36 HEAT. 



We can now use the bottle to determine the expansion of any other 

 liquid between and 100. Let 1 cc. of the liquid ut expand to 1 + A 

 at 100, and let <r , cr 100 be its densities at and 100. 



Then o- = o- 100 (l + A). 



Filling the bottle first at and then at 100 let a> , w 100 be the weights 

 of the liquid. 



We have o- = <o /V , and tr m = w 100 /V 100 . 



Then 1 + A = = -^ ^P. 



"ioo w ioo v o 



- -"(1+G). 



Whence we know A. 



Dilatometer Method. The dilatometer is now usually made in the 

 form represented in Fig. 26. B is a bulb with a fine graduated stem, s, 

 rising from the bulb and open at the top. Below, the bulb is con- 

 nected with a fine-bore tube with a slight thickening at t and open at e ; 

 st, is a screw stopper which can be put over the end of this tube, being 

 sprung over the thickening. On screwing the stopper, a pad effectually 

 closes the opening. This form of apparatus is very readily cleaned and 

 filled. 



First we must calibrate the bulb and stem, and measure its expansion. 

 Let W be the weight of mercury, density p , filling the bulb at from 

 e up to the zero of the scale. Then the volume V = W //o . 



Let the weight of mercury filling an observed number of divisions of 

 the stem be found. From this the volume of each scale division in terms 

 of the volume of the bulb can be found. Let it be AV . A, will be a 

 very small fraction. 



Now start with the bulb filled with mercury at up to the zero, and 

 raise the temperature to 100. Suppose that the mercury rises N 

 divisions. 



Let V expand to V 100 = V (l + G). 



Then the total volume of the mercury is 



V :00 + NAV 100 - V (l + G)(l + NX). 



:00 100 



But if y is the expansion of mercury we have 



V (l+y) = V (l+G)(l + N 



Whence 



Now repeat this operation with the liquid, of which the expansion 

 is to be determined, and let it rise from the zero division through n 

 divisions when the temperature is raised from to 100. Let 1 cc. 

 expand to 1 + A cc. Then the total volume at 100 is V 100 (l +n\) 



But this is also V (l + A). 



