18 os |. REPORT—1874, 
S(“), $(u), Ww) being any three kinematical functions of w; then, if P move on 
the surface 
F (a, y, 2)=0, 
F{f@), 6%), ¥E)} =9. 
Lx. Let P be capable of motion in the plane 
le-+-my -+-ns=p. 
(i) Let fiw) =v’ =(u)=y(w), then P’ describes the central conicoid 
le? +-my? +-nz? =p. 
(i) Let A(u)su’ =(u), (uw) =u, then P’ describes the paraboloid 
le? +-my? +-nz=p. 
There are more simple methods for the description of conicoids, but these are 
mentioned as examples of the general method given above. 
(iii) In two dimensions we can obtain the unicursal quartics from conics by 
putting fw=$(u)=* (Salmon’s ‘ Higher Plane Curves,’ art. 283), 
(iv) By putting /(w) =«?=o(u)=(w), we can describe the wave-surface from a 
surface of the second degree. 
6. Let 0,,0,,0, be three points fixed in space, and P,, Q,, P., Q,, P,, Q, six 
points connected with them in such a manner that O,, P,, Q, ave collinear, and 
O,P,=fA(0,P,), 
or pp=Si(), 
also p,=O, o=,(0,Q,) =fi("a)s 
Ps=9,P3=f(0,Q3) =fa("s)) 
Si(), F.(%), f,(u) being kinematical functions of uw; and let R,, R,, R, be three 
points such that O,R,=0,Q,, O,R,=0,Q,, O,R,=0,Q.,. 
Then, if P,, P,, P, be connected, and also R,, R., R,, it follows that if the P point 
be constrained to move on the surface 
F(p,, poy ps) =9, 
the R point moves on the surface 
FIACW ACD Fs) f=. 
Ex. Let P move on the sphere 
ap, + bp,’ +ep, =a, 
(i) Let f,(w)=Vu=f,(u)=f,(u), then R describes the surface 
ar, +br,+er,= a. 
If the motion be in two dimensions, we thus obtain a method for describing the 
Cartesian ovals, and by inverting these we have bicircular quartics and circular 
cubies (Salmon’s ‘ Higher Plane Curves,’ art. 281). 
Gi) FA,W= F=f =f, 
R describes the equipotential surfaces for three electrified points. 
P' moves on the surface 
On Approwimate Parallel Motion. By W. Havpen, 
On the Application of Kirchhoff’s Rules for Electric Circuits to the Solution 
of a Geometrical Problem. By Prof, Crerk Maxwett, M.A., F.R.S. 
The geometrical problem is as follows:— . - Sigh 
Let it be reqaited: to arrange a system of points so that the straight lines joining 
