ACKNOWLEDGMENT 
In addition to those made in the body of the text, it is appropriate at this place 
to make a more complete acknowledgment. Whatever merit this work possesses 
should be credited to the late Dr. John F. Hayford. His untimely death in March 
1925 brought this research to an abrupt termination, after it had been in progress 
continuously, under his direction and inspiration, since the fall of 1912, except 
during two years of the Great War. 
I first became connected with this research as a computer in 1913, and so 
served, intermittently, during summer vacations and other spare time, while an 
undergraduate in the School of Engineering of Northwestern University, of which 
Dr. Hayford was then Director. After graduating in 1920 I served full time on 
these studies, and became the principal assistant on them. At the end of 1924 the 
studies were temporarily halted because of exhaustion of financial support. They 
were to have been resumed again early in 1925, with the aid of a further grant 
from the Carnegie Institution, but Dr. Hayford's affliction and death, coming at 
this time, brought the project to an end. 
Early in 1926, at the request of the Carnegie Institution, I resumed work on 
the studies, but primarily with the object of rounding out in form for publication 
the work already accomplished by Dr. Hayford. At the time of his death, the 
evaporation formula as hereinafter presented had been derived, and its application 
to the investigation of the laws of flow of Stream A, Wagon Gap, Colorado, had 
been practically completed. The evaporation formula, and most of the numerical 
results obtained on Stream A together with the principles developed in connection 
therewith, are strictly those of Dr. Hayford. For the completion of the application 
of the principles developed on Stream A to Stream B; for the completion of the 
flood-flow study on Stream A, and the making of a similar one on Stream B, I, 
alone, am responsible. The completion of these items rendered possible a more 
precise determination of the freezing-melting constants, C, F and M. Studies with 
this object in view were also carried out by me in 1926-1927 to the extent possible 
in the time available. The Appendix to Part I and, in Part II, the application of 
the Pearsonian Generalized Probability curves to the determination of the "Rela- 
tion of S c to Mean, Median and Mode of Frequency Distribution" are entirely my 
own, although, in the latter case, the fundamental idea was furnished by Dr. 
Hayford. 
Except for some notes made in connection with the least-square computations, 
the studies as left by Dr. Hayford were all in numerical form, mostly as least- 
square computations. The principal task in connection with rounding out this 
work for publication, therefore, consisted in abstracting from these least-square 
solutions the theories, principles and numerical results which they embodied, and 
presenting them in logical order. This I have attempted to do in the pages which 
follow. This part of the work in addition to that stated in the preceding paragraph, 
is also entirely my own, and for which I assume full responsibility. 
J. A. Folse. 
Evanston, Illinois, October 29, 1929. 
XI 
