Dixon — Note on the Tensile Strength of Water. 63 



From these observations the tension may be roughly determined according 

 to the formula 



/3 = 



Fi ■ P. - P, 



when |3 = the coefBcient of compressibility of water, Vi = volume under 

 the lower pressure Pi, V^ = volume under the increased pressure Po. A 

 tension = Po will bring about the same change of volume in tlie opposite 

 sense. Evidently the apparent change of volume of the water due to this 

 tension must be corrected for the contraction of the glass cooling through the 

 range of the experiment. This may be allowed for by the formula 



(5ll-a{t,~t,)\' 

 T = tension ; 



a = coefficient of expansion of water over the range ; 

 g = coefficient of cubic expansion of glass = 2*4 x 10"'^ ; 

 ti = temperature of rupture ; 

 4 = temperature when tube is full. 



Introducing the correction for the elastic yield of the glass, this becomes 



y,^ (g - cj) {h - h) . 



1 fr'^ N^ 



B' - r' \7c 

 where li = external radius of tube, 

 r = internal radius of tube, 



k = compression modulus of glass (volume elasticity), 

 n = torsion modulus of glass (torsional rigidity). 



The value of a was obtained from the table of the volume of water at 

 different temperatures in Landolt-Bornstein, Physikaliseh-Chemische 

 Tabellen, by E. Bornstein and W. Meyerhofer, Berlin, 1905, pp. 38 and 39. 

 The compressibility coefficients /3 for different pressures and temperatures are 

 given on p. 60 of the same tables. 



In the accompanying table are recorded the experiments on eight different 

 tubes, and in it are recorded the radii H and r, the observed temperatm-e when 

 the tubes were full f-i, and the temperature at which the rupture took place 

 ti, together with a, the coefScient of expansion for water over the range 

 (4 - ^i), and finally the tension calculated according to the above formula. 



1 1 am iudebted to Mr. J. E. Cotter for adapting these formulae and rendering them suitable for 

 application to these experiments. 



