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A programme was published making the offer of prizes of forty and twenty pistoles, for the best determination of the area and the centre of gravity of any segment of the cycloid, and the dimensions and centres of gravity of solids and half and quarter solids which the same curve would generate by revolving round an abscissa and an ordinate.
How, then, will the water of streams differ at these times in turbidity and in the relative amount of solids carried in solution? In parts of England streams have been known to continue flowing after eighteen months of local drought, so great is the volume of water which in humid climates is stored in the rocks above the drainage level, and so slowly is it given off in springs.
It is from the extension of a certain natural geometry, suggested by the most general and immediately perceived properties of solids, that natural logic has arisen; then from this natural logic, in its turn, has sprung scientific geometry, which extends further and further the knowledge of the external properties of solids.
All of the regular constituents of the atmosphere are gases, and these, as compared with liquids and solids, are very light. Nevertheless the atmosphere has weight and, on this account, exerts pressure upon everything on the earth. At the sea level, its pressure is nearly fifteen pounds to the square inch.
Experimentation was naturally turned, however, to terrestrial gases and solids on fire, and it was found that these also produce like series of dark lines in the spectrum.
"If then a solid can be made to behave like a liquid, even with such pressures as are within our control, how are we to suppose that the solids would behave with such pressures as those to which they are subjected in the interior of the earth?
Or if solids should still seem to be material, there are astral bodies as well which are immaterial although physical; and as to ether and electricity, they are the very substance of spirit. All this I find announced in newspapers and even in books as the breakdown of scientific materialism: and yet, when was materialism more arrant and barbarous than in these announcements?
The interest of the results to which the researches on the continuity between the liquid and the gaseous states have led is so great, that numbers of scholars have naturally been induced to inquire whether something analogous might not be found in the case of liquids and solids.
"I'll have that dusky imp for an exercise boy," he announced. "He's built like an aeroplane all superstructure and no solids." For a month the training of Panchito went on each morning. Pablo's grandson, under Danny Leighton's tuition, proved an excellent exercise boy.
Thus it is that the whole of the elements of Euclid were merely an introduction to the comprehension of the "Platonic Solids," which must also, in their turn, be discarded when the within or essence of things has to be dealt with and not the without or appearance, no matter how "typical" that appearance may be.
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