422 Mr DAVIES on the Equations of Loci 



(e /t ,} The preceding deductions apply immediately to the first branch ly- 

 ing on the hemisphere next to P ; but similar ones also apply to that lying 

 upon the other hemisphere : and indeed the unrolled logarithmic furnished 

 by these two spherical symmetrical branches, correspond to the two symme- 

 trical branches which we ought to have in the common logarithmic. 



(f M ) The other projections, though giving neat results in an algebrai- 

 cal and geometrical point of view, do not call for any special discussion. We 

 shall therefore merely put them down for the first branch (P). 



Orthographic : 



ale 1 



.,>.,. - = vnF 



Stereographic : 



or r= 

 1- 



according as the first or second poles are taken for the second or first branch 

 of the curve. 



P. 347, 1. 14, for n cos a read x cos a 



~ 349, Eq. 6. for cos = read cos <p = 



350, Number the figure 28. 



In eq. (1 3.) for cot a 6 1 read cot a 6 1 



_ 351, Eq. (15.) for cot X sin 2 (p read cot X sin (p 



~~ 352, Number the figure (29.) 



355, In Note (B) of the former part of this dissertation, I employed 



the term " region" to designate the right octants of the sphere, formed by 

 two meridians at right angles to one another and to the equator. In some 

 subsequent inquiries} where I had occasion to frequently refer to these 

 regions, it occurred to me that the trouble of continually writing them 

 might be very much lessened, at the same time that greater perspicuity 

 would be produced, by merely putting down the number itself which ex- 

 pressed the quadrant of either (p or 6 in which the point spoken of was si- 

 tuated, this number being so marked as to prevent its being mistaken for 

 any thing else than a statement of that circumstance. The method em- 



