CHEMISTRY: E. C FRANKUN 
65 
curvature on U and 12i correspond. Thus equations (7) and (11) define 
transformations of surfaces ^ of the Ribaucour type. We call them 
transformations A. When in particular the surfaces C and C\ are 
associate surfaces, which is a special case of transformations if, the 
surfaces Co and Cio are likewise associate, and the surfaces and 
as defined in the preceding theorem, have the same spherical represen- 
tation of their hnes of curvature. 
By means of a generalized theorem of permutability for transforma- 
tions K in general we prove the following theorem of permutability for 
transformations A: If and 122 are two surfaces obtained from a surface 
il by transformations A, there exists a surface ^' which is in the relations of 
transformations A with 12i and 122, and 12' can be found without quadratures. 
Isothermic surfaces are surfaces C for which / = 0. In this case the 
transformations A are equivalent to the transformations of iso- 
thermic surfaces, discovered by Darboux and studied at length by 
Bianchi.^ 
Surfaces with isothermal representation of their lines of curvature 
are surfaces 12 in the sense that the surface C is the locus of the point 
midway between the centers of principal curvature of 12, and Co is at 
infinity. This case requires special study, but the results are analogous 
to those of the general case. However, the transformations A are now 
the same as the transformations of these surfaces established from 
another point of view by me.^ 
1 Eisenhart, Tram. Amer. Math. Soc. 15, 397-430 (1914). 
2Demoulin, Paris, C. R. Acad. Sci., 153, 703 (1911). 
3 Bianchi, Annali Mat. Milano, Ser. 3, 11, 93-158 (1905), 
^Eisenhai-t, Trans. Amer. Math. Soc, 9, 149-177 (1908). 
POTASSIUM AMMONO ARGENATE, BARATE, CALCIATE. 
AND SODATE 
By Edward C. Franklin 
DEPARTMENT OF CHEMISTRY. STANFORD UNIVERSITY 
Presented to the Academy. January 9, 1915 
It has been shown by me that reactions strictly analogous to those 
which accompany the solution of the hydroxides of zinc, lead, and alu- 
minium in aqueous solutions of potassium hydroxide take place when 
the amides of certain metals are treated with liquid-ammonia solutions 
of potassium amide. Thus, just as zinc hydroxide is known to dissolve 
in an aqueous solution of potassium hydroxide to form potassium aquo- 
