BY HEAT OF "WATER AND MEECUET. 24? 



The volumes of the glass were subtracted from the volumes of the water displaced, to 

 find the volumes of the mercury for 



where Uo is the volume of mercury at 0", b its coefiicient of expansion, W,(l+a,i) the 

 volume of the water displaced, and W„(l+«#) the volume of the bucket. Calculating 

 the relative coefficients of expansion of mercury for each series, and deducing by means 

 of these the volumes of the mercury at 0°, we arrive at the following formulae : — 



For Series I. U,=2-97477 + 0-0005400^. 



„ II. U,=3-18832+0-0003782#. 



„ III. U,= 3-03998+0-0005496i. 



„ IV. U,=4-07168+0-0007364!?. 



V. U,=4-30424+0-0007816#. 



It will be seen that the volumes calculated by these formulae agree closely with those 

 observed. 



The above formulae may, however, be written as follows : — 



I. U,=2-97477(l+0-0001815^), 

 II. U,=3-18832(l+0-00018130, 



III. U,=:3-03998(l+0-0001808^), 



IV. U,=4-07168(l+0-00018080, 

 V. U,=4-30424(l + 0-0001816^), 



where the coefficients are referred to the volumes of mercury at 0° equalling unity. 

 The mean of the coefficients is 



0-0001812, 



a number closely agreeing with Regxault's, namely, 



0-0001815. 



The above five series also prove that the air absorbed by the water during the time of 

 weighing does not influence the results ; for in Series I. the water in the cylinder Avas 

 boiled (to free it from air) only once during the time of the observations, the weighings 

 being made at the highest temperature first, and then on cooling the water gradually the 

 other weighings were taken, the water in the box not being stirred at all. 



In Series II. same remarks as for Series I. 



In Series III. the water was twice boiled, namely, before taking the weighings at 

 94°-0 and 44°-6 ; otherwise same remarks as for Series I. 



In Series IV. the water was twice boiled, namely, before taking the weighings at 

 95°-3 and 4°-7, and 63°-5 and 34°-4; the water in the box in which the cylinder stood 

 being stirred during the weighings. 



