hy Means of Graphical Methods. 



253 



recommend it. The second protractor, figure 2, is a measuring 

 scale, consisting of a series of stereographically projected 

 small circles drawn about the 0° and 180° points. It was 

 described in the former paper as protractor No. II, having a 

 circular form, but one-half of the circle, which is superflu- 

 ous, has since been cut awaj from the original plate. It will 

 be referred to in this paper as the small circle protractor. 

 The third protractor, figure 3, consists of a series of stereo- 

 graphicallj projected great circles, and will be referred to as 

 the great circle protractor. Purposely no numbers are printed 

 on this protractor, and those using it will do well to lay it 

 printed side down and number the graduation with India ink, 

 as shown in figure 3. If a number then happens to interfere 

 with the uses of the protractor, it may be easily washed away. 

 The uses of the protractors may be explained by reference to 

 figure 1. If y and y' are two points on a stereographic pro- 



jection, the great circle passing through them may be found 

 by centering the great circle protractor, figure 3, over the pro- 

 jection and turning it until an arc is found which passes 

 through, or proportionately near, y and y' . The position of 

 the protractor then determines the points a and h on the per- 

 iphery, and its graduation gives the angle at «, 33° 20^, or the 

 distance z to z' . Knowing the distance z to z\ the radius for 

 constructing the great circle may be taken directly from scale 

 No. 1 of the drawing paper. By now applying the small circle 

 protractor, figure 2, with its 0° and 180° points at a and J, the 

 distances a to y and a to y' may be determined from the grad- 

 uation, and the difference gives the distance y to y'. Thus a 

 great variety of measurements may be made with facility and 

 rather astonishing accuracy. 



A beam-compass is an essential for accurate work, as ordi- 

 nary dividers are not stiff enough to be relied upon for draw- 

 ing circles having long radii. A compass constructed on the 

 principles shown in figure 4 may be recommended, the idea 

 having been suggested by Professor Charles B. Pichards of the 



Am. Jour. Scr. — Fourth Series, Yol. XIV, No. 82. — October. 1902. 

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