70 
11. The posterior screw combination is right-handed in the left 
knee, and left-handed in the right. 
12. The two screw combinations in each knee are united, so that 
the anterior half of the anterior combination, and the posterior half 
of the posterior, are alone retained ; while the external femoral 
and tibial condyles respectively consist of the united basal portions 
of one of the threads in each combination ; and the inner condyloid 
surfaces respectively of portions of the other thread in each, but 
consequently towards the vertices of the fundamental cones. 
13. When the knee joint is fully extended, its anterior screw com- 
bination is screwed home, and its posterior is unscrewed ; when it is 
completely flexed the anterior combination is unscrewed, and the 
posterior screwed home. 
2. On the Exhibition of both Roots of a Quadratic Equation 
by one Series of Converging Fractions. By Edward Sang, 
Esq. 
It had been long known that every periodic continued fraction 
expresses the root of a quadratic equation, and in 1808 M. 
Lagrange demonstrated the converse proposition, that the roots of 
every numerical equation of the second degree may he expressed 
by such fractions. The subject has since been examined by M. 
Legendre in his “ Theorie des Nombres,” and also by Barlow, and 
the laws discovered have been applied to the resolution of certain 
classes of diophantine problems of the second order. 
The writers on this subject have considered the two roots of such 
equations separately, and have regarded the two series of fractions 
which converge to them as distinct. In the development of these 
fractions the quotients become periodic after one or more terms have 
been found ; resembling in this way the digits of a recurring deci- 
mal fraction of which some of the earlier terms are not recurrent. 
The object of this notice is to show that these two series form in 
reality parts of one general series, the multipliers of which are pe- 
riodic throughout. To this particular form of series it is proposed 
to give the name duserr , from the Persian jJ&jS two heads , or two 
leaders. 
The character of the duserr progression was exemplified by con- 
sidering the roots of the equation — 
5x Q -32xy + 3ly-z=zO. 
