OF DIALING. 373 



In the spherical triangle W D R, the arc W D is LECT. 

 given, for it is the complement of the plane's declination ,^ v ^^ 

 from S the south; which complement is 54 (viz. 

 90 36 :) the angle at R, in which the meridian of the 

 place D cuts the' equator, is a right angle ; and the angle 

 R W D measures the elevation of the equinoctial above 

 the horizon of Z, namely, 38! degrees. Say therefore, 

 as radius is to the co-sine of the plane's declination from 

 the south, so is the co-sine of the latitude of Z to tne 

 sine of RD the latitude of D : which is of a different 

 denomination 113 from the latitude of Z, because Z and 

 D are on different sides of the equator. 



As radius 10.00000 



To cosine 36 0'=RQ 9.90796 

 So co-sine 51 3tf=QZ 9.79415 



To sine 30 U'=DR (9.70211) = the 



latitude of D, whose horizon is parallel to the vertical 

 plane Zh at Z. * 



N. B. When radius is made the first term, it may be 

 omitted, and then, by subtracting it mentally from the 

 sum of the other two, the operation will be shortened. 

 Thus, in the present case, 



To the logarithmic sine of W R=54 0' 1U 9.90796 

 Add the logarithmic sine of R D=38 30' m 9.79415 



Their sum radius 9.70211 



gives the same solution as above. And we shall keep 

 to this method in the following part of the work. 



To find the difference of longitude of the places Z and 

 Z, say, as radius is to the co-sine of 38, degrees, the 



Note 113. That is, if the latitude of Z be north, that of D will 

 be south, and Y Z be situated in south latitudes, the latitude of 

 D will be north. 



Note 1 14. The co-sine of 36 0', or of R Q. Note by the Author. 



Note 115. The co-sine of 51 30', or of Q Z.Idem. 



