OP ARTS AND SCIENCES. 1G9 



the point iiKirked as the zenith may coincide with the proper pole of 

 the projection, keeping the point marked as the centre in position. 

 The co-ordinates of the chart will now be altitude and azimuth, in 

 terms of which we may read off the new positions of the {loints pre- 

 viously laid down in latitude and longitude. The origin of the azi- 

 muth readings is to be obtained from the known azimuth of the pole 

 of the ecliptic. It will rarely happen that any of the required points 

 will lie in the hemispliere opposite to that supposed to be exhibited on 

 the chart, but if this should be the case, these points can be laid down 

 as easily as the others, from which they may be distinguished by a 

 special form of marking, in order to prevent errors in reading their 

 co-ordinates after the paper has been turned. 



If we desire to convert right ascensions and declinations into equiva- 

 lent positions in latitude and longitude, we regard the circumference 

 of the projection as the solstitial colure. After marking the required 

 points upon the tracing paper, we turn it through an angle equal to the 

 obliquity of the ecliptic, and read off the new positions of the marks. 

 As the right ascension and declination of the zenith are known from 

 the sidereal time and terrestrial latitude, this method may be used to 

 obtain the celestial latitude and longitude of the zenith, which were 

 supposed to be known in the former example. If the azimuth of the 

 pole of the ecliptic is required, we may suppose the circumference of 

 the projection to represent the meridian, lay down the pole of the 

 ecliptic on the tracing paper, and turn it through an angle equal to the 

 complement of the terrestrial latitude. But the relative positions of 

 the zenith and ecliptic may generally be found still more readily from 

 the tables given below, with sufficient accuracy for many purposes. 



The chart may be used conveniently for determining zenith distances 

 and parallactic angles in a given terrestrial latitude by first drawing 

 the given parallel of latitude on the tracing paper, marking its inter- 

 sections with the meridians, and numbering these intersections. The 

 centre of the projection, and the pole, are likewise to be marked, as in 

 other cases. If the circumference of the projection is then regarded 

 as the circle of declination passing through a known star, we may set 

 the point marked as the pole to the place of this star, read its hour 

 angle along the traced parallel of latitude, and the corresponding 

 zenith distance and parallactic angle by the co-ordinates of the chart 

 at the point of the parallel thus determined. The azimuth of the star 

 may then be found, if desired, by supposing the triangle inverted, so 

 that the zenith distance will be read along the circumference. After 

 turning the paper to the corresponding position, the azimuth can be 

 read off on the traced parallel. 



