One may very easily fall into mistakes and errors when one is searching into the hidden causes of things, in the absence of real experiments, and this is easily apparent from the crass error of Cardan; who deems himself to have discovered the distances of the centres of the cosmos and of the earth through a variation of the magnetick iron of 9 degrees. For he reckoned that everywhere on the earth the point of variation on the Horizon is always distant nine degrees from the true north, toward the east: and from thence he forms, by a most foolish error, his demonstrative ratio of the separate centres. * * * * * {170} CHAP. XII. On the finding of the amount of variation: how great _is the arc of the Horizon from its arctick or antarctick_ intersection of the meridian, to the point _respective of the magnetick needle_. Virtually the true meridian is the chief foundation of the whole matter: when that is accurately known, it will be easy by a mariners' compass (if its construction and the mode of attachment of the magnetick iron works are known) or by some other larger horizontal versorium to exhibit the arc of variation on the Horizon. By means of a sufficiently large nautical variation compass (two equal altitudes of the sun being observed before and after midday), the variation becomes known from the shadow; the altitude of the sun is observed either by a staff or by a rather large quadrant. On land the variation is found in another way which is easier, and because of the larger size of the instrument, more accurate. Let a thick squared board be made of some suitable wood, the surface of which is two feet in length and sixteen inches in width: describe upon it some semicircles as in the following figure, only more in number. In the centre let a brass style be reared perpendicularly: let there be also a movable pointer reaching from the centre to the outmost semicircle, and a magnetick versorium in a cavity covered over with glass: then let the board be exactly adjusted to the level of the Horizon by the plane instrument with its perpendicular; and turn the lily of the instrument toward the north, so that the versorium may rest truly over the middle line of the cavity, which looks toward the point of variation on on the Horizon. Then at some convenient hour in the morning (eight or nine for instance) observe the apex of the shadow thrown by the style when it reaches the nearest semicircle and mark the place of the apex of this shadow with chalk or ink: then bring round the movable index to that mark, and observe the degree on the Horizon numbered from the lily, which the index shows. In the afternoon see when the end of the shadow shall again reach the periphery of the same semicircle, and, bringing the index to the apex of the shadow, seek for the degree on the other side of the lily. From the difference of the degrees becomes known [Illustration] {172} the variation; the less being taken from the greater,