1887. ] Permangame Acid. 115 
to that in the first flask, and this deposit increased perceptibly 
upon standing for some time. 
Finally a piece of freshly cut metallic sodium was introduced 
into a third similar flask containing the manganese gas. It 
gradually acquired a purplish tint, totally different from the ap- 
pearance which sodium assumes when exposed to the air. 
The existence has thus been proved of a gaseous manganese 
compound, which appears to be colourless but which at once yields 
a coloured compound in the presence of water. I now venture to 
suggest that this body may be and probably is, permanganic 
anhydride, since the solution of this body in water gives a clear 
pink solution, shewing all the reactions of aqueous permanganic 
acid. 
The reasons for regarding the pink vapours of Terreil and 
others as permanganic acid, have been already given. 
Since the above was written (August ’87) it has come under 
my notice that Franke has published, in the Journal ftir Prak- 
tische Chamie for July and August last, two papers upon the 
action of Sulphuric Acid upon Potassic Permanganate. He asserts 
that by this action he has obtained two somewhat volatile, highly 
coloured solids, to which he ascribes the formula MnO, and MnO,,. 
His evidence for the formation and reactions of these bodies how- 
ever appears to be somewhat unsatisfactory. 
(8) The equations of an Isotropic Elastic Solid in Polar and 
Cylindrical Coordinates, their solution and application. By C. 
CHREE, M.A. 
_ [Abstract.] 
Starting with the expression in ordinary Cartesian Coordinates 
for the energy of an Isotropic Elastic Solid, the author transforms 
this expression into polar and cylindrical coordinates, and thence 
obtains the corresponding internal and surface equations. 
To the development of these equations one general method is 
applied. Solutions are obtained for the internal equations involv- 
ing arbitrary constants, which are then determined from the 
surface conditions. 
A general solution of the polar equations is obtained in the 
case of a sphere or a spherical shell, for a spherical harmonic 
distribution of internal and surface forces. -This solution is 
extended to the case of any number of materials forming con- 
centric spherical shells, when the force on the bounding surface 
is purely normal; and it is shewn by this means how to treat a 
material whose structure varies continuously with the distance 
