Frbs which occur on particular dry kinds of soil, such as lime- rf one rocks, stiff clay, and so forth (Warming, 1909: 289).
If al, a2, ...a, n be the roots of f=o, (1, R2, -Ai the roots of 0=o, the condition that some root of 0 =o may qq cause f to vanish is clearly R s, 5 =f (01)f (N2) ï¿½ ï¿½;f (Nn) = 0; so that Rf,q5 is the resultant of f and and expressed as a function of the roots, it is of degree m in each root 13, and of degree n in each root a, and also a symmetric function alike of the roots a and of the roots 1 3; hence, expressed in terms of the coefficients, it is homogeneous and of degree n in the coefficients of f, and homogeneous and of degree m in the coefficients of 4..
Rf > a> b> o> a'> -Do; and then so that PT =c/Zir, and the curve AP is the tractrix; and the coefficient of contraction, or breadth of the jet breadth of the orifice - +i' A change of S2 and 0 into nS2 and nO will give the solution for two walls converging symmetrically to the orifice AA 1 at an angle zr/n.
30, 46 a 30), or the De Interpretatione, which he calls " the present theory " (rf j s 'Dv Oecopias, De Int.
When k2> 4u, the solution of (29) is, in real form, x = aie-_t/ri +aie)rf, (32)
Where ri, rf are the distances of mi, rni from their mass-centre G.
The frequency equation is therefore (o2g/a)(if2g/b) ~ (12) The roots of this quadratic in rf are easily seen to be real and positive.
Find Rf the resultant of this pressure, the weight of the block aabb acting through its centre of gravity, and any C~
A condition equivalent to the above, and necessarily connected with it, is, that at each pair of points of contact the inclinations of the curves to their radii-vectores shall be equal and contrary; or, denoting by r1, rf the radii-vectores at any given pair of points of contact, and s the length of the equal arcs measured from a certain fixed pair of points of contact dri/ds= drm/ds; (18)
In which ri is the greater radius, and rf the less.
To express this symbolically, let Wi, W2 be the weights of the bodies; P the effort exerted between them; S the distance through which it acts; R1, Rf the resistances opposed to the effort overcome by Wi, ~AT2 respectively; E1, Ef the shares of the whole energy E exerted upon Wi, W2 respectively.
Then v = ri (ri +ri)12 = (ri rf)2/2lrc. (34)