and the differettt Motions of the Earth s Axis.

Then, putting z — the semi-equatoreal diameter of any suchstratum , and supposing the corresponding semi-axis to be in pro-portion thereto, as w to i (which proportion may be assumed,either, as constant or variable), we shall, by writing z in the

room of a , and wz in the room of b, have — x wz s ; whole

15

fluxion, or indefinitely small increment, will, therefore be themomentum of the stratum or shell, whereof the semi-equatorealdiameter is z, and thickness (at that diameter) z; on the for-mer supposition, that the spheroid is every-where of the samedensity. But in the present case this momentum must be drawninto the quantity, which, according to hypothesis, exprcsseth themeasure of the density answering to the value of z ; whichquantity we will represent by D ; then will the product

—— x flux. ivx^ be the general fluxion of the momentum,

when the density is variable: and therefore the fluent of this last

expression, when z = a, and w = will be the true value

of the required momentum (R) in the present case.

After the same manner, the corresponding value of N (fromLem. III.) may be determined : for, retaining the above no-tation and suppositions, it is evident (from thence) that the said

value of N (which is there expressed by ~ x x a) — ^ x 8,

or — x ’A x a '— b l x will here, by substitution, become

« 5 3 '

I x x wz^ — w 3 * 5 ; and consequently that — x x D xflux. <wz s — -w^z* will be the required fluxion of the value ofN : where - is a constant quantity (by hypothesis), the forcebeing proportional to the distance, and the measure thereof (?)at the given distance a, equal to (3 X aS has been beforeshewn, in Prop. II.

Now from the whole of what is above laid down, it willappear evident, that the angular celerity of the motion aboutthe line A a (supposing that about the axis to be denoted by

E unity)