' NOTES 45; 



it into a negative one ? There is nothing of the kind in the science of number, 

 but there is something of the kind in the science of space. If in geometry- 

 there is something which can turn a Une through a right angle, then that some- 

 thing will, if applied twice, turn the same line through two right angles — turn 

 it from the positive position into the exact opposite and negative position. 

 Therefore the something which can turn a line through a right angle may be 

 admitted as the equivalent of V — i ; but in geometry only. But, even when 

 looked upon in this light, it is not in any way a number, but is a versor, that 

 is, an operation — which is quite different from any number. 



It seems to me (a very humble amateur) that such distinctions should 

 receive more attention in our books. For example, Whittaker and Watson 

 say on page 4 of their Modern Analysis that, " From the logical stand- 

 point, it is improper to introduce geometrical intuitions to supply deficien- 

 cies in arithmetical arguments " ; and yet they go on immediately to appeal 

 to geometrical intuitions in the case of complex numbers and then accept 

 Argand's diagram. To my painfully laborious mind this diagram is wrong 

 because it can apply only in two dimensions. The proper explanation of the 

 rectangular versor is not by means of Argand's diagram but by means of the 

 magnificent solution given by Hamilton — which applies to three dimensions 

 and is universally applicable. Why on earth, so many years after Hamilton, 

 do we continue to talk about Argand's conception v? Hamilton generalised 

 it just as Darwin generalised Lamarck's theory. Argand and Lamarck are now 

 both comparatively out of date. 



Hamilton's vectors and versors are not numbers but more than numbers. 

 They are the results of operators acting upon numbers and producing some- 

 thing else. The versor which is incorrectly written V — i is not a number but 

 something else. Why not abandon it entirely in algebra, and, if we use it 

 in geometry, use it in the sense of Hamilton and not of Argand ? Why 

 pretend what is not true ; why persist upon the number V — 1 when we do 

 not insist upon the logarithms of negative numbers to positive bases, and 

 other conceptions which are really non-existent because impossible ? Yet 

 our books go on repeating this tale, just as they repeat the fabulous equation 

 ^''= I I 



Scorbutic Cooking (R. Ross) 



Much work on Scurvy has been done recently by Miss Harriette Chick 

 and her colleagues at the Lister Institute and with the help of the Medical 

 Research Council. In the British Medical Journal for October 9 she and 

 Elsie J. Dalyell described an epidemic of scurvy in a children's clinic at 

 Vienna last year. The diet of the children should have contained enough 

 vitamines, and sufficient vegetables were provided for this purpose, but the 

 authors conclude that the scurvy was due to the fact that the vitamines in 

 the vegetables were destroyed ; and they make some very important remarks 

 upon the danger of over-cooking vegetables, and also some useful suggestions 

 for removing this defect. They advocate steaming vegetables instead of 

 boiling them. They also advocate the use of germinated seeds (beans, peas, 

 pulse, etc.), which are well known to contain much anti-scorbutic substance. 



In my opinion this matter is of very wide importance throughout this 

 country, and I do not think that it afiects children only. In my Malaria 

 Clinic (Ministry of Pensions) I see a very large number of cases of chronic 

 malaria. The treatment for this disease by quinine has now become almost 

 certain as regards the destruction and ultimate banishment of the parasites 

 of malaria ; but I gather that in many cases the men are quite possibly 

 suffering from an insufficient vitamine-content of their food. The large, 

 number of persons of inferior physique seen in this country suggests that 

 there are some universal errors in dieting. It is the fashion to attribute 



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