424 Mr DAVIES on the Equations of Loci 



number, is a question that might arise in a future stage of the investigation 

 of these subjects ; but I have found no case in which it appears to be of any 

 consequence whether we commence our expression by the distance from the 

 pole or from the equator. If it can operate at all, it will arise from the com- 

 bination of those indices in framing classifications symmetrical in their forms 

 an object that I can readily admit is likely to be of use in our description of 

 loci, though I have not met with any instance where I could apply it with 

 particular advantage. In case, however, of such method at any future time 

 becoming desirable, we can distinguish the two methods, by prefixing P and 



E to the indices respectively. Thus, E Q) designates in the second quad- 

 rant of positive revolution, and in the third positive quadrant of latitude 

 from the said point of revolution ; and P (~ *) signifies the same thing as 



formerly expressed by ( iY In our investigations, however, we have al- 

 ways reckoned from the pole, and, at the same time, employed the indices 

 without the P prefixed. 



P. 356, line after eq. 5. for points upon read two points for each value 

 of sin cj) 



__. 357, The statement here made is erroneous it originated in a mis- 

 take in the reductions. The equation of the locus of the intersection of the 

 perpendicular upon the tangent with the tangent, may be easily investigated, 

 and is at all events, though not a circle, yet a conic section. The same 

 conclusion is obtained by Professor GUDERMANN*, though his processes 

 have not the slightest resemblance to mine. 



Though the analogy is not invariable as to the identical figures, there is 

 still always a great resemblance. The figures, if not identical, are yet of the 

 same family. For the sake of illustration, I shall here, instead of that, add 

 the analyses of one or two other propositions. I must, however, first remark, 

 that the double sign should have been prefixed to the general focal equation 

 of the conic section at p. 358, viz. 



* CBELLE'S Journal fur der reine und angewandte Mathematik, 8er. band, 324 Seite. 



