50 Solution of a Mathematical Problem. 
Phocine Hybrid.—Finally, among mammiferous animals, 
remains to notice the singular fact discovered by the tiesdalek 
Steller, and mentioned by Rudolphi, that the sea-lion, Phoca ju- 
ta, 0 Behring’s island, produces young with the sea-bear, F 
ursina. “T have no doubt of this fact,” adds Prof. Rudolphi, 
“since Pallas speaks of Rudolphi with the — respect, and 
Telesius proved the accuracy of his observations.’ 
(To be continued.) 
Art. VIL.—Solution of a Mathematical Problem ; by O. Root. 
A straicut line whose length is (7) being so moved as alwa ays 
to terminate in the sides of a right angle, required the locus of its 
consecutive intersection. 
The sides of the right angle being taken as the axes of co- 
ordinates, the equation of the line oe length is given will be 
y=ar+b 
In this equation if we make r=0, we ‘ee y=b; when we make 
=0, we get r= —7 ‘These values of ry squared, give 
2 
b+ =r (2). This solved for (a) gives 
me 
(pa Bayt (3). 
The value of pe in i ofbdon (3), substituted in equation (1) 
waka 
gives I= (pF. ++6 (4). 
_ If we differentiate signin (4) allowing (8) only to vary, we 
dy it 3\2 
shall get at spy EH= =0..b=r(1- Ey)? 
this value of (6) substituted in equation (4) gives 
y=r(1— or )} , or by reduction, 
Tp etaps 5), 
which is the equation of the required locus, and is the e hypocye- 
loid, the radius of whose base circle is (7) the then of the given 
line, and the radius of its generating circle } 
We can show that (5) 1s the equation of aie hypocycloid as 
follows 
Ih the general equation for cycloidal curves we have 
ri 
y=(r+r’) cos. 04+(r+r’) cos, eee | 
facr’ (6) 
@= (rr) sin. 0+-(r-er’) sin. ina Jo 
“Ibid. Leco citat.—Prichard’s Researches, i, p. 142. 
