168 BUCKINGHAM: STEM CORRECTION OF THERMOMETERS 



coefficient of apparent expansion of mercury in the glass of which 

 the stem is made between f and f°, both of which are to be 

 expressed in terms of the scale used during the standardization. 

 The correction is often of importance and may in extreme cases 

 exceed 30° C. The two chief methods for determining it are those 

 described by Guillaume and Mahlke. 



In Guillaume's method, the quantity A is determined directly % 

 as a length. An auxiliary stem similar to a portion of the work- 

 ing stem, closed at both ends, partly filled with mercury, and pro- 

 vided with a scale of equal parts, is placed parallel and close to 

 the working stem and with its meniscus at the same level as that 

 in the working stem. The auxiliary stem must be long enough 

 that its lower end reaches into the region of uniform temperature 

 containing the bulb of the main thermometer, and the mean 

 temperature of the mercury column in the auxiliary stem is then 

 very nearly equal to that of the neighboring column of the same 

 length in the working stem. If the auxiliary stem were now 

 totally immersed the change in its reading would evidently be the 

 desired value of A. 



If the conditions are such that total immersion of the auxiliary 

 stem is possible the determination of A becomes extremely simple. 

 The scale reading of the auxiliary stem is taken in the position 

 described above. The instrument is then totally immersed, left 

 a short time to take the temperature of the bath, raised again 

 just far enough for observation of the meniscus, and read immedi- 

 ately. The glass of the stem being thick and a poor conductor, 

 this second reading is very nearly the exact reading for total 

 immersion. The difference of the two readings is the value of A 

 in terms of the scale on the auxiliary stem. 



If total immersion at the time of use is not possible, the auxili- 

 ary stem may be standardized separately and once for all by total 

 immersion in baths of known temperatures, so that its reading 

 for total immersion at any temperature f may be found from a 

 table. If t, which is the desired temperature, is known approxi- 

 mately, an approximate value of A may be found from a single 

 reading and the table. Greater accuracy requires a second 

 approximation by using a corrected value of t. For very accurate 



