of cubical expansion, etc. 



325 



at tins temperature on the axis of X we measure the ordinate 

 of the curve of the absolute expansion of water, and this 

 ordinate gives in volume the expansion of the vessel in the 

 determined range of temperature. 



The second method of determining the coefficient of cubical 

 expansion is that of floating a hydrometer, formed of the sub- 

 stance whose coefficient we would determine, in water at 0° C. 

 and then gradually heating the water till the hydrometer floats 

 to the same depth it did when the water was at 0° C. Calling 

 "W the weight of the hydrometer, and Y , D , Y t and D t the 

 respective volumes and densities of the water at 0° and t°, we 

 have Y D =W, and YJD^W, and if Y and D equal unity 

 we have Y^l/D^, or, the volume at t° is the reciprocal of 

 the density at t°, which is the same as if we took Y t directly 

 from the curve of the absolute expansion of water. Thus, 

 by having the true curve of the absolute expansion of water, 

 one may determine by either of the two methods just de- 

 scribed, the coefficient of cubical expansion of a solid without 

 measures of volume, of weight or of linear dimension. 



We will now describe the apparatus 

 used, give some measurements made with it 

 and discuss the accuracy of the methods. 

 Fig. 2 is the brass vessel used. It is a 

 cylinder 25*4 cms. long and 6*147 cms. inte- 

 rior diameter. A glass tube '203 cm. diame- 

 ter of bore is connected with the interior of 

 the cylinder as shown in Fig. 4. Into a 

 brass tube shown black in the figure is ce- 

 mented the glass tube. The lower opening 

 of these tubes, A, is ground into a cone. The 

 shoulder of this tube A rests on a thin leather 

 washer on the top of the tube B. A screw- 

 cap forces the tube A into close contact with 

 B. This manner of attaching the glass tube 

 to the cylinder was devised for convenience 

 in our experiments, but the glass tubes may 

 be directly cemented into the cylinder and 

 thus do away with the inner tube and screw- 

 cap. 



The cylinder is nearly filled with distilled 

 water and a rubber tube is led from the tube 

 of the cylinder into a vessel holding boiling- 

 water. The water in the cylinder is boiled 

 for a half hour and then the heat is with- 

 drawn. As the steam condenses the vessel fills with water. 

 The apparatus is allowed to cool down to the temperature of 

 the room. The cylinder and glass tube is now surrounded with 



