Solution 0/ Astronomical Problems, 69 



methods .. .a check upon the results o£ numerical calcu- 

 lations can be made. The importance of having some simple 

 method of checking cannot be overestimated""^. Lastly, 

 " most persons . . . use formula? and tables, as a rule, in a 

 mechanical way. With graphical methods . . . every operation 

 is clearly understood ... In the majority of cases, numerical 

 calculations are laborious, while graphical solutions appeal to 

 one like pictures, which, to a certain extent, tell their own 

 story ■'^f. On this account the stereographic methods for 

 educational purposes can hardly be too highly valued. 



Fedorow, WulfF, and Penfield have used the stereographic 

 net for the purposes of crystallography; and the latter has also 

 employed similar methods for navigation problems. 



AVe shall proceed to illustrate its use for the answering of 

 certain typical questions in astronomy. 



(1) To convert right ascension and declination into lon- 

 gitude and latitude. 



We suppose the celestial sphere stereographically projected 

 on the plane of the solstitial colure ; then the poles of the 

 equator and of the ecliptic lie on the circle s. Make the 

 north pole coincide with the point A of the net, and draw the 

 line OR (on the tracing-cloth) such that the angle ROC = i 

 (the obliquity of the ecliptic) {. Then with the aid of the net 

 mark in the positions of any number of stars whose right 

 ascension and declination are known. Turn the tracing-cloth 

 so that OR coincides with 00. The pole of the ecliptic now 

 coincides with A, and the longitude and latitude of all the 

 stars can at once be read off. 



(2) To convert longitude and latitude into right ascension 

 and declination. 



This is solved by a precisely siiitilar method. 



(3) To find the altitude and azimuth of stars whose north 

 polar distance and hour-angle are known. 



We project onto the plane of the meridian and then pro- 

 ceed as in (1), replacing the pole of the ecliptic by the zenith 

 and the obliquity of the ecliptic by the colatitude of the place 

 of observation. 



(4) Find the hour-angle and north polar distance of stars 

 whose altitude and azimuth are known. 



This is solved by the same method as (3). 



(5) Given the right ascension and declination of any 

 number of stars at the present day, draw a stereographic 

 map (on the plane of the horizon) which shall represent 

 the appearance of the heavens in given latitude at 

 4.40 P.M. at the winter solstice x years ago. 



* Penfield, loc. cit. pp. 121, 122. f Ibid. 



X The net of course serves the purpose of a protractor. 



