684 
AGRICULTURE: LIPMAN AND LINHART Proc. N. A. S. 
Details of the method, as well as numerous examples from biology, 
genetics, physics and agriculture will be given in two subsequent papers. 
1 Actually it was found that the chances are 20000 : 1 that a molecule of oxygen 
gas would have a resultant velocity, at 0° C, of less than 50 meters per second, or 
greater than 2500 meters per second, the mean being 353.6 meters per second. Here 
the mean is not the arithmetical mean of the variables, but the wth root of the products 
of the n (dependent) variables. The theoretical basis for this will be given in another 
paper. For a mathematical discussion see Galton and McAlister, Proc. Roy. Soc. 
Lond., 29, 1879 (365). 
A CRITICAL STUDY OF FERTILIZER EXPERIMENTS 
By C. B. Lipman and G. A. Link art 
* University of California 
Communicated by W. J. V. Osterhout, June 1, 1920 
Among the most expensive and time-consuming experiments in agri- 
cultural investigations have been those which attempt to ascertain the 
proper chemical amendments or fertilizers for soils. This applies in par- 
ticular to the long-term fertilizer experiments like those at Rothamsted 
in England, at State College in Pennsylvania, and at Wooster and Strongs- 
ville in Ohio. Conceived and inaugurated, as they were, at times when 
little or no real authentic information was available relative to the nature 
of soils and plants, it is but natural that fallacious and short-sighted plan- 
ning should have dominated them. It occurred to one of us that as critical 
thinking in this field has become more general, and facts more plentiful, 
it is high time that fertilizer experiments in general and the "long-term" 
experiments in particular be subjected to critical scrutiny. It seemed de- 
sirable to employ the statistical method for this purpose, particularly 
in view of the striking results obtained in this laboratory by our former 
associate, D. D. Waynick. It seemed clear to one of us that if, as Way- 
nick, and Waynick and Sharp had demonstrated, the variability of soils 
and of plants is very large even within selected and presumably uniform 
material, one could not expect previous fertilizer experiments to be of 
much value, since the factor of variability has been entirely ignored in 
their arrangement and study, and the probable error to which they were 
subject was not determined. Accordingly, Lipman and Waynick began 
in January, 1919, a systematic study by statistical methods of the results 
of fertilizer experiments at the Ohio and at the Pennsylvania Agricultural 
Experiment Stations. Mr. Waynick left this laboratory the following 
July, but with a number of interruptions, the work has been continued, 
and we hope to issue the voluminous data, together with a critical dis- 
cussion of them, in due course . Since the work may be a long time in the 
press, we deem it wise to present here a few of the salient and most im- 
