Few subjects deserve attention better than the problem of teaching higher mathematics to the average student.

Any man who does work in the world will some day, even though he may be a classical scholar investigating variants in manuscripts, be the worse for not knowing more mathematics ; and if he is not too closely limited by his environment he may even realise this fact. A goodly proportion of the work of the world must be done by quite ordinary folk. Something will be gained if the average student is helped even a little by being enabled to use the calculus and to think of its machinery as an engineer thinks of a drill, and not as a West Coast native thinks of a Ju-ju.

An illustration may be taken from the Astronomer Royal's recent text-book. A star of the third magnitude is very much brighter than a star of the fourth magnitude. But the fourth-magnitude stars are more numerous than the third-magnitude stars, so that in fact we receive more light from the fourth-magnitude than from the third-magnitude stars. To raise all fourth-magnitude stars to the third magnitude would increase our light more than to raise all third-magnitude stars to the second magnitude.