88 Mr. Nixon on the Measuremeni of the 



The curves whose intersections give the foci are equilateral 

 hyperbolas. (See fig. 2.) 



Fig. 2. 



It is easy to show generally that the equation to the curve 

 being 



Ax"' + Bxy + Cy"- + Dx + Ey + F = 0, 



the foci result from the intersection of the curves : 



{B^-^ AC}{x^-f) + {'i BE-^ DC} X- {2 BD-4> EA} y 



+ E^-^ CF- D'+4>AF=0 

 {B'-4^AC}xy+ {BD-2AE}x+ {BE-2DC}y + 2BF-ED 

 — S{B'-4!AC}i^+{2BD-4>AE}y + D'-4>AFlcosxy= 



VI 1 1. Particulars of the Measurement, by various Methods, of 

 the instrumental Error of the Horizon-Sector described in 

 Phil. Mag. vol. lix. By John Nixon, Esq.* 



nPHE horizon-sector may be described, sufficiently for our 

 -*• present purpose, as a telescopic-level, having attached to 

 each side of its telescope a vertical plate with a divided arc 

 carrying at the centre of the divisions a short horizontal axis 

 on which moves an index supporting a spirit-level. The Ys 

 are fixed to a bar of brass, of which one end, formed into a 

 sort of horizontal axis, connects the bar to a frame or stand 

 beneath, which latter serves, by means of rack-work, &c. to^ 

 raise or depriess the telescope. 



Communicated by tho Author: see Phil. Mag. vol. lix. p. 130, 



First 



