720 Dr. G. W. C. Kaye on the Expansion, and 



over the range - 190° to + 100° 0. by the formula (also given 

 above) 



lt ~~ =:(-388f + -001682£ 2 --0- ) 504* 3 ) 10~ 6 . 

 'o 



which indicates a minimum length at —84°, and that the 

 length at — 157° is equal to the length at 0°. 



Dorsey* in 1907, using Fizeau's method, worked over a 

 range of —170° to +10° C. with two samples of silica 

 tubing, one transparent, the other not. The latter shows 

 results which are out of sequence. The results for the trans- 

 parent specimen are given by Dorsey as coefficients of ex- 

 pansion for isolated ranges of 20° round and about various 

 temperatures selected. To facilitate comparison these results 

 have been graphically interpolated by the writer, and so 

 caused to yield the expansions at a suitable number of equi- 

 distant temperatures — from which by summation the values 

 of (l t — l]o)ll\o* and thence of (l t — Z )// , were obtained by 

 making use of Ohappuis' and Schetd's results (above) for the 

 range to 10°. A selection of these final values thus 

 obtained are tabulated (along with ScheeFs) in Table II. 



Table II. 



Temp. (0- 



ik-k)lh. 



Scheel 



, 1907. 



Dorsey, 1907. 



(Heraeus.) 



(Zeiss.) 





xio~ 6 



xio -6 



xio -6 



-10° C. 



-19 



-37 



-3-2 



-20 



-34 



-70 



-61 



-50 



-4-9 



-146 



-129 



-80 



-2-1 



-17-7 



-14-7 



(-84) 



(+0-6) 



(-17-7) 



(-146) 



-100 



+2-1 



-149 



-13-4 



-150 



+21 



-34 



+ 4-0 



-190 



4-47 



4-21-6 



+17-2 (-170°) 



Their graph indicates a minimum length at —77° and gives 

 Z_ 145 =/ , Dorsey's non-transparent specimen also showed 

 a minimum length at about —80°. Having regard to the 



* Dorsey, Phys. Kev. xxv. p. 88, July 1907. 



