EXPANSION OF LIQUIDS. 35 



We may use these values to give us the specific gravity at any 

 temperature. For if p is the specific gravity at and if p t is that at t" 

 and A is the expansion of unit volume at when raised to t, we have 



Po = Pt (l+ A). 



The specific gravity of mercury at is, according to Regnault, 

 13 '596. Then the specific gravity at 100, for example, is 



Po _ 13-596 _ . .._ 

 />ioo- 1+A -pol82- 



Determination of Liquid Expansion, using the known Ex- 

 pansion of Mercury. We may use our knowledge of the specific 

 gravity of mei-cury to gauge a vessel at different temperatures and then 

 fill it with a liquid of which we require the expansion. Two methods 

 are employed, one which we may illustrate by the use of a specific 

 gravity bottle, the other in which a dilatometer, virtually a thermo- 

 meter bulb, is used. 



Specific Gravity Bottle Method. In its original form the specific 

 gravity bottle is a flask of thin glass with carefully ground stopper 

 perforated by a very fine tube. When the bottle is filled with liquid 

 and the stopper is inserted, the excess of liquid is forced out through this 

 tube, and it is assumed that the stopper takes a definite position. There 

 is a newer form in which the bottle is a U-tube with two fine tubes 

 turning out horizontally from the ends of the U and provided with 

 stoppers. A mark is made in each fine tube, and the liquid occupies the 

 U and the fine tubes to the marks. Any excess of liquid may be easily 

 removed. 



The first aim is to determine the expansion of the bottle. For 

 simplicity, we will suppose that we are going to heat it from 0. to 

 100 C. We first fill the bottle, when surrounded with ice at 0, with 

 mercury, and find the weight W of this mercury. Then we fill it when 

 surrounded with steam at 100 and we find the new weight W 100 of the 

 mercury. 



Let V be the internal volume of the bottle at 0. and 



Y 100 100 C. 



Let p a be the density of mercury at and 



Pm " 100 



Let G be the expansion of 1 cc. of the internal volume of the bottle 

 from to 100 



7 mercury. 



Then V 10Q = V 8 (l + G) and Po = Ploo ( 1 + y). 

 From the weighings 



V = W / Po : V 100 = W 100 //>ioo- 

 Then Y (l +G) = W m / Pm . 



w w 



and w .?(l+G)= ^ 



Po Pm 



W n W 



^f-^-^ 1 ^ 



Since we know y we obtain 1 + G. 



