On a protractor for use in constructing stereographic and gnomonie projections of the sphere. (With Plates III, IV, IV a and V.)

The protractor of which an account is given in the following pages is intended to facilitate the construction of stereographic and gnomonie projections of the sphere, especially on the part of students of crystallography. The fundamental properties of these projections, on which its design depends, have long been known, and have been the basis in the past of methods somewhat similar to those about to be described. Any novelty there may be in the device is to be sought therefore in the convenient arrangement of its parts, and in the ease with which it may be constructed and used, rather than in the principles which it embodies. We will consider first the construction of the protractor, then its application in tile case of the stereographic and gnomonic projections, and in conclusion will deal with a few points of interest in the history of these projections.