The practical problems of fluid motion, which are amenable to **mathematical analysis** when viscosity is taken into account, are excluded from treatment here, as constituting a separate branch called "hydraulics" (q.v.).

If an iron ship be swung when upright for deviation, and the mean horizontal and vertical magnetic forces at the compass positions be also observed in different parts of the world, **mathematical analysis** shows that the deviations are caused partly by the permanent magnetism of hard iron, partly by the transient induced magnetism of soft iron both horizontal and vertical, and in a lesser degree by iron which is neither magnetically hard nor soft, but which becomes magnetized in the same manner as hard iron, though it gradually loses its magnetism on change of conditions, as, for example, in the case of a ship, repaired and hammered in dock, steaming in an opposite direction at sea.

Instead of observing the deviation solely for the purposes of correcting the indications of the compass when disturbed by the iron of the ship, the practice is to subject all deviations to **mathematical analysis** with a view to their mechanical correction.

It can only be contrived by means of complicated **mathematical analysis**.

Wallis having meanwhile published other works and especially a comprehensive treatise on the general principles of calculus (Mathesis universalis, 1657), he might take this occasion of exposing afresh the new-fangled methods of **mathematical analysis** and reasserting his own earlier positions.