TRANSACTIONS. OF SECTION K. 805 
due to temporary differences in the soil caused by previous inequalities of manage- 
ment or cropping, by the unequal incidence of pests and diseases, or by the indi- 
viduality of the plants. 
Of these sources of error, (1) diminishes with the skill of the experimenter and, 
to a certain extent, with the size of the plot; (2) can only be corrected by 
enlarging the number of the plots receiving the same treatment ; (3) can be 
minimised by continuing the experiment for a sufficient number of years, The 
Rothamsted experiments afford several cases which enable one to estimate the 
magnitude of the errors (2) and (8), cases where there are two plots receiving 
treatment which is wholly or nearly identical, so that both plots are likely to be 
similarly affected by the season. The method adopted has been to reduce each 
year’s results for the two plots to a uniform standard, taking the mean of the two 
plots as 100, thus eliminating seasonal fluctuations and giving each year the same 
weight in taking out a mean over the whole period. The results are plotted to 
show graphically the individual variations from the mean; the probable error of 
the mean result and the mean error of a single result are calculated by the method 
of least squares. 
For example, taking forty-nine years’ results of the two unmanured plots on 
the grassland mown for hay every year, the true means of the two plots are in 
the ratio 94°3 : 105°7, with a probable error of +0°8. The average deviation of a 
single year’s result from the mean result for that plot amounts to +815. There 
is thus a permanent difference of about 11 per cent. in the yield of the two plots, 
due to differences of soil and situation ; this represents the magnitude of errors (2). 
Putting the two sets together to represent the ideal unmanured plot we obtain a 
probable error of 40°67 in the mean result, and an average deviation of any 
single result from the mean of +9°9. As unmanured plots are subject to greater 
sources of error, the results of other manured plots were examined by the same 
method, with the following results :— 
| Average Devia- 
Cro | Sizeof . Durationof | Probable Error tion of Single 
P | Plots | Comparison | of Mean Result Result from 
Mean 
Acre Years Per cent. 
| Hay . - { 49 | + 0'8 + 815 
| Wheat . oe = 52 + 0°6 + 6°2 
Wheat . 5 52 +0°8 £82 
Barley . rr 40 + 0°43 +40 
Mangels } 28 +0°5 + 4°0 
The observations are rarely numerous enough to permit of plotting the 
differences from the mean to see if they yield a normal curve of error. Other 
cases are discussed to ascertain the probable error when several plots are employed 
or the experiments continued over a short period ; certain sources of error in the 
interpretation of the results of field experiments were also considered, In general, 
it is concluded that the probable error of any single plot result is not less than 
10 per cent. 
3. The Determination of the Availability of Insoluble Phosphate in 
Manures. By T. 8. Dymonp, £.J.C., and Grorce CuarKe, 4.2.0. 
Many suggestions have been made in recent years for the use of a solvent for 
phosphatic manures which, while dissolving that part of the phosphate which is 
quickly attacked in the soil and available as plant food, leaves the remainder 
unacted upon. The two most largely employed solvents are a weak solution of 
citric acid, and a stronger solution of citric acid partly neutralised by ammonia. 
The authors have had occasion to use both these solvents in the analysis of a 
large number of samples of basic slag (among other manures). They find that the 
phosphate dissolved by the acid ammonium citrate solution per cent. of total 
phosphate is generally lower the higher the percentage of total phosphate in the 
