VOL. XXXI.J PHILOSOPHICAL TRANSACTIONS. 515 



A. Draw fik, and ke parallel to ke, meeting ce in e. Because bp =: be, and 

 KP = KE, the angle kbp = kbe. But the angle kBP is greater than kBe ; 

 hence kp is greater than ke. But because ac is the 4th part of the parameter 

 at A, the focus of the parabola will be somewhere in the circumference of the 

 circle, described with the centre a and radius ac. Let that focus be p, and 

 draw pk. Then because pk is greater than pk, it will also be greater than ke. 

 But as the parabola passes through k, pk ought to be equal to ke. Therefore 

 neither can a parabola be drawn to pass through a point k more distant than k, 

 nor can the body be projected to a distance greater than ak. q. e. d. 



Prop. xi. Given the same; to find the Locus of the point k, or to describe 

 the curve, which touches all the Parabolas described with the same vertex a and the 

 same parameter. — Let the given vertex be a, fig. Q, and in the direction of 

 gravity draw ca equal to the 4th part of the given parameter. Then describe a 

 parabola, whose principal vertex shall be c, and its focus a ; and it will be the 

 curve sought. 



For draw any line ak, in which take ap = ac, and draw cb perp. to CA, 

 and let k be the point found in the preceding proposition. In ac produced 

 take cc = ca, and draw ce parallel to ce ; also draw kec parallel to ac. By 

 the foregoing prop, ke is = kp ; hence, since also ap is = ac, and cc := Ee 

 by constr. therefore Ke is = ka ; hence k is in the parabola described with the 

 focus A and principal vertex c. q. e. d. 



And bisecting the angle ake by the line kb, this will touch both the parabola 

 described to the focus p through a and k, and to the focus a through k. Hence 

 the parabolas mutually touch each other, q. e. d. 



An Account of the Moose-Deer* in America. By the Hon. Paul Dudley, 



F.R.S. N°368, p. 165. 



The moose is an animal thought peculiar to North America. There are two 

 sorts, the common light grey moose, by the Indians called wampoose ; these 

 are more like the ordinary deer ; they spring like them, and herd sometimes to 

 the number of 38 together. 



The other is the large, or black moose, which is the chief of the deer-kind. 

 He has several things in common with other deer, and differs from them in 

 several things; but in all very superior to them. The moose is shaped much 

 like a deer, he parts the hoof, chews the cud, has no gall, and his ears are 

 large and erect. The hair of the black moose is a dark grey, and on the ridge 



• Cervus Alces. Linn. 

 1" ■ 3 U 2 



