205 
of Edinburgh, Session 1880 - 81 . 
By means of a small telescope, with a micrometer scale in the eye 
end, the ratio of the internal and external radii was measured for 
each end of each tube. The tube was then cut into five, seven, or 
nine lengths, and these were numbered (in order) by marked slips 
of paper inserted into them. They were then carefully and strongly 
sealed at each end, a small quantity of shot being put into each to 
make them sink in water. 
By means of the external gauge I have already described to the 
Society, the pressure at which Nos. 1, 3, 5, &c., gave way was 
measured, and it was found that when the tube from which they 
were cut was stronger at one end than at the other, the break- 
ing pressures for the separate pieces were in the proper order of 
magnitude. The results were, as was to be expected, not very 
accordant ; but, as a fair average result, the common lead glass 
gives way when subjected to a shear of about 1 ± — L 
(combined with a compression of about 
1 
600 
in 
every direction). 
Hence a very thick tube of such glass will not resist more than 
about 14 tons weight on the square inch of external pressure. 
The formulae from which this was calculated are given in my 
paper of May 17, 1880 (Proc., vol. x. p. 572). They give, for a 
pressure of one ton weight per square inch, the following for the 
innermost layer of a cylindrical tube of external and internal radii 
eq and a 0 : — 
Kadial compression 
a , 
a i ~ a o 2 
Tangential 
Longitudinal 
a. 
a. 
8100 
1 
+ 
2 -« A8100 ‘ 3200 
3200/ ’ 
joo)’ 
a. 
a n 
af 8100° 
The first terms of these expressions indicate a uniform compression, 
the other terms the crushing shear. [It is curious to note that this 
compression is less (for the same pressure) in a solid rod ( a 0 = 0) 
where there is no shear, than in a tube.] 
The walls of these tubes, when they gave way, were crushed into 
fine powder, which gave a milky appearance to the water in the 
compression apparatus. But the fragments of the ends were larger, 
