It is not difficult to imagine infinitesimals of fractional or even of irrational order, and thus we find again that scale of the mathematical continuum which has been dealt with in the preceding pages.
The mathematicians of the Berlin school, Kronecker in particular, have devoted themselves to constructing this continuous scale of fractional and irrational numbers without using any material other than the whole number.
In the first place we must obtain the necessary dimensions, and then, reducing the number of feet to fractional parts of an inch, form a scale suitable for carrying out the whole.
Those ninth-parts of humanity notoriously eked out their fractional existence by asking nine times too much for the clothing which civilisation, and perhaps a change of climate, render more necessary to us than to our ancestors the Picts.
This we would fix at some small fractional part of the annual value of the land in rent charge,--say at one penny per acre.
The former is enticed away by the use of quicklime, while the other two are separated by the process of fractional distillation already referred to.
He will thus learn how many of his steps make 100 yards and will become familiar with the appearance of the whole distance and of its fractional parts.
Sight setting therefore in this exercise should include, more often than not, "fractional ranges" and windage data.
The point system of widths has been applied to spaces, the thickness being graduated by points and half-points, instead of the fractionaldivision of the em.
Take it,” he repeated, still presenting the trifling bit of fractional currency: “I owe it to you.
Deaths outright from exposure and starvation are now perhaps uncommon, but for the multitude there are only miserable houses, uncomfortable clothes, and bad and insufficient food; fractional starvation and exposure, that is to say.
Clotilde, sincerely feeling Marko to be of as fractional a weight as her tone declared him.
That part of any expression under a fractional form which is situated below the horizontal line signifying division.
The bodies present in the latter may be separated by fractional distillation, while the contents of the gaseous residue may be further differentiated by the air of still lower temperatures, such as are obtainable by liquid hydrogen.
Fractional coins passed by metallic weight; the shifts in the price of copper in New York and London determined the number of pennies which farmers received for their silver dollars, even on the threshold of Tibet.
Until the outbreak of war subsidiary coinage was copper and aluminum; this has been replaced by fractional paper, circulating decimally without discount for exchange into larger bills.
It is but fair to mention that the homoeopathic treatment did not cure the disease; but the manifest operation of this fractional dose, that could not possibly be denied, is a fact of considerable importance.
If these fractional doses are inert, and yet the disease is cured, then must the successful treatment be solely ascribed to the dietetic regimen and the efforts of nature.
In the museum close by, however, some fractional restorations indoors serve to give a very excellent idea of the appearance of at least two of the ancient buildings.
In Indiana, all the lands purchased of the Indians have been surveyed, and with the exception of about ninety townships and fractional townships, have been offered for sale.
A confused and baffling whirl of sounds ensued, in which all sorts of fractional bids and offers mingled, till '46 emerged from the chaos.
They generally reap a harvest of pennies and fractional currency.
Thus in fractional distillation, each condenser or retort in the apparatus shown in Fig.
In Kepler's form of stating the law the radius vector is supposed to travel with the planet and in each day to sweep over the same fractional part of the total area of the orbit.
This same striving after accuracy leads to the introduction of fractional numbers to represent gradations of brightness intermediate between whole magnitudes.
The townships and fractional townships will be offered in the order in which they are above designated, beginning with the lowest number of section in each.
