385 
5. Let geodetic lines issuing from the same point upon a 
line of curvature, and passing through the umbilics o, o’, meet 
the line of curvature again in the points p, p’.. Then will the 
locus of the point of concourse of the geodetic lines op’, o’p, 
be a line of curvature of the same species as the given one. 
The following note, by Mr. M. Roberts, on a theorem 
relating to the Hyperbola, was also read: 
Let s denote the difference between the infinite are and 
the asymptote of the hyperbola, whose equation is 
a oy? 
a b? 
and let s’ be the length of the quadrant of the curve which is 
the locus of the feet of perpendiculars dropped from the centre 
upon its tangents; also, let =, =’ denote the same things in 
reference to the conjugate hyperbola 
a 2 
7a ties 
and we shall have 
3 a ee 
ss’ + =3/ = in {e —Vae— bs} 
_ where we suppose a >#, and denote by s an are of the first 
_ hyperbola, measured from the vertex to the point whose coor- 
_ dinates (2’, y’) are 
Z 2 
>? 
_ Ifa = 5d the hyperbolais equilateral ; the derived curve is the 
_ ¢ommon lemniscate, s = 3, s’= »’; and 
*.. ss’ = ja’, 
a theorem proposed by Mr. W. H. Talbot, and proved by M. 
_ Sturm, in vol. xiv. of Gergonne’s Annales de Mathematiques, 
page uv. ; 
rinse 
__ Professor Harrison read the following paper on the ana- 
aS tomy of the elephant : 
Cf Having had, within the last few weeks, an opportunity of 
examining the body of an elephant which died in this city, 
a 2K 2 
 —— y= Ve — B. 
