ASTRONOMY. 65 



angle, and therefore the rules of trigonometry can- 

 not be directly applied to them. If, however, C 

 be the centre of the spheroid, and if AC and BC 

 be joined, the angles PC A, PCB, are deduced 

 from the latitudes, 61. b. Then, in the solid angle 

 at C, are given the two plane angles PCA, PCB, 

 and the inclination of their planes, viz. the differ- 

 ence of longitude, or the angle at P ; therefore the 

 angle ACB may be found by the same case of 

 spherical triangles as before. Hence the straight 

 line AB is also found, the radii CA, CB being gi- 

 ven, 61. 



c. In this way also, are found the angles at the base 

 of the triangle PAB, or those which the plane 

 ACB makes with the planes ACP, BCP. These, 

 however, are not the true azimuths, which are the 

 angles that the plane ADB makes with ADP, and 

 that ABE makes with PEB. 



To find these last ; if DB be drawn, then in the tri- 

 angle BCD, BC, CD, and the angle BCD are gi- 

 ven, whence DB is found. Then in the triangle 

 ADB, all the three sides are given ; wherefore the 

 angle ADB may be found. Next, in the triangle 

 BED, the sides BE, ED, DB are given ; there- 

 fore the angle EDB, and its supplement PDB are 

 found. Therefore the three plane angles ADP, 

 ADB, PDB, which contain the solid angle at D, 

 are given ; whence the inclination of the planes 

 may be found, and therefore the angle which the 

 plane PAD makes with the plane ADB, that is, 



VOL. II. E the 



