He successfully considers the systems of two and three simultaneous ternary quadratics.
A pilgrimage feast must be fixed in date to ensure the simultaneous presence of the pilgrims. There are, besides, seeming references to the feast in the early prophets, as Hosea xii.
(a m b n) k (ab) kamkbn-k x, x - x it is clear that the k th transvectant is a simultaneous covariant of the two forms.
It may denote a simultaneous orthogonal invariant of forms of orders n i, n2, n3,...; degree 0 of the covariant in the coefficients.
Heating or exposure to sunlight reduces it to the red oxide; it fires when ground with sulphur, and oxidizes ammonia to nitric acid, with the simultaneous formation of ammonium nitrate.
His fleet, too, lingered uselessly in the harbour, till after a defeat in which Eurymedon perished, though the simultaneous land attack was unsuccessful.
Ptolemy knew but of a few latitudes which had been determined by actual observation, while of three longitudes resulting from simultaneous observation of eclipses he unfortunately accepted the least satisfactory, namely, that which placed Arbela 45° to the east of Carthage, while the actual meridian distance only amounts to 34°.
In Transylvania, however, the common peril evoked by the Turkish incursion and a simultaneous rising of the Vlach peasantry had knit together the jarring interests of Magyars, Saxons and Szeklers, a union which, under the national hero, the voivode Janos Hunyadi, was destined for a while to turn the tide of war.
When, in the spring of 1769, the first serious campaign was opened by a simultaneous attack by three Russian armies on the principalities, the Crimea and the buffer state of Kabardia, the Turks, in spite of ample warning, were unprepared.
In general it will be simultaneous covariant of the different forms n 1 rz 2 n3 a, b x, ?
Duplex telegraphy consists in the simultaneous transmission of two messages, one in each direction, over the same wire.
The only new problem introduced is the simultaneous transmission of two messages in the same direction; this is sometimes ruplex called " diplex transmission."
The closed ovary implies a mode of fertilization which is profoundly different, and which was probably correlated with a simultaneous development of insect life.
Turkey was at this time the only neutral state in Europe; it was of vital im- Treaty of portance that she should not be absorbed into the Napoleonic system, as in that case Russia would have been exposed to a simultaneous attack from France, Austria, Turkey and Persia.
Since (ab) = a l b 2 -a 2 b l, that this may be the case each form must be linear; and if the forms be different (ab) is an invariant (simultaneous) of the two forms, its real expression being aob l -a l b 0.
May be a simultaneous invariant of a number of different forms az', bx 2, cx 3, ..., where n1, n 2, n3, ...
For the cubic (ab) 2 axbx is a covariant because each symbol a, b occurs three times; we can first of all find its real expression as a simultaneous covariant of two cubics, and then, by supposing the two cubics to merge into identity, find the expression of the quadratic covariant, of the single cubic, commonly known as the Hessian.
As regards simultaneous binary forms, the system of two quadratics, and of any number of quadratics, is alluded to above and has long been known.
If ai, bx, cx be different forms we obtain, after development of the squared determinant and conversion to the real form (employing single and double dashes to distinguish the real coefficients of bx and cz), a(b'c"+b"c'-2 f'f") +b(c'a"+c"a'-2g'g") +c(a' +a"b'-2h'h")+2f(g'h"+g"h'-a' + 2g (h ' f"+h"f'-b'g"-b"g')+2h(f'g"+f"g'-c'h"-c"h'); a simultaneous invariant of the three forms, and now suppressing the dashes we obtain 6 (abc+2fgh -af t - bg 2 -ch2), the expression in brackets being the S well-known invariant of az, the vanishing of which expresses the condition that the form may break up into two linear factors, or, geometrically, that the conic may represent two right lines.
2 cos w xy+y 2 = X 2 +2 cos w'XY+Y2, from which it appears that the Boolian invariants of axe+2bxy-y2 are nothing more than the full invariants of the simultaneous quadratics ax2+2bxy+y2, x 2 +2 cos coxy+y2, the word invariant including here covariant.
In general the Boolian system, of the general n i °, is coincident with the simultaneous system of the n i °' and the quadratic x 2 +2 cos w xy+y2.
These are knocked off, ground up with water, freed from metal-particles by elutriation, and the paste of white lead is allowed to set and dry in small conical forms. The German method differs from the Dutch inasmuch as the lead is suspended in a large chamber heated by ordinary means, and there exposed to the simultaneous action of vapour of aqueous acetic acid and of carbon dioxide.
Various currents are then passed through the magnetizing coil, the galvanometer readings and the simultaneous magnetometer deflections being noted.
Honda subjected tubes of iron, steel and nickel to the simultaneous action of circular and longitudinal fields, and observed the changes of length when one of the fields was varied while the other remained constant at different successive values from zero upwards.
Invasion and conquest was the simultaneous Catholic reaction in Hungary.
Simultaneous equations in two unknowns x and y may be treated in the same way, except that each equation gives a functional relation between x and y.
The result of his discovery was an entire revolution in the knowledge of diseases of the chest; but it would be a mistake to forget that an essential factor in this revolution was the simultaneous study of the condition of the diseased organs as seen after death.
Calcium cyanamide has assumed importance in agriculture since the discovery of its economic production in the electric furnace, wherein calcium carbide takes up nitrogen from the atmosphere to form the cyanamide with the simultaneous liberation of carbon.
If simultaneous, cause is effect and effect cause.
The actual formation of this salt is not quite clear; but it is certainly conditioned by the simultaneous contact of decaying nitrogenous matter, alkalies, air and moisture.
Quadruplex telegraphy consists in the simultaneous transmission of two messages from each end of the line.