ZOOLOGY: J. LOEB 
313 
4: 0, a = {a,,a,, . . . ),^={h,,h2., . . . ). (9) 
2, . . . 
Suppose that there exists a number B such that 
^l,\D,>\^Br, i=\,2, .... 
where Dki is the cof actor of the element d/k/byu in (9). Let it be assum- 
ed that for every e > 0 there can be found a number de > 0 such that, for 
I Xj - aj \S de {j = 1, 2, . . .) it follows that \ fi(^, (3) \ ^e (i ^ 1, 2, 
. . .). Then there exist positive constants (c, d), 0 < d ^ 1, 0 < c ^ d, 
such that to every ^ satisfying \ xj — aj \ ^ crj there corresponds one and 
only one solution of (2) in the region defined by \ yj — I ^ drj. Further- 
more, the solution ry {xi, X2, . . so determined is Ci for all ^ satisfying 
I Xj - aj \ S crj. 
The problem of obtaining continuation properties for the solution 
-q (^) is not developed in the present paper because the form of the 
hypotheses used here does not readily lend itself to this generalization. 
^ Cf . an equivalent theorem proved in Bolza's Vorlesiingen iiher Variationsrechnung, p. 
423, part (b). 
^ dfversigi af Kongliga Vetenskaps Akademiens Fdrhandlingar, 56, 395-411 (1899). 
^ These Pr,oceedings, 1, 350 (1915). 
^ Atti dei IV Congresso Inter nazionale del Mathematici, 2, 98 (Roma, 6-11 Aprile, 1908). 
" Introduction to a Form of General Analysis, New Haven Mathematical Colloquium. 
6 Paris, Bull. Soc. Math., 27, 215 (1899). 
'Ibid., 36, 95 (1908). 
^ Cf. Kowalewski, Einfiirung in die Determinanten-Theorie. 
» Paris, Bull. Soc. Math., 31, 184 (1903). 
THE SEX OF PARTHENOGENETIC FROGS 
By Jacques Loeb 
ROCKEFELLER INSTITUTE FOR MEDICAL RESEARCH. NEW YORK 
Read before the Academy. April 17. 1916. Received. April 21, 1916 
When it was established that larvae could be produced from unfer- 
tilized eggs by chemical methods,^ a number of secondary problems 
arose. Foremost among these was the question whether or not the 
organisms thus produced were capable of developing into normal adults. 
This was at first considered improbable, especially by those who ac- 
cepted Oscar Hertwig's statement that fertilization consisted in the 
fusion of the egg and sperm nucleus. Since no such fusion takes place 
in artificial parthenogenesis, it became obvious that either Hertwig's 
definition of fertilization was wrong or that artificial parthenogenesis 
was merely a pathological phenomenon not capable of leading to the 
formation of a normal organism. 
dfi {a, ^) 
