Resistance of Globes

Assume that a globe moves uniformly forward through a fluid enclosed and compressed in a cylindric canal.

Its resistance is to the force by which its whole motion may be generated or destroyed in the time in which it describes eight third parts of its diameter.

• This is in a ratio compounded of the ratio of the orifice of the canal, to the excess of that orifice above half the greatest circle of the globe and the duplicate ratio of the orifice of the canal, to the excess of that orifice above the greatest circle of the globe.

The ratio of the density of the fluid to the density of the globe, nearly.

This appears by Corollary 2. Proposition 37. and the demonstration proceeds in the same manner as in the foregoing proposition.

Scholium

In the 2 last propositions we suppose (as was done before in Lemma 5.) that all the water which precedes the globe, and whose fluidity increases the resistance of the same, is congealed.

If that water becomes fluid, it will somewhat increase the resistance.

But in these propositions that increase is so small, that it may be neglected, because the convex superficies of the globe produces the very same effect almost as the congelation of the water.