown that the complete solu- 

 tion of the question is possible by employing the mode of expe- 

 riment with plugs, suggested by Professor Thomson, and carried 

 out to a certain extent by that gentleman and Mr. Joule under 

 the auspices of the Royal Society. 



§ 14. Suppose the air that occupies the volume DC is com- 

 pressed into half the space [dC] ; we know, if it passed through a 

 plug and were allowed to expand from the greater to the lesser 

 density without performing work, that a thermal depression will be 

 exhibited which indicates that the pressure at the double density 



is less than two atmospheres by about ^-^. (See paper in Philo- 

 sophical Magazine above referred to.) If dC represents the 

 volume at two atmospheres, we should have the point d situated 



1 DC 

 _^ X "Tj- below the middle point between D and C. "We have 



now to suppose the air represented by DC to pass through a plug 

 into air of half an atmosphere tension, i. e. to have its volume 



