of Edinhurgli, Session 1883-84, 707 
sum of the similar triangles on CA and CB— and this is any tri- 
angle on AB, ((7.) 
Finally, if any triangle, AEF, he described on AE, since AE and 
corresponding lines are sides of a right-angled triangle, it follows, by 
the result last proved, that the triangle AEE = sum of corresponding 
triangles ; and in like manner for any triangle described on AF, 
Thus the whole .rectilineal figure BEF . . . . A is equal to the 
similar and similarly described figures on CA and BCj lohicli is 
Prop. 31 of Euclid, Bk, YL (H.) 
It may be remarked that the following two interesting results, 
proved in the case of isosceles triangleSj are true for any similar 
triangles described on the sides of ABC. 
(1) If perpendiculars be drawn from the vertices G and P (fig, 1) 
on the hypotenuse AB, the parts of them intercepted by the sides 
BC and CA resj^ectively are each equal to the altitude HF of the 
triangle on AB. 
(2) If CH meet AB in and HF be perpendicular to AB, 
then 
ACGB= AHYB+ ACNF, 
and ACPA= AHHA- ACYF, 
so that ACGB-i- ACTA = AAHB, 
When ABC is isosceles, the triangle CHF disappears.- 
3. Eeport on the OphiueoiIjEA of the Faroe Chanhei, mainly 
collected by HAI.-S, “Triton” in Aiigtist 1882, with 
some Eemarks on the Distribution of the Order, By 
W. E, Hoyle, M.A, (Oxon,), M.E.C.S,, Haturalist to the 
“ Challenger ” Commission. (Plate YII,) 
Some time ago Mr John Murray kindly placed in my hands the 
Ophiuroidea collected by H.M.S, “ Triton” in the Faroe Channel, 
with the request that 1 would draw up a report upon them, and the 
object of the present paper is to communicate to the Society the 
results of my investigations,- 
The collection contains no new species, but one specimen appears 
to be a well-marked variety of Amphiura hellis, Lyman, a species 
