**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.