Expansion and Thermal Hysteresis of Fused Silica. 719 

 cylinder of silica prepared by Zeiss. His new formula reads 



-^- = (-388* + -001682* 2 - -0 5 504* 3 ) 10~ 6 , 



which gives results in good agreement with Chappuis' over 

 the same range. 



The results in Table I. give for the range 0° to 100° some 

 values of (l t — lojjlo* derived from the above formulae. 



A result of Randall's (see later) at 80° is also tabulated. 



Table I. 



Temp. (t). 





(h-lo)/l - 





Chappuis. 

 1903. 



Scheel. 



Randall. 

 1910. 



1903. 



1907. 





X10" 6 



xio" 6 



X10' 6 



X10" 6 



10° C. 



4-0 



34 



40 





16 



6-4 



5-5 



66 





20 



8-2 



7-0 



8-4 





50 



22 



20 



23 





80 



38 



35 



39 



33 



100 



50* 



47 



50 





* Extrapolated. 

 Low Temperatures. 



At low temperatures the experiments of Scheel and of 

 Dorsey claim attention. In January 1907 Scheel f pub- 

 lished some results dealing with the expansion over the range 

 — 190° to +16° C. of a silica cylinder made by Heraeus. 

 These were embodied in the formula 



U — 'o 



(•217* + -00238* 2 ) 10" 



which indicates a minimum length at —46°. 



Later in the year Scheel J gave the results of experiments 

 on],;a silica cylinder made by Zeiss. They are represented 



t Scheel, Bent. Phys. Gesell. Verh, ix. p. 3, Jan. 1907. 

 X Scheel, ibid. ix. p. 718, Dec. 1907. 



