( 760 ) 
d a z dz 
dVd0 ~ dff 
EK=° • < i > 
This equation gives rise to quadratures in the following cases: ' 
a. z = a0 - f /(r), Buhl, 1. c., vol. 8, p. 439, comp, also Tisserand, 
“Rec. compl. d’exercices”, p. 426. 
b. l(z) = a 6 -h/(r), Bum,, 1. c. p. 440. 
, = A r aw (0+«> + «*.+ 
d zx=rf t (0)+/*(#)> 
e. z sin (0 
/. z=zr~ l ^+ c , 
9- 2 — — 6* -\r 21 (r). 
2. The differential equation of the asymptotic lines of 6—f(r,z) 
in r and z we find by eliminating 0 between (1) and 6= f{r,z). 
We find: 
This equation-gives rise to quadratures in the following cases: 
a. 0 = l(r)+/<*). 
b. 0 — arc cos— Buhl, 1. c., vol. 9, p. 343, 
besides a few others mentioned above. 
3. In an analogous way we tind the differential equation of the 
asymptotic lines in z and 0 of r= f(z,0). 
It runs: 
Besides in the above mentioned 
cases this equation gives rise to 
quadratures for r =/, (z)f t (0), surfaces of Jamet (Ann. de l’eeole 
norm. sup. ; 1887, Suppl., page 50 etc.; further: Picard, “Traite 
d’analyse” I, 2 nd ed., page 433). 
The classes of surfaces found above are not strictly separated; 
some even are to be regarded as subclasses of others. They can be 
ranked according to the most general types to be found among them, 
whilst others fall under these types, namely as follows: 
