Mechanical Science. 431 
sure this compressed gas assumes such a volume that its density 
shall be of the same order or kind as that of the atmosphere, then 
the two first forces become insensible: the molecules are no longer 
sensibly subject except to the repulsive force of their caloric, 
and are obedient to the laws of Mariote and Gay-Lussac, 
from which they depart in the very compressed state, as results 
from the experiments cited. In pursuing by similar but precise 
experiments the ratio between the pressure, the temperature, 
and the volume, it would be seen how they approached more 
and more to the general laws of aériform fluids\—Annal. de 
Chimie, xxi. 22. 
2. Mathematical Prize Question.—The following has been 
proposed by the class of mathematics of the Royal Academy of 
Sciences of Prussia: ‘‘ To give a complete mathematical theory 
of the luminous or coloured circles which form around the sun 
and moon, and such an one as will equally agree with the 
results of observations, and with the known properties of light 
and the atmosphere.” 
This question was proposed for 1822, but is extended to 
1824. The possible influence of the inflection and polarization 
of light is to be considered. Memoirs are to be sent in before 
the end of March 1824. The prize is 50 ducats. 
3. Survey of the Heavens.—The indefatigable Bessel has 
commenced an important work, which every lover of astronomy 
must wish to see followed up with success. It is a general 
survey of the heavens in zones: and the first part of the work 
is already in the press. 
4. Improvement in Metallic Casting.—Iron and metallic cast- 
ings are said to be very much improved, by subjecting the 
metal, when in the moulds, to pressure. This is done by making 
a part of the mould of such a form as to receive a piston, which, 
on the metal being introduced, is made to press on it with any 
' required force. It is stated that castings obtained in this way 
are not only free from the imperfections generally incurred in 
the usual mode, but have a peculiar soundness of surface and 
closeness of texture, qualities of the utmost importance in 
ordnance, rolling cylinders, &c. The improvement belongs to 
Mr. Hollingrake, who has obtained a patent for it. 
5. Canal Navigation.—The tread-wheel has been applied by 
M. Van Heythuysen to the propelling of barges on canals. 
The object is to obviate the use of horses. The apparatus is 
made light and separable from the barge, and it is found that 
two men can propel a barge by it, at the rate of five miles per 
hour. The saving of the expense of horses and track-roads 
promises to make this application of human power very valuable. 
