The news of the sudden decease of the above named gentleman, who was a mathematical master at the “Shop” for a period of more than a quarter of a century, will be received with feelings of profound regret by many officers of the Royal Artillery and Royal Engineers.

Mr. Jackson left evening study (7.15) on the 17th October in his usual health, but was picked up unconscious just outside the West Lodge at 7.30 p.m., and conveyed to the Plumstead Infirmary, where he died the morning after without having regained consciousness.

Nothing was known of the sad occurrence in the “Shop” until after his death. So passed away one who was universally respected and esteemed, and who was held in great regard by all who knew him, both from his refined and gentle character and high intellectual attainments.

That the advantage of using vector analysis in mathematical physics has met with so little recognition by British applied mathematicians must appear rather strange to those of other countries. There are probably not more than half a dozen among us who habitually use vector methods and notation, at any rate in published work. The fact is still more surprising when we recall the work of Maxwell and Heaviside, seeing that the former gave a sort of authority to the curl and divergence, while the latter had so much to do with the systematic development of the vectorial calculus.

Perhaps the chief reason why vector analysis has not come into more general favour with us is that our leaders in applied mathematics have not felt the need of it. It has often been remarked, and perhaps with some degree of truth, that nothing can be accomplished by vector methods that cannot also be done by Cartesian analysis ; and therefore, it is argued, the change is unnecessary and useless. If we had to deal only with minds of special mathematical ability and analytical insight, this conclusion might be accepted. But with the average student so much of his attention is occupied in dealing with the complex array of symbols of partial differentiation to which he is often led in Cartesian analysis, that he is unable to grasp the inner meaning of the work. It is difficult for him in many cases even to see exactly what is expressed in the formulae obtained, involving as they do the three components of a vector quantity in combinations not easy to visualise. And even if the student succeeds in following the argument it is often almost impossible for him to remember either the train of reasoning or the result arrived at. He does not perhaps see why his equations should be differentiated partially with respect to x, y, z and added, or with respect to z, y and subtracted.

I suppose that most teachers of Elementary Mathematics, when first they broach the subject of finding the circnrnference of a circle, write on their blackboards for comparison

and draw the conclusion that “as these results agree a far as the third figure, the approxinlatioll π=3 1/7 can reasonably be expected to get the first 3 figures of your answer right.” The purpose of this paper is to allalyse to some extent a few practical rules of this type.