the Elements Carbon, Boron, and Silicon. 



167 



T 2 — T\, ...T ra — T n _! fulfil certain conditions. Between y T and the 



systems 



w w w 



T„, T,, T e 



, T 3 ,...Tj 



To 



the relations hold good : — 



dT, 



W ( 



,= G( T y T dT, 



VT 



w 



Tt„ 



■=<M r. 



^T 



dT. 



If the differences T,-T , T 9 -T„ . . . T n -T n _! of the limits 

 of integration be taken so small that the parts of the area between 

 them are represented as trapezes, we may set down the following 

 equations : — 



W 1 



W -¥, 



GC^-TJ 



: y T , 



w ,-w lt . 1 _ 



How great the differences of the values T , Tj, T 2 , . . . T n may be 

 taken without introducing material differences between the true 

 values ofy T and the values as calculated depends upon the nature of 

 the functiou y T . Preliminary experiments proved that the average 



W — W _ 



specific heat -~£ — „" * of the elements carbon and boron 



within the temperature-intervals 0° to 100°, 100° to 200°, and 

 200° to 300°, altered almost with the temperature. For these 

 two elements, therefore, the temperature-differences T L — T , 

 T 2 — Tj, . . . may rise to 50°. At high temperatures, between 

 500° and 1000°, experiment showed that the specific heat of 

 carbon changed but very slightly as the temperature rose; within 

 these limits, therefore, the temperature-differences may amount 

 to 200°. For silicon, as the result of experiment, from 100° to 

 200° a temperature-difference of 50° was allowed ; from 0° to 

 100° this difference must not exceed 30° to 40°. 



The methods and the apparatus by means of which the values of 



