250 Mr. H. L. CallsnJar. [Dec. 10, 



form of instrument above described are very simple. They are, (1) 

 that the two sets of connecting tubes should be of equal volume and 

 at the same mean temperature ; (2) that the mass of air enclosed in 

 the standard pressure bulb should be equal to that in the thermo- 

 metric and mercury bulbs ; (3) that the pressures should be adjusted 

 to equality. 



Let w be the mass of air in the standard pressure bulb and its 

 connecting tubes, and let p be its pressure. Let Y be the volume 

 of the bulb, and its temperature measured on the scale of the 

 air thermometer. Let v be the volume of the connecting tubes, and 

 0' their mean temperature ; then we have 



where Jc is a constant. 



Let m^ be the mass of air in the thermometric and mercury bulbs 

 and their connecting tubes, and let pi be its pressure. Let Vi, V m be 

 the volumes of the air in these bulbs respectively at the tempera- 

 tures 0i and m ; then we have as before 



Pi ii 

 If now we make ra = m ]} and p = p 1} we have the equation 



The term v/0' disappears from the equation, and if we also make 

 = m by keeping both the mercury and standard pressure bulbs in 

 melting ice, the value of 0i is accurately given by the very simple 

 expression 



It is convenient, and at the same time more symmetrical, to make 

 the volume of the standard pressure bulb adjustable with mercury. 

 It is then possible to take observations with the same thermometer at 

 different pressures. By this means, as explained in a previous paper,* 

 we- can investigate with some accuracy the behaviour of gases at high 

 temperatures, and thus reduce the indications of the air thermometer 

 to the true scale of absolute temperature. 



The form of instrument above described is designed for the most 

 accurate work. For rough purposes, and especially for small ranges 

 of temperature, very much simpler instruments may be constructed 

 on similar principles. 



It is evident, from an inspection of the equations already given, 

 that the compensation is still sufficiently accurate for rough work, 

 provided that the difference of pressure is small, and that the volume 



* < Phil. Trans.,' A, 1887, p. 223. 



