Density of Water with the Temperature. H3 



data we may deduce that ordinary glass between 0° and 

 300° undergoes a change of volume indicated by the equation 



and the linear expansion of glass by- 



^=1+0-000027 t. 

 The apparent expansion of mercury, as observed in the glass thermo- 

 meter, will be -t- , and at 100° it will equal 1-015459. Every degree of 



the mercury thermometer will correspond to a volume of 0-00015459, 

 and 50° of the mercury thermometer will answer to an apparent volume 

 of 1*0077295. The question then arises, What will be the true tem- 

 perature t, above or below 50°? When £=50°, the apparent volume 



equals ~ o U1350 = 1'0076896 : hence the difference between this volume and 

 that at which the mercury thermometer shows 50° is equal to 00000399, 

 corresponding to o- 258 nearly. Therefore, if the variation of the volume 

 of the glass were expressed lineally (t, e. if the coefficient of expansion 

 of glass were constant), then, when the mercury thermometer showed 

 50°, the true temperature would be 50° -258 and the correction for the 

 readings of the mercury thermometer would be positive. This correction 

 would remain positive so long as the variation in the coefficient of 

 expansion of glass were less than that of mercury ; for which latter the 

 value of b in the parabola V = l-\-at-{-bt 2 is 9000 times less than a. But 

 when this relation grows greater for glass, then the correction will be- 

 come negative. Let us illustrate this by an example, taking the same 

 expansion for mercury as above, and for glass 



vt = l +0-000025 £+0-00000002 t 2 ; 



i. e. let us suppose that its coefficient of expansion changes more rapidly 

 with the temperature than mercury. The apparent expansion of mercury 

 up to 100° will be as before, since the volume of the envelope will be 

 1-0027 at 100° ; therefore one degree will again correspond to 0-0001546 

 of the volume and a reading of 50° on the mercury thermometer will be 

 obtained, when the apparent volume equals 1-0077295. But at the true 



temperature £=50°, the apparent volume will be 1 . 0ol5 ^ i) = 1*0Q77391. 

 Hence when the mercury thermometer shows 50°, then the true tempe- 

 rature will be 49° -938, and the correction for the readings of the mercury 

 thermometer at 50° will then be negative. All the investigations which 

 have been made on the corrections for mercury thermometers by com- 

 paring them with the hydrogen thermometer, show (as mentioned in a 

 subsequent note) that the correction for readings, verified in every other 

 respect, of mercury thermometers is negative • i. e. the true temperature 

 is Lower than that shown by a mercury thermometer which has been 

 corrected for zero, calibre, &c. throughout the entire range from 0° to 100°. 

 Hence it is clear that (1) the variation of the volume of glass does not pro- 

 ceed according to a linear function of the temperature, which is the same 

 in the case of the expansion of mercury (the latter follows from Regnault's 

 determinations of the true expansion of mercury) ; and (2) the coefficient 

 of expansion of glass increases relatively more rapidly than that of mercury. 

 I thought it well to demonstrate the last two propositions for three 

 reasons: — (1) I have nowhere met with a simple, objective treatment of this 

 subject ; (2) generally the proportionality of the expansion of glass to tin- 

 temperature is adopted without further discussion, or else the absence of 

 this proportionality is considered as not proved, Hagen, Matthiessen, and 

 others being cited; and (3) in the question of the expansion of water. 

 true data for the expansion of glass are of very great importance. 



Phil. Maq. S3. 5. Vol. 33. No. 200. Jan. 1892. 1 



