66 Mr. F. D. Brown's Notes on Thermometry. 



exposed stem to a temperature higher than that indicated by 

 the subsidiary thermometer. The value of (T— t) therefore is 

 too great, and consequently also that of C. 



In order to meet this difficulty, Dr. Mills, instead of endea- 

 vouring to give to (T— t) its proper value, has made a large 

 number of experiments with different thermometers with a 

 view to assign a more satisfactory value to m, and has thus 

 been led to draw the following conclusions : — The value 

 •0001545 of the coefficient m is invariably too great. This 

 coefficient varies with the thermometer employed, and also 

 with the number of divisions of the thread exposed ; so that, 

 instead of assigning one definite value to m for each thermo- 

 meter, we must give it a value 



m = a + /3N, 



where a and |8 must be determined for each thermometer. 



Professors Thorpe and Riicker, on the other hand, while 

 admitting that the value m= -0001545 may be generally too 

 large, maintain that it is sufficient to replace it by some other 

 single number, and that the employment of the varying coeffi- 

 cients a + jSN is unnecessary; they support this opinion by 

 showing that in Dr. Mills's own experiments the alterations in 

 the value of C, caused by the introduction of the term /3N, do 

 not amount to more than one or two hundredths of a degree, 

 and are therefore insignificant. Dr. Mills, replying to this, 

 states that the change in the correction C brought about by 

 the term |3N often amounts to so many hundredths of a degree 

 that it cannot be neglected. 



Now it is clear that by merely placing a second thermometer 

 halfway up the exposed thread, only the roughest idea is ob- 

 tained of the real temperature of the thread. Suppose, for 

 example, that T=100°, and that t is taken at 15°, being sub- 

 ject to an error of 5° : the value of (T—t), which is 85, will 

 be subject to an error of 5°, or about 6 per cent. What, 

 therefore, can be the use of attempting to determine the coeffi- 

 cient (3, of which the value would appear ordinarily to be about 

 0*0000002, when so great a source of error is left unprovided 

 for? 



In all experiments in which I have had occasion to use 

 mercurial thermometers, I have endeavoured to avoid any cor- 

 rection for the exposed thread, by making the apparatus and 

 thermometers employed of such relative dimensions that the 

 whole thread and bulb, except the topmost division, are at the 

 same temperature. When this is impossible, and when the 

 experiments require such extreme accuracy, it seems to me that 

 the first thing to be done is to surround the exposed portion of 



