One has only to glance down the list of past presidents, which includes Sylvester, Whitehead, Nunn, Hardy and Eddington, to be acutely conscious of the honour of occupying this chair. It would be pleasant to be able to sing, with the King of Barataria, that “the duties are delightful and the privileges great.” The chief duty appears to be the delivery of a presidential address—hardly a pleasure even for the deliverer—and privileges there are none. I notice, however, that I am the fiftieth president of this Association, and that if the A.I.G.T. is included I represent the 57th variety. I am only the third former member of Her Majesty's Inspectorate (which is much older than this Association) to hold office, the others being Mr. W. C. Fletcher and Miss L. D. Adams, in 1939 and 1960 respectively.

The way in which people spend their money is a matter of considerable interest. It is a topic which can be studied from many points of view and with varying degrees of sophistication, but it is well worth considering with the aid of a few graphs or Engel curves. Ernst Engels published his first account of Belgian working class family budgets in 1857 and his name is still associated with this study, though many of his conclusions concerning expenditure patterns have been falsified by subsequent changes in economic and social conditions.

These curves are used to illustrate the way in which expenditure on particular goods and services changes as household income increases. Data for their construction is obtained from household budget inquiries and is usually given in the form of average expenditure per household on a wide range of commodities for a limited number of income groups.

The name ANTELOPE stands for “A Nor (Transistorised Element) Logic Operations Patchboard Experiment.” It was originally designed by Mr. R. L. Lindsay, a mathematics master at Reading School, in the early part of 1965, to demonstrate how a complicated computer can be built up from a number of simple circuits. Mr. Lindsay left Reading School before it was fully operational for logic experiments, although it had been used for binary arithmetic.

After a series of lessons on Symbolic Logic by Mr. J. Periton as part of the second year sixth form English course, two sixth formers developed a method of representing logical arguments by electronic circuits.

In a technological university most undergraduates study mathematics. For engineers this is post A-level G.C.E. and in many cases is taken to a considerable depth. However, some departments admit students with only O-level G.C.E. mathematics and these people are taught the pure mathematics corresponding to that for A-level in the first session. Within the University of Aston this system is used on the Environmental Health Course. This is an undergraduate, four year, sandwich course for the training of public health officers. The students are sponsored by Local Authorities, who provide their practical training. Most of the students enter the University with at least two A-levels, which are usually a selection from Chemistry, Physics, Biology, Botany, Zoology.

§1. Our first theory concerns a set of elements, denoted by letters a, b, c, … and words derived from them. The simplest word, apart from a single letter, has the form ab; other words are formed by adjoining a letter on the right to a previous word. Thus ab, abc, abcd are words. We shall say e.g. d is “hooked on” to abc.

The only statements about words in the theory are of the form X = Y, where X, Y are words, and the sign = has the usual properties. The statements are general in the sense that if any word be substituted for a letter in X or Y, and X', Y' be the new words so got, then X' = Y'. Furthermore if X = Y, then Xa = Ya. Note that if e be hooked on to abcd, we get (abcd)e, which is written abcde.