In Part I is given a survey of the results of a statistical examination of the yield of the plots of Broadbalk “Wheat field during 67 years. The main features of the comparison of mean yields are well known; the comparative rates of decrement, shown in Section 5, supply a class of facts well worthy of further study. Particularly striking are the relatively slow rates of decrement of plots 2b and 8, compared with plot 7, which would seem to show a permanent advantage in very high nitrogenous dressings, and to emphasise the need for caution in the application of the principle of diminishing returns. The evidence of the influence of potassium sulphate and its substitutes, sodium sulphate and magnesium sulphate, shown in Table V, is also very striking. An unsuspected feature of the changes of mean yields, which precludes the possibility of obtaining from these data true curves of exhaustion has appeared in the slow changes which have taken place in all the plots in a similar manner. In Part II the mathematical methods by which the variation has been analysed has been discussed, partly as a justification of novel procedure, partly, to make clear that the three types of variations found have been genuinely distinguished. In Part III such evidence as is available has been presented, in order to throw light upon the possibility that the changes in mean yield have been caused by variations in the prevalence of weeds at different periods.

One point of importance which should be emphasised is that average wheat yields, even over long periods, from different fields or for different seasons cannot approach in accuracy the comparison of plots of the same field in the same seasons. The advantage of the method adopted by Lawes in the permanent experiments which he instituted is very evident. The effects of weather clearly require that the seasons should be identical, unless the series be very long, but the slow changes in mean yield show that even comparatively long series of different years from the same field cannot be accurately compared. Within the same field, however, the slow changes have almost proportional effects, and comparison between the mean yields of neighbouring plots may be made with great accuracy. The only case in which changes in mean yield sensibly affect the comparison of averages is that of plots 17 and 18. In comparing these with plots 3 and 4, 5, 7, and 10, it would be more accurate to confine attention to high yielding periods, at which the disturbing causes are at their minimum.

It is believed that the deviations from the smooth curves, which have been freed, for the most part, from the effects of exhaustion and weeds, form statistically homogeneous material for the study of meteorological effects.