154 Mr. J. Y. Buchanan on the Use of the Globe 



and I have used it for a number of years, is one published 

 by Mr. E. Bertaux, of 25 Rue Serpente, Paris. It has a dia- 

 meter of 22 centimetres, and is covered either with black 

 slate cloth for drawing on with slate pencil or chalk, or with 

 parchment paper for drawing on with Jead pencil. To this is 

 adapted a system of divided circles of the same radius as the 

 sphere, called the metro spliere, which is the invention of 

 Captain Aved de Magnac, of the French navy. The metro- 

 sphere consists of one complete circular band of brass, the 

 upper edge of which is a great circle of. the sphere. It is 

 divided into degrees throughout one half of its length, num- 

 bered from 0° to 180°. At right angles to this circle a 

 semicircular band of the same radius passes across from 

 one side to the other. The edge of this semicircle, which is 

 turned towards the graduated half of the complete circle, 

 springs from 0° and 180° respectively, and it coincides with 

 a great circle of the globe. The combination of circle or 

 equator and semicircle or meridian bridging its diameter 

 resembles a crown. At the apex of the crown or pole of 

 the equator a movable quadrant is pivoted. It can traverse 

 the whole of the part of the sphere enclosed by the divided 

 part of the equator and by the meridian, and it can be 

 clamped anywhere in the divided part of the equator. The 

 quadrant is divided into degrees, as is also the meridian. 

 When in use the metrosphere rests on the globe, so that 

 there is complete contact, and it can be shifted all over its 

 surface. It is possible by its means to draw and measure 

 any arcs or angles on the surface of the globe, and conse- 

 quently to solve graphically all problems of spherical geometry 

 with an accuracy which depends only on the dimensions and 

 workmanship of the globe and metrosphere. It is convenient 

 to have a scale of chords of arcs of great circles of the sphere, 

 so that arcs may be measured or laid off with a pair of com- 

 passes. The real usefulness of the globe is not to be learned 

 by theory or precept, but by actual experience in the solution 

 of problems, whether the study be astronomy, or navigation, 

 or geography, or crystallography. Within the bounds of a 

 paper like the present it is possible only to show the general 

 direction in which it is of use in the study of the last-named 

 science. 



The fundamental data for the determination of a crystal 

 are the angles which its faces make with each other. These 

 are measured with the goniometer. Let us follow the process 

 as applied to a polyhedron of any number of plane faces, 

 arranged in any way so as to completely enclose the space. 

 The polyhedron or crystal is attached to the goniometer, by 



