Aj Hence the system of values also causes to vanish in this case; dx and by symmetry aj and Fz also vanish.
AJ - ., _ A aJ ï¿½.
=wj, - aj aj - aj a °aa1 +2a 1aa2 +3a 2aa3 +...
=0, - aj aj aj nal aao +(n-1)a2 at i -} (n - 2)a 3aa2+...
Moreover, if we add the first to the fourth we obtain aj 2w ak = 7 1=6, j, =0j, where 0 is the degree of the invariant; this shows, as we have before observed, that for an invariant w= - n0.
If 0 be the degree of an invariant j - aj aj a; oj =a ° a a o +al aa l +...
+anaan naj n.-1 aj naj =a l aa ° +a 1 a2c3a1...+a2aan and, herein transforming from a to x, we obtain the first evectant (-) k, x1x2 aak k Combinants.
Along the jet surface A'J', q = Q, b-a' ch nSl= cos 110= a-a la - b sh nft=i sin nO=i a'>u=a'erl"> -oo, giving the intrinsic equation.
If we omit the gyrostatic terms, and write qr = Cre, we finc~, for a free vibration, (aj,1~2 + birX + Cm) C~ + (asrX2 + birX + Cm) C2 +
The relative velocity pet-pendicular to P~Pi of the teeth at their point of contactthat is, their velocity of sliding on each otheris found by supposing one of the wheels, such as I, to be fixed; the line of centres CXCi to rotate backwards round C~ with the angular velocity aj, and the wheel 2 to rotate round C2 as before, with the angular velocity az relatively to the line of centres CiC2, so as to, have the same motion as if its pitch-circle rolled,on the pitch-circle of the first wheel.
Af d4e tan ~,+ cot 4i~ ~ (40) aj d~i tan ~1+cot ti)
Let W be the weight of a flywheel, R its radius of gyration, ai its maximum, aj its minimum, and A=~1/8(a1+ai) its mean angular velocity.
Mahrka (death) mark masg Thraetaona Fritn Feridun gp (water) gp b hvato (self) khot khOd raucah (day) roj rz haca aj az.
In repairing this work the perfectly safe form shown by the dotted lines ka, kj was substituted for the flat surface aj, and this alone, if originally adopted, would have prevented dangerous shearing strains.
Shakal, to weigh), originally a Jewish unit of weight (5 1 r, of a mina, and 3 o aj of a talent) and afterwards a coin of the same weight.