130 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
Substituting the value of y from the first into ‘the second equation 
we have: 
Ys MEM ee) nt 
0— Be +sS ie — =) (7-2) 
0= a Ts —2,)a+ St «) (4 —_— ) by (17,) and (17,') 
By lo a 
v, x x. 
=i fe y ot) a a eas — ores 
(Ft) ets ews | 2 
Corresponding to the hi a we have: 
tc Y, Ly — 2, ' Y, %y—, 
et MAY RI 
and Se to the second : 
Cay 
Y= me _ de “x, (- ni)! az, Be za =i by ly cig 
Denoting hat constants by %,, 2%, Ys Yq» respectively, we have 
then the equations of a pair of generatrices of the hyperboloid (13) 
perpendicular to the zy - plane: 
xis me by (17,) 
x Zz 
eas y= i= y (20,) 
&. Yx 
t= Ba My; Y= G2 (20,") 
Similarly the pair of generatrices perpendicular to the yz - plane: 
Yx %,. 
a > er ba 20, 
yee es ae (20,) 
Ys 2 
aire (Visca Taq (20,") 
and that perpendicular to the za - plane 
Z @ 
ait Va a tila io (20,) 
&. x, 
= za rire? a te (20,*) 
Now the second line of each pair intersects the chord, as may be 
proved thus: The equations of the chord (1, 2) are any two of the 
following three equations: 
LE 6 
pte ete (21,) 
