Constants of Igneous Rock, 



13 



advantage inasmuch as the (small) coefficient of thermal 

 expansion is known * . The bulbs are supposed to have been 

 so thoroughly fired at the outset that all permanent volume 

 changes have vanished. It is clear, however, that by using 

 the above manometer in case of the constant-pressure method, 

 the coefficient of expansion of the bulb may also be measured 

 by air volumetry. Let the manometer volume be changed 

 while the (high) temperature of the bulb is nearly constant by 

 varying the manometer pressure. Then, if H l7 V l5 T 1; and 

 H 2 , V 2 , T 2 , be two successive readings of the pressure, volume, 

 and temperature, respectively, at the manometer, and if 

 /(T) = (l + /3T)/(lH-aT), where /3 is the coefficient of ex- 

 pansion of porcelain, and a that of air, it follows that 



H Y 



B 1 Y 1 



ff /(W-^/(Ti] 



/m+Sg/CP))— = nprn 



(i) 



where T is the (high) temperature and v the zero volume of 

 the bulb, and where 2 contains the corrective members (stem 

 volumes and temperatures) . If H 2 be the barometric height 

 for the day, T can be at once computed by the ordinary 

 formula, and /3 may then be computed from /(T) in (1). In 

 the following table the measurements for T alternate with the 

 measurement for /3 in time series, so that corresponding 

 values are given. 



Table I. — Thermal Expansion of Porcelain. 



Time. 



T. 



(ixlO G . 



Time. 



T. 



0x10°. 



m 

 5 



568 





m 

 4 



o 



978 





8 



(564) 



22 



16 



(993) 



37 



18 



560 





24 



1002 





21 



(564) 



26 



26 



(1004) 



27 



40 



567 





32 



1006 





In view of the fact that the quantities on which /3 ultimately 

 depends are of the same order of magnitude as the stem error 

 2 (of which more presently, §§17, 18), this method cannot 



* Deville and Troost, C. R. lix. p. 162 (1864). 



