314 On the Use of the Globe 



surface for drawing on with lead pencil. To this is adapted 

 a system of divided circles of the same radius as the 

 sphere, called the metrosphere, 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, 

 numbered from o 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 o and 1 80 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 arc or angle 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 solid geometry. 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 polyhedra, of 

 which crystals are a limited class. 



The fundamental data for the determination of a crystal 

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



