;_' Mi;. K H. SMITH ON TIIK CONSTKTCTIOX OK 



taken from HOVESTADT'S treatise on Jena glass. The values given are 0-0000231 for 

 Jena 16'" glass and 0'0000222 for Verre dur. 



For each tube, L and the corresponding W were determined for several different, 

 I nit approximately equal lengths, the extremities of the columns being situated in 

 approximately the same positions. The measurements were made at some temperature 

 other than 0C., as will be seen by reference to Mr. KEKLINO'S report. A correction 

 was therefore necessary. 



Let L, be the length at t C., corrected for all inaccuracies of the standard metre 

 employed, the expansion of the same, and inclusive of the equivalent lengths of the 

 menisci of the mercury column. Let W 2 be the corresponding weight of the mercury. 

 Then the mean cross-section S of the tube at t C. is equal to W 2 /L 2 A(l yt), 

 where A, as before, is the density of mercury at 0C., and y is the coefficient of 

 cubical expansion. 



If /8 be the coefficient of cubical expansion of the glass, then the mean cross-section 

 So at C. is W 2 /L 2 A (1 yt) ( I I/ft), the glass being assumed as isotropic. 



The mean cross-section Sj of another length L,, nearly equal to L^, and occupying 

 approximately the same position, may now be found with the aid of the formula on 

 p. 63. For S^ = L,/\ L 2 + I' (1 - a;) + /" ( 1 - //) J-. 



On each standard tube an indicating mark was etched. When the observations for 

 L 2 were made, the distance of this mark from the nearest extremity of the column 

 was noted. The lengths /' and I" were thus calculable. The standard length Lj 

 depended on the final grinding of the tubes ; its exact position having been noted 

 on the calibration curve, the mean line of the standard portion of the curve was 

 obtained with an Amsler planimeter, the result afterwards being checked by 

 calculation. The area bounded by that portion of the axis designated by /', the 

 two ordinates passing from its extremities to the curve, and the portion of the curve 

 thus isolated, was similarly found. In general, the mean line of this small area 

 differed in position from that of L 1( but the ratio of the cross-sections was immediately 

 determinate. Unit value being assigned to the cross-section of L 1( that of /' was 

 found and is denoted in the formula by x. Similarly that of I" is represented by y. 



As an example of the calculation, the first measurements of the tube M (see also 

 Table III.) are given. 



In this example 



La = 59 centims. approximately. 



/' - 0-25centim. x = 0-9942. 



/" = - 0-46 centim. y = 1-0090. 



Hence 



(1 - r) = 0-0058 and (1 - y) = - 0-0090, 

 and 



W{L,> + I' (I - x) + I" (I - i/)J = 59. (59 - 0-00145 + 0'00414), 



