REPORT ON THE PRESSURE ERRORS OF THE THERMOMETERS. 29 



It is here that the tube first gives way to pressure, and it does so probably because of radial extension. 

 For the expression (b), above, is, for glass, numerically per ton of pressure 



__ ? / 1 . oi 1 \ 



aJ-o^SlOO ^32007 ' 



This vanishes, or there is no radial compression, whatever be the external pressure, when 



= 1-6a o. nearly, 



as stated in the text above. It is worthy of notice that this expression is independent of a^, and thus 

 that, in all tubes, if the outer radius exceeds the inner at least in the proportion of 1-6:1, there is a 

 cylindrical element whose thickness is not diminished by compression, and its radius is in all cases 

 1-6 times that of the inner bore. For all values of r less than this there is radial extension, and its 

 utmost value is at the inner surface, where for T tons pressure it amounts per unit of length to about 



T 4 



_ __ _ 

 5300 al-al' 



From some experiments made for the purpose, I find (Proc. E.S.E., 1881) that ordinary lead glass 

 gives way when the shear is about ljj^ (coupled with 5 <jth of compression in all directions). 

 It is not clear whether it is the shear or the mere radial extension (in this case = 3 4o) under which 

 the glass yields. This question is of importance when we consider internal pressure. At any rate, it 

 follows that no tube (of this kind of glass), however thick, can stand more than about 14 tons external 

 pressure. [The calculations here given are, of course, based on the assumption that glass accurately 

 follows Hooke's Law until it gives way. This is certainly not quite exact, but we do not yet know 

 the amount of the deviation. I hope to approximate to it by the comparison of gauges of different 

 thickness. But the true effects cannot largely differ from those based on the assumed generality of 

 Hooke's Law.] 



"WTien the pressure is internal we have 



' dx oJ- 



whence the corresponding conclusions may be drawn. In particular, the increase per unit volume of 

 the substance of the tube is 



n oj 



k a*-a*' 



which, in thick tubes of small bore, is very small compared with the compression produced by the 

 same pressure applied externally. Also the increase per unit volume of the interior is 



In very thick tubes of narrow bore this is roughly , the value of which in glass is about 7^0- only 

 for one ton pressure. Also, according to the two separate hypotheses above, the utmost internal pres- 



