240 
MR. J. J. MANLEY ON THE APPARENT 
volumes ; also, that whilst the one is a true sphere, the form of the other is ellipsoidal. 
It follows, therefore, that although the volumes are identical the superficial areas of 
the two vessels will be somewhat different. 
I desire to express my indebtedness to Mr. H. Hilton, formerly Fellow of Magdalen 
College, Oxford, for his kindness in determining for me the changes that occur in the 
superficial area of a prolate spheroid as the ratio of the major and minor axes is varied 
within the limits 1 : 1 and 1 : O'667. Mr. Hilton’s results are here given in tabulated 
form :— 
Ratio of axes of prolate' 
spheroid of volume 
= 200 c.c. 
' 
0-95 
0-90 
0-80 
0-75 
0-667 
Surface of spheroid in' 
square centimetres 
. = 165-39 
165-48 
165-71 
166-79 
167-71 
169-93 
From the above data it follows that when the ratio of the axes is 1 : 0'765, the 
superficial area of the spheroid is greater than that of a sphere of the same volume by 
2 sq. cm. Very similar changes are found for corresponding oblate spheroids. 
(6) /Sg. Of the Weight of a Water Shin on the Surface of Jena Glass. —^Having 
satisfied ourselves that the superficial areas of two vessels of similar form and equalised 
volumes may differ considerably, the next obvious and important step in our enquiry 
was to determine, as accurately as possible, the weight of water vapour that might 
condense upon a glass surface. It is well known that glass is hygroscopic, and that 
difierent varieties of glass exhibit distinctly different hygroscopic properties. In all 
the final experiments described in this paper, vessels of Jena glass only were used ; we 
therefore confine our attention to that particular glass and its comportment towards 
aqueous vapour. 
By repeated trials we at last obtained a suitable and almost perfectly spherical bulb 
of Jena glass ; the attached tube, which was short and of small diameter, was drawn 
out and bent round so as to form a small hook, the tip of which was sealed before the 
blowpipe. A small stool bridged one of the balance pans and upon it was placed a 
cylinder containing a little distilled water. The glass sphere was then, by means of 
a fine silver Vvdre, suspended from the balance and placed within the cylinder and as 
near the water as circumstances permitted. Observing the usual precautions for 
refined weighing, the apparent weight of the sphere was repeatedly determined ; when 
its weight was found to remain constant the water was removed from the cylinder 
and a similar volume of concentrated sulphuric acid introduced. After the lapse of 
some considerable time the apparent weight of the sphere was repeatedly re-determined. 
The barometer was read and reduced for temperature, and the temperature of the 
balance case noted at intervals ; finally, the mean diameter of the glass sphere was 
measured and the corresponding external area calculated. We now possessed all the 
