78 PROCEEDINGS OF THE AMERICAN ACADEMY 



ambiguity on that subject. In deciding among the three systems, we 

 should be guided by the following rules : — 



1st. The system should be perfectly definite, so that the same 

 temperature should be indicated, whatever the thermometer. 

 2d. The system should lead to the most simple laws in nature. 

 Sir William Thomson's absolute system of thermometry, coinciding 

 with that based on the expansion of a perfect gas, satisfies these most 

 nearly. The mercurial thermometer is not definite unless the kind of 

 glass is given, and even then it may vary according to the way the 

 bulb is blown. The gas thermometer, unless the kind of gas is given, 

 is not definite. And, further, if the temperature as given by either of 

 these thermometers was introduced into the equations of thermo- 

 dynamics, the simplest of them would immediately become compli- 

 cated. 



Throughout a small range of temperature, these systems agree 

 more or less completely, and it is the habit even with many eminent 

 physicists to regard them as coincident between the freezing and boil- 

 ing points of water. We shall see, however, that the difference 

 between them is of the highest importance in thermometry, especially 

 where differences of temperature are to be used. 



For these reasons I have reduced all my measures to the absolute 

 system. 



The relation between the absolute system and the system based on 

 the expansion of gases has been determined by Joule and Thomson 

 in their experiments on the flow of gases through porous plugs 

 (Philosophical Transactions for 1862, p. 579). Air was one of the 

 most important substances they experimented upon. 



To measure temperature on the absolute scale, we have thus only 

 to determine the temperature on the air thermometer, and then reduce 

 to the absolute scale. But as the air thermometer is very inconvenient 

 to use, it is generally more convenient to use a mercurial thermometer 

 which has been compared with the air thermometer. Also, for small 

 changes of temperature the air thermometer is not sufficiently sensi- 

 tive, and a mercurial thermometer is necessary for interpolation. 

 1 shall occupy myself first with a careful study of the mercurial 

 thermometer. 



(6.) The Mercurial Thermometer. 



Of the two kinds of mercurial thermometers, the weight ther- 

 mometer is of little importance to our subject. I shall therefore con- 

 fine myself principally to that form having a graduated stem. For 



