426 
MESSRS. T. E. THORPE AND J. W. RODGER OH THE RELATIOHS 
marked ends served, of course, to give the dimensions of the bore at the ends of the 
length BC. In each case the length of the major and minor axis of the elliptical 
section of the bore vras determined. The method employed was as follows :— 
One of the pieces, AB or CD, was fixed vertically in a cork, the marked end upper¬ 
most, and projecting a millimeter or so above the cork. The cork was placed 
centrally in a circular brass disc, on the circumference of which were four marks 90° 
apart. This disc stood on a piece of paper, on which were ruled two lines at right angles 
to one another, the marks on the disc coinciding with the lines on the paper, and the 
whole arrangement placed so that the section of the bore of the tube was in the 
field of the telescope of a horizontal cathetometer, which was graduated to read to 
•0001 centim. By rotating the cork, the major axis was, by trial, brought parallel 
to the cross-hair of the telescope, and the minor axis was then measured. On 
rotating tlie disc through 90° by means of the marks on its circumference and the lines 
on the paper, the major axis could next be ascertained. 
Some thirty measurements made in this way gave the following mean values 
observed at 17°‘2 :— 
Major axis. 
Minor axis. 
End . 
•017207 
•016175 
End Bo 
•017200 
•016412 
Correcting for the expansion of the glass and of the scale of the cathetometer, these 
numbers give at 0° as values for the mean section of the bore of the tube 
Semi-major axis, '008603; semi-minor axis, ‘008148. 
If these measurements could have been taken as absolute lengths in centimeters, no 
further observations need have been made on the dimensions of the section of the 
tube. It is very difficult, however, to obtain an instrument which will give such 
readings for lengths so small; we have, therefore, regarded the above as relative 
measurements, and have obtained the true lengths of the semi-axes by combining the 
preceding measurements with what we have taken as the true mean radius of the tube 
as determined by weighing with mercury, in the manner shortly to be described. 
On receiving the glischrometer from the maker, the first point to decide was 
whether the bore of the tube had been modified in the process of sealing. A thread 
of mercury was introduced into the tube of such a length that it could be measured 
when on either side of the zone of sealing, or when its central portion was in the 
region of the zone. Eighteen measurements were taken by the horizontal cathe¬ 
tometer, six wlien the thread was in somewhat difterent positions in each of the three 
regions indicated above. The following mean values were obtained:— 
