68 ' Mr. H. Hilton o?i the Graphical 



shown in fig. 1) is sufficient for most purposes: and simplicity 

 and economy are gained by confining ourselves to a single 

 net. 



Wulff's net consists o£ a series of arcs o£ coaxial circles 

 intersecting in tv\o real points A and B, and a series o£ arcs 

 of coaxial circles orthogonal to them ; we shall allude to these 

 lines as m and Z respectiAely. 



To draw a circle through two given points on the tracing- 

 cloth which shall be the projection of a great circle, we turn 

 the cloth till both points lie on the same line m, and then trace 

 this line through *. The angular distance between these 

 points can be at once read off on the net. To find the pole 

 of the projection of a great circle, we turn the net till the 

 projection coincides with one of the lines m^ and then read off 

 the position of the pole on the net. To find the angle at 

 which two great circles cut, we measure the angle at which 

 their projections cut; either by drawing tangents at their 

 intersection and measuring the included angle, or perhaps 

 better by measuring the distance between their poles f . 



It may be objected that graphical methods of solving 

 astronomical problems are far inferior in accuracy to methods 

 of calculation. To this it may be replied that for many 

 problems {e. g. those connected with the duration of twilight) 

 a solution correct to within 30^ or so is, from the nature of the 

 case, all that is required. Moreover, " most persons have 

 never studied spherical trigonometry, and those who have 

 studied it usually regard the solution of a spherical triangle 

 as at least a laborious, if not a difficult matter-'^ J. Even a 

 man accustomed to numerical calculations could hardly solve 

 with the use of tables the problems we shall consider as 

 quickly as he could solve them by the aid of the stereographic 

 net even with very little practice. If it is required to solve 

 a large number of problems of the same kind, the saving of 

 time by the graphical method is enormously greater. In 

 fact, what is practically only a single problem by the graphical 

 method is often a whole series of distinct problems by the 

 usual procedure {e. g. " trace the changes in the duration of 

 twilight during the year in any given latitude '') . Moreover, 

 Penfield has shown that with practice and care the errors in 

 the graphical method can be reduced considerably below 10^. 

 Again, " by making use of the graphical stereographic 



* That is, if the points are botJi marked with a x , or hoth with a o ; 

 if one is marked with a x and the other with a o, we must tm-n the net 

 till the points lie one on each of two lines m equally inclined to AOB. 



t Wulff, he. cit. pp. 15, 16. 



X Penfield, loc. do. p. ]21. 



