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LVIIL— ON A MECHANICAL METHOD OF CONVEETING 

 HOUB-ANGLE AND DECLINATION INTO ALTI- 

 TUDE AND AZIMUTH, AND OP SOLVING OTHEE 

 PEOBLEMS IN SPHEEICAL TEIGONOMETEY. By 

 A. A. EAMBAUT. 



[Read, April 20, 1887.] 



The principle of this instrument is by no means new. It was in- 

 vented by De St. Eigaud, a Jesuit father, about the beginning of 

 the seventeenth century, in the form of a sundial, which is described 

 in the ninth edition of the Encyclopaedia Britannica. 



The application of the principle, however, to the problem of 

 converting the place of a star from one set of co-ordinates to 

 another has never, so far as I am aware, been pointed out. 



In the spherical triangle, whose vertices are the pole, the zenith, 

 and the star, and whose sides are, therefore, the complements of 

 the latitude, the declination, and the altitude respectively, while 

 its angles are the hour-angle, parallatic angle, and north azimuth, 

 we have the following relations : — 



sin h = sin <5 sin (p + cos 8 cos cos t, (1) 



and sin S = sin h sin $ + cos h cos $ cos A, (2) 



in which h = altitude, A = azimuth, 



3 = decimation, t = hour-angle, 



<p = latitude. 



The construction due to De St. Eigaud, and on which the 

 principle of this instrument is based, is as follows : — 



With C as centre, and AC as radius (see fig. 1), describe a 

 semicircle. Draw CF at right angles to AC. Make the angle 

 FAC equal to the latitude. Draw FL at right angles to AF. 



Now to find a star's altitude, being given its hour-angle and 

 declination, make FAG equal to the declination, and ACD equal 

 to the hour-angle. Draw DE at right angles to AC. With Q as 

 centre, and GA as radius, describe a circle cutting DE in I. Then 

 the angle between Gl and FC is the altitude. 



