But like every pure theory the principles of conjugate pressures in earth may lead to danger if not applied with due consideration for the angle of repose of the material, the modifications brought about by the limited width of artificial embankments, the possible contraction away from the masonry, of clayey materials during dry weather for some feet in depth and the tendency of surface waters to produce scour between the wall and the embankment.
The circuits in which the batterybattery P and and d being galvanometer called the ratio branches placed are called conjugate circuits, and the circuits P, Q, R, and S are called the arms of the bridge, the '44 S arms and S the measuring arm.
This conjugate condition is finally brought to a close by the nuclear fusion in the basidium.
From one cell to another or C, A further stage in which whether two daughter nuclei from sm l the first aecidiobecome conjugate in one cell, spore (a) and the intercalary is not yet clear.
(22) Conjugate functions can be employed also for the motion of liquid in a thin sheet between two concentric spherical surfaces; the components of velocity along the meridian and parallel in colatitude 0 and longitude A can be written d¢_ i _ d4, I dip _ dy (13) d8 sin - 0 dX' sin 0 dX de' and then = F (tan O.
The self-conjugate circle is a 2 sin 2A +0 2 sin 2 B +y 2 sin 2C = o, or the equivalent form a cosAa 2 +bcosB(2 +ccosCy 2 = o, the centre being sec A, sec B, sec C.
Idium), a reduced fertilization which denotes their derivation, through the Uredineae, from more typically sexual forms. No one has yet t.-ade out in any form the exact way in which the association of nuclei tr -.-es place in the group. The mycelium is always found to contain conjugate nuclei before the formation of basidia, but the point at which the conjugate condition arises seems very variable.
In (1,3) satisfy the conjugate or orthogonal relations anaiai+aiiaiai+.
The problem is identical with that of finding the common conjugate diameters of the ellipsoids T(x, y, I) =const., V(x, y, 1) =const.
If we write r for PN, then y= r cos a, and equation 9 becomes 13.7,T - I) This relation between y and r is identical with the relation between the perpendicular from the focus of a conic section on the tangent at a given point and the focal distance of that point, provided the transverse and conjugate axes of the conic are 2a and 2b respectively, where a= p, and b 2 = -.
In all these cases the internal pressure exceeds the external by 2T/a where a is the semi-transverse axis of the conic. The resultant of the internal pressure and the surface-tension is equivalent to a tension along the axis, and the numerical value of this tension is equal to the force due to the action of this pressure on a circle whose diameter is equal to the conjugate axis of the ellipse.
The resultant of the internal pressure and the surface-tension is equivalent to a pressure along the axis equal to that due to a pressure p acting on a circle whose diameter is the conjugate axis of the hyperbola.
When the conjugate axis of the hyperbola is made smaller and smaller, the nodoid approximates more and more to the series of spheres touching each other along the axis.
When the conjugate axis of the hyperbola increases without limit, the loops of the nodoid are crowded on one another, and each becomes more nearly a ring of circular section, without, however, ever reaching this form.
It is notorious among engineers that retaining walls designed in accordance with the well-known theory of conjugate pressures in earth are unnecessarily strong, and this arises mainly from the assumption that the earth is merely a loose granular mass without any such adhesion.
WHEATSTONE'S BRIDGE, an electrical instrument which consists of six conductors, joining four points, of such a character that when an electromotive force is applied in one branch the absence of a current in another branch (called the conjugate branch) establishes a relation between the resistance of the four others by which we can determine the value of the resistance in one of these, that of the others being assumed to be known.
Of f=0, :and notices that they become identical on substituting 0 for k, and -f for X; hence, if k1, k2, k 3 be the roots of the resolvent -21 2 = (o + k if) (A + k 2f)(o + k 3f); and now, if all the roots of f be different, so also are those of the resolvent, since the latter, and f, have practically the same discriminant; consequently each of the three factors, of -21 2, must be perfect squares and taking the square root 1 t = -' (1)ï¿½x4; and it can be shown that 0, x, 1P are the three conjugate quadratic factors of t above mentioned.
If 4) = rx.sx, the Y2 =1 normal form of a:, can be shown to be given by (rs) 4 .a x 4 = (ar) 4s: 6 (ar) 2 (as) 2rxsy -I- (as) 4rx; 4) is any one of the conjugate quadratic factors of t, so that, in determining rx, sx from J z+k 1 f =o, k 1 is any root of the resolvent.
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.
If we put qo= Sq' - Vq', then qo is called the conjugate of q', and the scalar q'qo = qoq' is called the norm of q' and written Nq'.
If "=4), the term of the first order vanishes, and the reduction of the difference of path via P and via A to a term of the fourth order proves not only that Q and Q' are conjugate foci, but also that the foci are exempt from the most important term in the aberration.
Of the wedge of immersion and emersion, will be the C.P. with respect to FF' of the two parts of the water-line area, so that b 1 b 2 will be conjugate to FF' with respect to the momental ellipse at F.
Of the fluid, equal to the weight vertically upward through the movement of a weight P through a distance c will cause the ship to heel through an angle 0 about an axis FF' through F, which is conjugate to the direction of the movement of P with respect to an ellipse, not the momental ellipse of the water-line area A, but a confocal to it, of squared semi-axes a 2 -hV/A, b 2 - hV/A, (I) h denoting the vertical height BG between C.G.
Uniplanar motion alone is so far amenable to analysis; the velocity function 4 and stream function 1G are given as conjugate functions of the coordinates x, y by w=f(z), where z= x +yi, w=4-Plg, and then dw dod,y az = dx + i ax - -u+vi; so that, with u = q cos B, v = q sin B, the function - Q dw u_vi=g22(u-}-vi) = Q(cos 8+i sin 8), gives f' as a vector representing the reciprocal of the velocity in direction and magnitude, in terms of some standard velocity Q.
All objects, therefore, which lie beyond a certain point (the conjugate focus of the dioptric system of the eye, the far point) are indistinctly seen; rays from them have not the necessary divergence to be focused in the retina, but may obtain it by the interposition of suitable concave lenses.
Sca, through,, u rpov, measure), in geometry, a line passing through the centre of a circle or conic section and terminated by the curve; the "principal diameters of the ellipse and hyperbola coincide with the "axes" and are at right angles; " conjugate diameters " are such that each bisects chords parallel to the other.
Proposition 14 shows how to draw an ellipse through five given points, and Prop. 15 gives a simple construction for the axes of an ellipse when a pair of conjugate diameters are given.
The two nuclei when once associated are termed" conjugate "nuclei, and they always divide at the same time, a half of each passing into each cell.
It is known that zoogametes, which usually conjugate, may, when conjugation fails, germinate directly (Sphaerella).
Gametes which fail to conjugate sometimes assume the appearance of zygospores and germinate in due course.
It also follows that a line half-way between a point and its polar and parallel to the latter touches the parabola, and therefore the lines joining the middle points of the sides of a self-conjugate triangle form a circumscribing triangle, and also that the ninepoint circle of a self-conjugate triangle passes through the focus.