And Rs 1400 crores for **MP** govt.

If the co-ordinate axes coincide with the principal axes of this quadric, we shall have ~(myz) =0, ~(mzx) =0, Z(mxy) = 0~ (24) and if we write ~(mx) = Ma, ~(my1) = Mb, ~(mz) =Mc2, (25) where M=~(m), the quadratic moment becomes M(aiX2+bI,s2+ cv), or **Mp**, where p is the distance of the origin from that tangent plane of the ellipsoid ~-,+~1+~,=I, (26)

The reason for this is readily seen; if a mass M of any gas occupies a volume V at a temperature T (on the absolute scale) and a pressure P, then its absolute density under these conditions is O = M/V; if now the temperature and pressure be changed to l and P,, the volume V l under these conditions is VPT/PIT1, and the absolute density is **MP**,T/VPT I.

Let **MP** =y represent the forward displacement of the particle originally at M, and NQ = y +dy that of the particle originally at N.

**Mp**, Posterior Dicerocardium; Jurassic. muscle.

The latter equation expresses that the angular momentum **mP** sing O~t about the vertical OZ is constant.

Witne **mp** is Htl!

**Mp** belonged to the repertoire of the Korahites, or they were intended to be sung in the Korahite style.

+mp4dp4 +...) =exp **Mp** g dp 4+ï¿½ï¿½ .

The formula then becomes area =z(**MP**.NB+NQ.

Thus grew with the up the Holy Roman Empire, that strange state which, **mp** directly descending through the empire of Charlemagne from the empire of the Caesars, contained so many elements foreign to ancient life.

These equations are proved by taking a line fixed in space, whose direction cosines are 1, then dt=mR-nQ,' d'-t = nP =lQ-**mP**. (5) If P denotes the resultant linear impulse or momentum in this direction P =lxl+mx2+nx3, ' dP dt xl+, d y t x2' x3 +1 dtl dt 2 +n dt3, =1 ('+m (dt2-x3P+x1R) ' +n ('-x1Q-{-x2P) ' '= IX +mY+nZ, / (7) for all values of 1, Next, taking a fixed origin and axes parallel to Ox, Oy, Oz through 0, and denoting by x, y, z the coordinates of 0, and by G the component angular momentum about 1"2 in the direction (1, G =1(yi-x2z+x3y) m 2-+xlz) n(y(y 3x 1 x3x y + x 2 x) (8) Differentiating with respect to t, and afterwards moving the fixed.

ALUM, in chemistry, a term given to the crystallized double sulphates of the typical formula M 2 SO 4 ï¿½ **MP**' ï¿½(S04) 324H20, where M.