Restricted Substitutions We may regard the factors of a binary n ip equated to zero as denoting n straight lines through the origin, the co-ordinates being Cartesian and the axes inclined at any angle.
Of exceptional interest are the letters from Jerusalem describing the hostility of the maritime coast and the disturbances of the IIabiru (" allies "), a name which, though often equated with that of the Hebrews, may have no ethnological or historical significance s But Egypt was unable to help the loyalists, even ancient Mitanni lost its political independence, and the supremacy of the Hittites was assured.
The Greeks equated Ubasti with their Artemis, confusing her with the leonine Tafne, sister of Shoou (Apollo).
It has been equated on philological grounds to the Leja.
If the form, sometimes termed a quantic, be equated to zero the n+I coefficients are equivalent to but n, since one can be made unity by division and the equation is to be regarded as one for the determination of the ratio of the variables.
If the forms be identical the sets of symbols are ultimately equated, and the form, provided it does not vanish, is a covariant of the form ate.
Then a binary n", equated to zero, represents n straight lines through the origin, and the x, y of any line through the origin are given constant multiples of the sines of the angles which that line makes with two fixed lines, the axes of co-ordinates.
In general any pencil of lines, connected with the line a x by descriptive or metrical properties, has for its equation a rational integral function of the four forms equated to zero.
The linear invariant a s is such that, when equated to zero, it determines the lines ax as harmonically conjugate to the lines xx; or, in other words, it is the condition that may denote lines at right angles.
In the first class come equations in a single unknown; here the function which is equated to zero is the Y whose values for different values of X are traced, and the solution of the equation is the determination of the points where the ordinates of the graph are zero.
6), and the diffracted rays make an angle ¢ (upon the same side), the relative retardation from each element of width (a+d) to the next is (a+d) (sin 9 +sin op); and this is the quantity which is to be equated to mX.
The moment of inertia of the body about the axis, denoted by But if is the moment of inertia of the body about a mean diameter, and w the angular velocity about it generated by an impluse couple M, and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is C i pµ sin 0- C2µ 2 sin 0 cos 0; (4) and equating this to the impressed couple (multiplied by g), that is, to gN = (c 1 -c 2)c2u 2 tan 0, (5) and dividing out sin 0, which equated to zero would imply perfect centring, we obtain C21 2 cos 0- (c 2 -c 1)c2u 2 sec 0 =o.
The most striking coincidence is Jebel Usdum, by some equated with confidence to Sodom.
The latter range, the Chimen-tagh, is identical in its western parts with the Piazlik-tagh and in the east must be equated with the Tsaidam chain of Przhevalsky; and it is probably continued westwards by the range which the Russian explorers call the Moscow Range or the Achik-tagh, running north of the Achik-kol and, according to Przhevalsky, connecting on the west with the Tokuz-davan.
After a certain discount for friction and the recoil of the gun, the net work realized by the powder-gas as the shot advances AM is represented by the area Acpm, and this is equated to the kinetic energy e of the shot, in foot-tons, (I) e d2 I + p, a in which the factor 4(k 2 /d 2)tan 2 S represents the fraction due to the rotation of the shot, of diameter d and axial radius of gyration k, and S represents the angle of the rifling; this factor may be ignored in the subsequent calculations as small, less than I %.
The mancus was equated with thirty pence, probably from the time of its introduction.
Another remarkable indication of the decay of the ceorl's estate is afforded by the fact that in the treaties with the Danes the twihynde ceorls are equated with the Danish leysings or freedmen.
But it is doubtful whether Tell Ham can be considered as a corruption of Kefr Nahum, the Semitic name which the Greek represents: and there is not here, as at Khan Minyeh, any spring that can be equated to the Heptapegon of Josephus.
Tiwes, whence "Tuesday") and equated with the Roman Mars.
If the inclination of the string to the vertical does not exceed a few degrees, the vertical displacement of the particle is of the second order, so that the vertical acceleration may be neglected, and the tension of the string may be equated to the gravity mg of the particle.
Let M be the moment of the unbalanced couple required to produce the deviation; ther by equation 57, 104, the energy exerted by this couple in tht interval dt is Macit, which, being equated to the variation of energy gives da R2W da -
In virtue of the mystic identity between the cosmic phenomena and sacrifice, Rita may be also viewed as the principle of the cultus; and from that sphere it passes into conduct and acquires the meaning of morality and is equated with what is " true."
On the whole, then, the work expended in producing two units of interface is 2T1+2T2-4T'12, and this, as we have seen, may be equated to 2T 12.
The Weight Is Sometimes Equated To The Product Of The Capillary Tension (T) And The Circumference Of The Tube (27Ra), But With Little Justification.