nits distance ; and let the law of the elasticity be such, that the several loxodromlo sphela shall have precisely similar aneeeseivo folds on the resulting cylinder, that is, let them take a regular screw-like form. The meridians will then all become straight lines parallel to one another ; end if the membrane be then fixed in its cylindrical shape, that is, if it lose its elasticity, and if one of the meridians be alit all the way down, and the cylinder unrolled into a plane, we shall have beforn us Mereator'a projection, as shown in the following diagram. The degree. of longitude remain everywhere the same, thole, of latitude increase sensibly. The map goes up to 80' of latitude, and any part of the remaining 10' might be drawn; but no space would be sufficient for the whole of the remainder. Any two points A and B, being given, the line A B joining them points out, on the supposition that all the meridiana look toward* the north, the most direct course on which a ship can sail from one to the other : if a compass were placed at A, then A a would show, A it being the north direction, tho point of the compass on which to steer. Again, from o to n the moat direct course
is on the dark line C D ; but o E, E D, is another way of coming to the tame point. It must be remembered that the extreme lines on the right and left represent the same meridian, as they ooincided before the cylinder waft divided for the purpose of being unrolled.
It thus appears that we have a map on which the sailing course between any two places is found by simply drawing a right line. Another advantage, depending upon the nature of the rhumb line however, and not on the projection, is the simplicity of the rule by which the di/stance sailed can be determined. This is pointed out in Hu ems-Um The preceding is Mereator's projection of the whole 360 degrees of longitude up to 80 degrees of latitude. A chart, as in other cases, is a part of the projection, enlarged to a convenient size.