Consider the traces these surfaces cut on any sphere r =a: we have de/de = **2e** sin a cos e/{cos t - aR2 dR/de}, which is positive and has a maximum in the middle latitudes; so that, proceeding from the pole to the equator along any meridian, the angular velocity would continually in crease, at a rate which was greatest in the middle latitudes.

If the thickness of the film is greater than **2E**, there will be a stratum of thickness c-**2E** in the middle of the film, within which the values of p and x will be pc and In the two strata on either side of this the law, according to which p and x depend on the depth, will be the same as in a liquid mass of large dimensions.

Next consider the motion given by = m ch 2(77a)sin **2E**, tii= -m sh 2(na)cos **2E**; (I) in which > ' =o over the ellipse a, and =1'+IR(x2+y2) =[ -m sh 2(7 7 -a)+4Rc 2 ]cos 4Rc2 ch 2n, (2) which is constant over the ellipse n if 4Rc 2.