the Mercury Unit with the British Association Unit, 19 



R, W, r, p, L have already been defined. L is measured 

 in centimetres ; 



fi is the coefficient correcting for conicality of the tube. 

 Let 



L = length of tube at tf°, measured by brass bar at t b '° ; 



I = „ thread of mercury filling the tube at 0°, 

 referred to bar at t b °; 

 Bh = correction to L ; for junction of column of mercury 

 with terminals = *82 diameter of tube ; 



p = specific gravity of mercury at 0° C. =13*595 ; 



y = cubic expansion of mercury per degree ='0001795 ; 



g= „ „ glass „ „ =-000025; 



b = linear „ bar „ „ = "000019 ; 



^o = temperature of brass bar, to which lengths are re- 

 duced, = 8°-7 C. 



W 



Then, volume of thread at 0° C. = — • 



P 

 Mean section of tube at 0° 



W 1 



p l{l + b{t b '-t )} 



= w (1+jgQ 



" p L{l + b(t b '-t )} 

 Reduced length of tube at 0° 



_ (L + 8L){l + b(t b '-t )} 



1 + iK 



Hence 



R _ lQ-V. / t.(L4-8L){l+6(^-< )} pLU+bih'-to)} 

 1 + igf ' W(l+i gt') 



Solving for r, 



WRW(l + ifft'f 



r ~ P/J .L(L + SL){l+b(h'-t () )}{l + b{t b '-t )} 



or 



r=^(l- B ±yi + %ffW-2m'-t<>)}. . (4) 



The ends of the tube containing the mercury opened into 

 the ebonite cups about two thirds filled with mercury. Upon 

 the assumption that these may be considered infinitely large 



02 



