A number of introductory statistics books published during recent years have presented the basic theory of point estimation (see, for example, [1]–[4]). The time now seems ripe for a few cautionary tales to be told, or retold, for there is more to the estimation of a parameter than searching for an unbiased estimator or maximising the likelihood of a random sample. Having said that, I need at once to emphasise the distinction between methods of estimation on the one hand, and properties of estimators on the other. For a particular problem, the method of maximum likelihood, fcr example, provides a possible set of estimators for the parameters involved. Other methods such as least squares or minimum-χ2 might provide alternatives; but no estimator should ever be put to use until its properties have been investigated in some depth. And here lies the rub; for, as I intend to show in the following paragraphs, the choice of criteria by which one estimator is judged superior to another rests, ultimately, with the individual statistician or researcher responsible for the estimate produced. In other words, no completely objective solution to the estimation problem is tenable.

In 1924 The International School of Geneva was founded to cater for the families of the diplomats and officials working in the headquarters of the League of Nations. Since then, and with much greater speed since 1947, schools have been set up in many of the famous towns and cities throughout the world for the children of parents who, for one reason or another, spend some part of their working lives in foreign countries. The children who attend these schools come from very varied backgrounds, tend to move even during the later years of their schooling and have an almost undefined variety of plans for their future education or professional training.

A semi-regular tessellation is one consisting of regular polygons of the same length of side, with the same ‘behaviour’ at each vertex. By this we mean that the polygons appear in the same order (though different senses are allowed) at each vertex. The three regular tessellations are for convenience included here as special cases of semi-regular ones. An example of a semi-regular tessellation is that with triangle–triangle–square–triangle–square in cyclic order, at each vertex. A shorthand notation (‘Schläfli symbol’) for this is 3.3.4.3.4.

In Gazette No. 394 (December 1971), R. H. Bromley raised an interesting question: what is the rôle most appropriate to each of the two familiar forms of the derivative, Leibniz’s dy/dx and Lagrange’s f′(x)?

Most elementary differential equations texts treat reduction of order and variation of parameter as separate—and seemingly unrelated—methods. The purpose of this short article is to show how these two well-known methods may be regarded as special cases of a more general algorithm, and to clarify the conditions under which they are applicable. We suggest that this algorithm be called ‘parametric reduction’.