Ox THE MECHANICAL EQUIVALENT OF HEAT 349 



As I only use the mercurial thermometer to compare with the air 

 thermometer, and as either definition is equally correct, I will not 

 further discuss the matter, but will use the first definition, as being 

 the simplest. 



In the above formula I have implicitly assumed that the apparent 

 expansion is only a function of the temperature; but in solid bodies 

 like glass there seems to be a progressive change in the volume as time 

 advances, and especially after it has been heated. And hence in mer- 

 curial and alcohol thermometers, and probably in general in all ther- 

 mometers which depend more or less on the expansion of solid bodies, 

 we find that the reading of the thermometer depends, not only on its 

 present temperature, but also on that to which it has been subjected 

 within a short time; so that, on heating a thermometer up to a certain 

 temperature, it does not stand at the same point as if it had been cooled 

 from a higher temperature to the given temperature. As these effects 

 are without doubt due to the glass envelope, we might greatly diminish 

 them by using thermometers filled with liquids which expand more 

 than mercury : there are many of these which expand six or eight times 

 as much, and so the irregularity might be diminished in this ratio. But 

 in this case we should find that the correction for that part of the 

 stem which was outside the vessel whose temperature we were deter- 

 mining would be increased in the same proportion; and besides, as all 

 the liquids are quite volatile, or at least wet the glass, there would be 

 an irregularity introduced on that account. A thermometer with liquid 

 in the bulb and mercury in the stem would obviate these inconven- 

 iences ; but even in this case the stem would have to be calibrated before 

 the thermometer was made. By a comparison with the air-thermom- 

 eter, a proper formula could be obtained for finding the temperature. 



But I hardly believe that any thermometer superior to the mercurial 

 can at present be made, that is, any thermometer within the same 

 compass as a mercurial thermometer, and I think that the best result 

 for small ranges of temperature can be obtained with it by studying 

 and avoiding all its sources of error. 



To judge somewhat of the laws of the change of zero within the 

 limits of temperature which I wished to use, I took thermometer No. 

 6163, which had lain in its case during four months at an average 

 temperature of about 20 or 25 C., and observed the zero point, after 

 heating to various temperatures, with the following result. The time 

 of heating was only a few minutes, and the zero point was taken imme- 



