Manchester Memoirs, Vol. Ixv. (1921), No. 5 5 



But we have, accurately 



2d 2 = Rh 2 ..... (iv) 



and therefore comparing (iii) and (iv) 



R = //i +I£- 0*1288^) . . . (v) 



We have from (iii) to a first approximation 



, 2d 1 



h = — , 

 r 



and to a second approximation 



or 



a, = — — *£ 



1 r / r J 



h* 2a 2 \ 6a* 



*-2 



Substituting the exacter value in the second term on the R.H.S. of 

 (v) and the more approximate value in the third term we obtain, after a 

 little reduction 



R " l 1 + 5? " °'°° 4 V 



or, quite accurately enough for our purpose 



R *\ t + &) • • • ■ H 



Substituting this value of r in equation (ii), expanding and neglecting 



r L 



terms of order higher than -^ we have finally 



T = g r -(pA - ph) + gP? . . . (vii) 



as the working equation from which to calculate the surface tension. 



The cathetometer used by us was constructed to read in inches. In 

 our case, therefore, equation (vii) takes the form 



T = gr x 1-27(0^ - ph) + g -^- 



= A{pA - P h) + &£ . . . . (viii) 



gm. 

 where densities are measured in - — , r is measured in cm., and ft, and h in 



c.c. l 



inches. 



With one of our tubes, r — 0*03317 cm., and consequently 



log A = 1*6162. 



The table immediately following gives the figures obtained in a de- 

 termination of the surface tension of benzene. 



