High Temperatures. 175 



The difference between the observed expansions and those 

 calculated according to the formula amounts in both cases to 

 less than 0-01 mm . 



The largest measured difference between the observations 

 upon the cold bars before and after heating to 1000° was 

 O025 mm ; it was generally much smaller. 



Porcelain. — The expansion of Berlin porcelain was also 

 measured upon a bar of similar dimensions — unglazed in order 

 that it might afterward be used at still higher temperatures. 

 Plane surfaces were ground upon each end in the same posi- 

 tions as for the metallic bars, and upon these, divisions about 

 - 15 mm wide but very sharply defined were cut upon a lathe 

 with a thin copper disc, five at each end. The readings at the 

 highest temperature were at first somewhat difficult, for the 

 divisions are but little brighter than the background. With 

 illumination from outside, however, excellent readings could 

 still be obtained after the candle power had been increased. 



This bar had a mean length at 0° of 4:8347 mm and yielded 

 the following results for the expansion : 



A s (mm) 



t 



Observed. 



Calculated. 



S^yiULLlJ 



250° 



0-382 



0-391 



0-790 



375 



0-628 



0-612 



1-299 



500 



0-845 



0-850 



1-749 



625 



1-093 



1-105 



2-261 



750 



1-307 



(1-377) 



2-703 



875 



1-615 



(1-666) 



3-340 



1000 



1 977 



(1-972) 



4-089 



Observations were made with the porcelain bar. at tempera- 

 tures between the original four, when it was found that the 

 observed expansions could not be represented by a curve of the 

 second degree. The following formula is approximately true 

 between 250° and 625°, 



A = [2954 t + 1-125 t 2 ] 10" 9 



and yields the observed value again at 1000°, while for 750° and 

 875° the differences are considerably larger than the errors of 

 observation. Below 250° also the values obtained from the 

 formula are too large. The coefficient of expansion clearly 

 increases more rapidly after red heat is reached than below 

 500°, and for the interval between remains nearly constant. 

 The observed value at 1000° coincides with the calculated 

 value again, which shows this temperature to be the point of 

 intersection of two curves. 



It may be further remarked that the various series of obser- 

 vations, after the preliminary heating to remove any tension 



