A Negotiations were resumed with Napoleon for the evacuation ad Rome by the French troops; but the emperor, though he saw by wee that the temporal power could not for ever be supported sti **Jy** and by French bayonets, desired some guarantee that the Pr Roman evacuation should not be followed, at all events wa, stion.

And when the two factor lines are at right angles to one another, or 0=42, the product is simply ix" -}-**jy**"-}-kz", the unit line perpendicular to both.

Also, if 0 be the angle between them, and x", y", z" the direction-cosines of a line perpendicular to each of them, we have xx' +yy'+zz' =cos 0, yz' - zy" = x" sin 0, &c., so that the product of two unit lines is now expressed as - cos0+ (ix" +**jy**" +kz") sin 0.