386 



Mr DAVIES on the Equations of Loci 



2d, Referred to Astronomical or Polar Co-ordinates. 



Let P and PE be the pole and meridian of reference ; then, if the perpen- 

 diculars PL, PV, and SPX be drawn to the tangent, normal and radius-vec- 

 tor (that is, to MS, MX, and MP), we shall have PS, PX the subtangent 

 and subnormal, and PL, PV the perpendicular from the pole upon the tan- 

 gent and normal. Put EPM = <9 and PM = 0. Then the values of the 

 several functions of the parts of the figure will be as in the following Table. 



TABLE II. 



PAIITS RELATIVE TO THE TANGENT. 



