THE AID OF THE ACHROMATIC FRINGES. 



39 



a brass tube are given in figures 38 and 39 and are quite satisfactory, if the 

 tube is properly protected from loss by radiation. 



If for the steel tube a= io~ 6 Xi2, equations (3) and (6) then give us 



I2XlO- ( 



or about 40 scale-parts of the ocular micrometer per degree of temperature. 



25. Available liquids. It remains to select suitable liquids for experiment. 

 For water at 27, a=io~ 5 X27, ci, p=i, or dd/dp = o.ooiQ; for ethylic 

 alcohol at about 18, a=io- 5 Xno, = 0.58, p = o.'jg, whence d$/dp = 0.017; 

 for ether at 18, a=io~ 5 Xi63, = 0.56, p = o.f2, whence dd/dp = o.o2&, pres- 

 sures being measured in atmospheres. Thus for the four tubes specified in 

 23, the respective displacements in the ocular micrometer would be (per 

 atmosphere) : 



I Ae' = 2.7] water alcohol 



II i.i i A^" = o.o8 0.68 



III 

 IV 



ether 

 1.14 



.6 



The case of water may be dismissed, for here the thermal displacement per 

 atmosphere, Ae", is a small fraction of the elastic displacement in the ocular 

 micrometer. But alcohol and ether show satisfactory conditions. Thus a 

 sudden half -turn of the lever of the screw compressor producing 100 atmos- 

 pheres would displace the fringes, in case of tube III and ether, 173 scale- 

 parts elastically and 114 scale-parts thermally, together 287 scale-parts. 

 Stops of 30 atmospheres would be advisable. Tube IV with 63 (elastic) and 

 114 (thermal) scale-parts, is even more advantageous. All this implies, how- 

 ever, the adequate absence of thermal conduction from liquid to tube, initially. 



It remains to estimate the diminution of A$ owing to the completed parti- 

 tion of heat between the liquid and the tube. If A#' is the increment of the 

 combined system of liquid and tube, the ratio will be 



At? 



>--r\ c p 

 r\* cp 



if c' and p are the specific heat and density of the solid. This ratio for the 

 tubes and liquids in 23 and the corrected ke" are as follows: 



