of work" which brings unity into so wide a range of mechanical phenomena and is the forerunner of the still more widely inclusive principle of energy. He

also discovers the conditions under which a single push or pull can be regarded as equivalent to two others, and applies his knowledge to the analysis of the stresses in simple frameworks like the suspension-bridge and the cantilever.

From these preliminary studies we pass in the third year to mechanics proper, which is conceived as an attempt to bring under the rule of general mathematical laws the more important types of motion found in physical nature. In studying changes of velocity we take care to avoid a common hindrance to clear ideas by giving attention to change of direction equally with change of speed. Another point of importance is that, instead of confining consideration to the progressive motion of falling bodies and projectiles, we study, side by side with these types of movement, the periodic type represented by the swinging pendulum and the vibrating spring. The simpler grammar of kinematics having been thus mastered we move on Ato kinetics. Using Mr. Goodwill's invaluable Vector Balance 1 we reach clear ideas about 1 mass and

momentum, and learn how the rate of change of momentum measures the force between interacting bodies. The notion of kinetic energy is also introduced, and is linked up with the principle of work studied in the second year.

The work is continued during the fourth year in the same spirit. That is, the object pursued is a clear grasp of fundamental principles rather than virtuosity

1 See Goodwill, Elementary Mechanics (Clarendon Press, 1913), Chap. II.

in solving complicated problems. The former simple study of pendulum movement develops into the theory of harmonic and circular motion, which is extended to include a simple study of progressive and stationary harmonic waves. Finally we seek to establish the fundamental principles of rotary motion as illustrated by the phenomena of bicycling, spinning tops, the gyroscope, etc.1

The course ends here, but if it were to be continued into an "advanced course" it would have a natural completion in a simple study of the elliptic orbits of the planetary system. This requires rather more mathematics than is likely to be learnt in an ordinary four-years' course, but if treated in the way indicated. by Clerk Maxwell,2 would be well within the resources of a fifth-year mathematician. The study of wavemotion should also be continued in the "advanced course" to the point where the student can appreciate Fourier's celebrated method of analysing periodic movement and its application to tidal prediction and similar matters.3

The second of the three subordinate courses is devoted to geology. Of this it is sufficient to say that it runs through the last three years, is very modest in scope, and deals partly with questions which arise inevitably in the study of geography and partly with matters, such as the paleontological record and the

1 In dealing with these subjects the teacher will gain much help from Crabtree, Spinning Tops and Gyroscopic Motion (Longmans, 1901), as well as from Prof. Perry's well-known little book, Spinning Tops (S.P.C.K., 1910).

2 In his wonderful but sadly neglected little book, Matter and Motion (S.P.C.K., 1888).

3 For an elementary treatment of these subjects the author may refer to his Exercises in Algebra (Longmans, 1914), Part II., Section

emergence of man, which are more closely connected with biology. It need hardly be pointed out that local circumstances should have a determining influence on the topics to be studied in this course, especially in the final year.

We have lastly to describe the third of the subordinate courses. This represents an attempt to restore to something like its due place in the curriculum the mother and queen of all the physical sciences-astronomy. A certain amount of astronomical information is necessarily given in every course on geography, and is, indeed, regarded as part of what " every one should know." Our aim is to place this common knowledge upon a proper basis of firsthand observation and inference, and, while enabling the teacher to get rid of an undesirable element of dogmatism in his teaching, to lead the pupil into what often proves the most attractive of all the highways of science.

The course enters into the curriculum of each of the first three years. In the first year we seek by means of simple observations and graphic records to establish the apparent rotation of the sun and stars about an axis directed to the near neighbourhood of the pole star, and to explain the principles of civil time-measurement. In the second year our observations and records are similarly directed towards the discovery of the apparent annual motion of the sun, which is the basis of the calendar. The third year carries the argument into wider fields. Working with the methods learnt in the earlier years and using the data printed in Whitaker's Almanack, the student sees how the elliptic motion of the sun and moon is established, and how eclipses are caused and can be predicted. Finally he learns something about the architecture of the solar

system, studies Kepler's laws, and is shown how the relative and absolute dimensions of the planetary orbits have been discovered.

As in the case of biology, any further development of the subject is left to the individual's initiative and the school Scientific Society. It should, however, be noted that the study of spectrum analysis in the fourth year brings the course, for a moment, back to astronomy on one of its most attractive sides. And, as we have already suggested, the boy who continues mathematics as part of an "advanced course" should follow the astronomical argument on from Kepler to Newton, and should make acquaintance with the dynamical foundations of the theory of elliptic

motion.

It will probably be agreed that the curriculum we have outlined is liberal enough to satisfy any reasonable demands. The criticism to be expected is, indeed, that it is too full. The reader who is inclined to think thus should, however, remember our insistence that the proper aim of a general course in science is to give, not an exhaustive knowledge of detail nor a mastery of laboratory technique, but what we have called a realization of the scientific life and an appreciation of its more important contributions to the world of ideas and the welfare of man. A great deal of time is consumed at present in work that does little towards the fulfilment of that aim. Occasional practical exercises of the "drill" type will always be necessary to give the pupil a sound grasp of a principle or a method, but a much wider range of useful instruction would be possible if it were generally recognized that technical exercises of this kind divorced from the development. of a definite scientific argument have comparatively

little value, and have received too much emphasis in the past.

On the other hand, it is admitted that the programme presupposes favourable circumstances including, besides a reasonably good material equipment and enthusiastic teaching, a full measure of time. Where the conditions are less favourable the scope of the scheme must be narrowed, but the work should still, we urge, be carried out with the same aims and in general accordance with the same principles of method. This is, in particular, the reply we would offer to the question what should be done in the Elementary School. The supersession of the "schools of science" was followed, we have said, by a notable diminution in the amount of science taught in Elementary Schools. The reaction has, perhaps, gone too far, but it was hardly to be regretted, since it gave opportunity for strengthening the primary curriculum where it was weakest, namely in the "humanities." In a curriculum planned to end at latest at the age of fourteen there was, in fact, no room for an extended course in science which would not squeeze out or attenuate courses of study of still greater general importance. But with the advent of universal instruction up to the age of eighteen the situation will be radically changed. It will be possible to ease the pressure during the primary period by postponing topics which were included in the scheme of study not because they were appropriate to the age of the pupils, but because they were deemed of essential importance and there was no other opportunity of teaching them. Schemes of -science instruction can be planned in which the period

1 About five hours per week, exclusive of the time given in lessons in mathematics and geography, to some of the topics set down as part

of the course in science.