108 



SCIENCE. 



[N. S. Vol. XVIII. Xo. 447. 



0]V USES OF A DRAWING BOARD AND 



SCALES IN TRIGONOMETRY AND 



NAVIGATION.* 



It may seem a little strange that any- 

 one should think it worth while to call 

 special attention to a drawing board and 

 scales as a means of solving spherical tri- 

 angles and a few somewhat similar prob- 

 lems. For, accurate results can be ob- 

 tained through simple computations and 

 rough results by aid of suitable diagrams 



Suppose the dimensions of the drawing 

 board to be about 22 by 40 inches. Let it 

 be trimmed, as it were, with a metallic 

 border three margins of which are divided 

 into degrees and fractions of degrees so 

 as to form a large rectangular protractor, 

 as sketched in Fig. 1. The border of the 

 fourth side may be graduated uniformly 

 from its center, where is situated a pivot 

 or pin about which the scales may revolve. 





Fio. 2. 



composed chiefly of curve systems. Such,' 

 for instance, are many cartographic pro- 

 jections of the great and small circles of 

 a hemisphere. But where results reliable 

 to about 5' of arc or angle are required, 

 and where computation is to be altogether 

 dispensed with, it seems to me that the 

 methods about to be described certainly 

 possess merits which have not heretofore 

 been fully recognized. 



•Belivered before the Philosophical Society of 

 Washington, January 31, 1903. 



The scales to be used in the solution of 

 spherical triangles are scales of sines, co- 

 sines, tangents, etc., like those shown in 

 Fig. 2, but having, of course, much finer 

 graduations along the edges. For use 

 upon a 20-by-40-inch board, the extreme 

 length of the scales should be about 30 

 inches. For increasing the size of the di- 

 visions, we shall suppose sines and cosines 

 to have been multiplied by 2 in constructing 

 the scales. In addition to trigonometrical 

 scales it is supposed that we have several 



