_B._ Then place the middle of the needle on the points _a_, _b_, _c_, so that they may freely turn; and set the barb which is at D towards the north, and that which is at C towards the south. You see plainly by this, that the angles of inclination through the arch D C taken altogether, are double to a right angle. For when the south point of the needle, looking north, as at D, comes to look south, as at C, it must make half a circle. _A._ That is true. And if you draw the sine of the arch D _a_, which is _d a_, and the sine of the arch B _a_, which is _a e_, and the sine of the arch D _b_, which is _b f_, and the sine of the arch B _c_, which is _c g_, the needle will lie upon _b f_ with the north-point downwards, so that the needle will be parallel to A D. Then from _a_ draw the line _a h_, making the angle _e a h_ equal to the angle D A _a_. And then the needle at _a_ shall lie in the line _a h_ with the south point toward _h_. Finally, draw the line _c h_, which, with _c g_, will also make a quarter of a right angle; and therefore if the needle be placed on the point _c_, it will lie in _c h_ with the south point toward _h_. And thus you see by what degrees the needle inclines or dips under the horizon more and more from D till it come to the north pole at B; where it will lie parallel to the needle in D; but with their barbs looking contrary ways. And this is certain by experience, and by none contradicted. You see then why the degrees of the inclinatory needle, in coming from D to B, are double to the degrees of a quadrant. It is found also by experience, that iron both of the mine and of the furnace put into a vessel so as to float, will lay itself (if some accident in the earth hinder it not) exactly north and south. And now I am, from this compounded motion supposed by Copernicus, to derive the causes why a loadstone draws iron; why it makes iron to do the same; why naturally it placeth itself in a parallel to the axis of the earth; why by passing it over the needle it changes its poles; and what is the cause that it inclines. But it is your part to remember what I told you of motion at our second meeting; and what I told you of this compounded motion supposed by Copernicus, at our fourth meeting. ========== CHAPTER IX. OF THE LOADSTONE AND ITS POLES, AND WHETHER THEY SHOW THE LONGITUDE OF PLACES ON THE EARTH. _A._ I come now to hear what natural causes you can assign of the virtues of the magnet; and first, why it draws iron to it, and only iron.