8 PROF. lin:il I.. r.U.I.KNDAR AND MR. HERBERT MO-SS 



till** M-l.lon, .lini-ml in temperature from the gauge by so much as 1 C., and the 

 ,lir -f t.-mprrature t-d in the majority of the ol*ervations was less than 1 C. 



Tl- minimi convetion to the value of h was therefore extremely small, and 

 intr.Nlui-.-d v.-rv littl.- uiuvrtainty in the reduction. 



r,,iisul.-iiii^ the equilibrium of the columns, we have the hot column H 2 at a 

 t,-m|M-ratun- /,, together with the difference of level h in the gauge at a temperature 

 f. lwlnno-d liy tlit- cold column H, at a temperature t it together with the cross tubes 

 '/If at a temperature t. The mean coefficient of expansion ia a between ti and t a in 

 trims of the volume at t t , which is the coefficient most directly given by the 

 observations, is easily obtained by reducing the columns to a common temperature t\. 

 We thus obtain the equation 



-00018 (-*,)} = H, = H,-dH, . . (l) 

 which, with a few simple approximations in the small terms involving h, reduces to 



A'), ......... (2) 



where // denotes the corrected and reduced value of h given above. 



The expatision between t t and t 3 may further be expressed as a fraction of the 

 volume at O e C. by multiplying by the factor (l + 0'00018* 1 ). The uncertainty of this 

 reduction will not exceed 1 in 40,000 unless ti exceeds 25 C. Thus, 



Mo (f.-fi) = (l + 0'00018,) A'/(H 2 -//), ...... (3) 



where (,a,) denotes the mean coefficient *, to t a in terms of the volume at C. 



The expansion between C. and t a in terms of which the results are generally 

 tabulated, may readily be deduced by adding the expansion between C. and fc to 

 that between f, and t, in terms of the volume at C. Thus, 



(4) 



but this involves a correction of quite a different order of magnitude, and requires the 

 >f ai to be accurately known, unless ti is very small. 

 two last reductions may be included together in the formula 



A', ........ (5) 



but since the correction term ^ lH , may be nearly as large as h', it is desirable to 



from the 





