Dr. W. G. Bickley : In the first place some explanation may be looked for as to why one so apparently unsuitable should be entrusted with the task of opening this discussion. It is years since I was associated with school teaching; at present drawing is difficult, and proper instruction of pupils, and criticism of their work, would be almost impossible. Admittedly I was rash enough to try to help the programme secretary by proposing this subject for discussion, and then the Council would not let me escape the punishment for my temerity.

In a comparatively short paper, no complete survey of the range of agricultural problems whose solution involves statistical methods can be given. I have therefore chosen to confine myself to one particular theme, the development of the modern field experiment, even though this has meant that I must present a rather unbalanced picture on account of the omission of other important topics such as the use of sampling methods. During six years in the Statistical Department of the Rothamsted Experimental Station, I spent much time in the planning and analysis of a large annual programme of field experiments, and I have illustrated my paper with examples drawn from the work of this Station, at which many of the new ideas in field-experimentation were first tried. I have not attempted to discuss mathematical details at all fully, for the pure mathematics of statistics is a large subject in itself; my present concern is to show some of the practical applications of the theory.

There is a problem which is much in favour at present of which one version is this : a man has 12 pennies among which there may be a counterfeit coin, which can only be told apart by its weight being different from the others. How can one tell in not more than three weighings whether there is a counterfeit penny, if so which one it is, and whether it is heavier or lighter than a normal penny? (Math. Gaz., XXIX (1945), pp. 227–229; XXX (1946), pp. 231–234.) This puzzle seems to have originated in America. The purpose of the present note is to make clear what is the best possible solution in the most general case of any version of the problem. No originality is claimed for these solutions, as no doubt many of them have been obtained independently many times before : but I am not aware that any complete and systematic account has yet been published.

Mary Rose was busy with her homework. John, her brother, had gone the Pictures with some friends, and her parents were out as well. So Mary we quite alone. The shades of evening were falling, and the fire glowed cheerful in the grate. But the growing gloom and the soothing warmth made Ma feel rather drowsy. She looked at her book with heavy eyes and ree “Multiply 2–763 by 100”. Then she put down her pen with a sigh, as rested her head wearily on her hands.