—" 
oe 
January ia, 1917] 
LETTERS TO THE EDITOR. 
{The Editor does not hold himself responsible for 
opinions expressed by his correspondents. Neither 
can he undertake to return, or to correspond with 
the writers of, rejected manuscripts intended for 
this or any other part of NatuRE. No notice is 
taken of anonymous communications.] 
Meteorology and Wheat Shortage. 
In looking through some old papers I came across 
one entitled ‘‘The Law of Sequence in the Yield of 
Wheat for Eastern England for 1885-1904,"’ contri- 
buted by Sir Napier Shaw to the Hann Band der 
meteorologischen Zeitschrift, 1906, pp. 208-16 (Bruns- 
wick: Fried. Vieweg und Sohn, 1906). From a study 
of the rainfall and its connection with the amount of 
the harvest, Sir Napier Shaw applied the method of 
harmonic analysis to the quantity in question, and 
obtained a formula according to which its fluctuations 
are periodic, the period being eleven years. In 
Fig. 42 (p. 212) curves are shown in which the agree- 
ment between the calculated and observed results is 
very close. It now becomes interesting in the light of 
recent events to extend Sir Napier Shaw’s predictions 
for a further period of eleven years, with the following 
results, the numbers representing average yield in 
bushels per acre :—The highest maximum of about 
35:5 should have occurred in 1909-10, followed by a 
minimum of about 29:5 in 1911-12. The predicted 
yield next rises to about 32-5 in 1912-13, and then 
decreases, the lowest minimum being about 27-0 
bushels per acre and occurring at the beginning of the 
war, in 1914-15. From now on the predicted yield 
should increase, but would not reach its former maxi- 
mum of 35-5 until 1920-21. For the period 1915-17 
the predicted yield is not much more than 29 bushels 
per acre. It will be seen, therefore, that, according 
to theory, it was to be expected, both here and abroad, 
that England’s wheat supply, so far as it depends on 
the eastern counties, would be at its lowest at and 
about the present time. G. H. Bryan. 
Pror. Bryan’s reminder of my worl: of twelve years 
ago upon the yield of wheat in the eastern counties of 
England comes at an opportune moment. It may be 
of interest to recall how the ‘theory,’ to which he 
refers, arose. In considering the figures for the yield 
of wheat for England in the twenty-one years 1884 to 
1904, I had noted that they were so closely related to 
the rainfall of the “principal wheat-producing dis- 
tricts" (approximately the part of Britain east of a 
line from Portland to Inverness) for the previous 
autumn that one might almost rely upon losing a 
bushel and a quarter per acre from the crop for every 
inch of rain recorded for the region in the previous 
autumn. There were some exceptional years, and in 
the hope of getting something still more amenable to 
rule I restricted the area to the counties of the meteoro- 
logical district ‘‘England East,” and took out the 
figures for wheat from the returns of the Board of 
Agriculture and for rainfall from the Weekly Weather 
Report. From these it appeared that every inch of 
rain in the autumn meant a loss of 2-2 bushels of 
wheat per acre for the eastern counties, but the occa- 
sional exceptions were not less pronounced than for 
the wider area, but more so. 
Trying to circumvent these vexatious exceptions to 
an obviously useful general rale, I was working with 
a.graph of the twenty yields 1885 to 1904, and dis- 
covered accidentally that it was reversible with refer- 
ence to the epoch 1895-96. The individual values varied 
from 25-2 to 36-3, but the means for the pairs of years 
1895-96, 1894-97, 1893-98, and so on, were nearly iden- 
NO. 2463, VOL. 98] 
« 
NATURE 
369 
tical; the means of any other set of pairs not so. The 
only explanation of a reversibility of that kind that I 
could imagine was the combination (possibly fortuitous 
or occasional) of a series of periodic variations of any 
periods whatever which happened to be concurrent in a 
node in 1895-96. By a crude process of trial and error 
1 was led to the conclusion that the best representa- 
tion of the actual figures on that basis was to be got 
by combining a sine-curve of eleven years period with 
five of its harmonics of selected amplitude, each with 
a node at 1895-96; five of the nodes were ascending, one 
descending. This is a different matter from taking 
any graph between zero values eleven years apart 
and finding the harmonic components that will give 
the best fit, because the graph that I was working 
with crosses the zero line twelve times in twenty years. 
There is little or nothing suggestive of an interval of 
eleven years, but it followed from my analysis that 
the figures must repeat themselves after eleven years, 
a conclusion which I had not previously conjectured, 
but which turned out to be verified in an astonishing 
number of cases, and led to a most accurate prediction 
of the yield for 1905, which was then unknown. 
There were thus two ‘“‘theories’’ in the field, one 
that the yield of wheat depended (negatively) upon 
the rainfall of the previous autumn, the other that the 
figures repeated themselves after eleven years in conse- 
quence of the periodic changes with a fundamental 
interval of which ‘televen years’’ was the nearest 
whole number. A curious point was that the years 
which were exceptional as regards the rainfall-rule did 
not appear as exceptions to the rule of reversal with 
regard to 1895-96. Thus the year 1903 is 6-2 bushels 
in defect of the rainfall-rule, but it compensates the 
yield for 1888 quite properly; on the other hand, 1904 
gives a yield 4 bushels too small to compensate the 
yield of 1887, but 1t agrees quite well with the rainfall, 
while 1887 itself does not. In fact, if 1887 had agreed 
with the rainfall the repetition in 1898 and compensa- 
tion in 1904 would have been quite good. 
Thus there is a good deal of tantalising attraction . 
about either ‘“‘theory,’”’ and the relation of the one to 
the other. Mr. R. H. Hooker took the matter up, and 
discussed the yields of the various crops in relation to 
the weather conditions of different parts of the year in 
a well-known paper published by the Royal Statistical 
Society. He gave his opinion in favour of autumn 
rainfall as against ‘‘eleven years,’’ in spite of the 
triumphant success of the latter’s first prediction, that 
for 1905, which gave 32-8 bushels per acre to compare 
with an actual 32:0, whereas autumn rainfall would 
have given 37:6. 
I have not looked into the matter critically since 
1906, although the question is obviously one of im 
mense practical importance, particularly at the present 
time, when the extension of the wheat area is being 
urged. To some of my friends the period of eleven 
years, which in this case could not be evaded or con- 
cealed, is anathema, and to others all such imagined 
periods and apparent relations are more likely to turn 
out will-o’-the-wisps than beacon-lights. So I thought 
it best to let the question rest until another eleven 
years had expired. That time has now arrived, and 
the question certainly deserves further investigation. 
But there are certain pitfalls in the way of the con- 
tinuance of the investigation. ‘‘ Autumn rainfall” is 
a conventional expression, so is ‘‘eastern counties” 
in regard to the yield of wheat. One is apt to get 
off the line of continuity if one tries to deal with the 
matter amid the press of other things. And even with 
the additional figures properly computed we shall not 
necessarily secure the continuity which the investiga- 
tion requires. The years that have elapsed have been 
memorable for the progress that has been made in the 
successful breeding of wheat, and success in breeding 
