C. Barus — Resistance of Stressed Glass. 343 



molecular break-up. It is therefore necessary to estimate the 

 value of the former influence. 



The radii of the tube being p 1 =-26 em and p. 2 =-19 cm , the sec- 

 tion is about q='l cm \ Supposing the tenacity of glass to be 

 6 - 5 XlO 8 dynes per square centimeter, this tube should bear 

 65 kg. Tubes are rarely free from imperfections, such as 

 result from insufficient annealing, and it is moreover difficult 

 to apply traction in an experiment like the present, without 

 some flexural or other strain across the section (tendency to be 

 crushed between the slabs, A, B, at the supports for instance). 

 Hence I found it practically difficult to strain these tubes with 

 more than a pull of about 25 kg., without producing rupture. 

 But from all this it appears clearly that the longitudinal ex- 

 tension produced by 18 kg. is much below the maximum for 

 the given dimensions and mean strength of tube. 



If the tenacity of glass be 6*5 XlO 8 and Young's modulus 

 5*5xlO u , the values given by J. D. Everett,* then the maxi- 

 mum longitudinal extension is '0012. Again since Poisson's 

 ratio for glass is nearly £, it follows that the corresponding 

 radial contraction is about - 0003. 



Finally the resistance R of a hollow-cylinder, of length Z, 

 radii p y and /? 2 , and specific resistance s, to conduction across 

 the walls of the tube is (M being the modulus of Brigg's 



s s 



logarithms); £=^r^ 7 lo g pjp^'^^ log pjp, . . . (1). 



To evaluate the resistance effect of elastic change of dimen- 

 sions, R is to be regarded as a function of I, p 1 and /? 2 . In 

 view of the symmetrical occurrence of the last two variables, 

 and if the simplifying relation 4idp 1 / p 1 =4cdp 2 /p i =dl/l, nearly, it 

 follows that dR'/R=(dR'/dl)dl/R+(dR / /dp 1 )dp 1 /R+(dR'/dp 2 ) 

 dp 2 /R= — dl/l, where the accent has reference to elastic change. 

 Nevertheless radial contraction enters in case of an apparatus 

 of the form figure 1, in which decrease of bore during traction 

 lengthens the column of mercury contained. If X be the length 

 of this column before stretching, its length during stretching 

 is X(l-\-2dp 1 /p 1 )=X(l+(l /2)dl/l). Hence in consequence of 

 elongation of the mercury column, dR"IR— — {Xj 21) dl / 1, nearly, 

 where I is the length of the hot part of the column. Hence 

 the elastic discrepancy is 



{SB + dB")/B=-(l + \/2l)dl/l (2). 



In none of my apparatus did X exceed 2*5 I. Moreover X is 

 always one shank of a IT-tube. Therefore "003 may be as- 

 sumed as a decidedly superior limit of the numeric of equa- 

 tion (2). 



* Everett : Units and Phys. Constants, p. 56. These data are reduced from 

 Eankine's "Rules and Tables," p. 895. 



