7i6 



NA TURE 



[June 3, 1922 



by symbols on paper. Industry and business have 

 benefited considerably from the application of this 

 unbusinesslike mathematical method ! 



The fact is that the most practical sciences, and the 

 only sciences that have been applied industrially, are 

 the exact sciences of chemistry, physics, and engineer- 

 ing — sciences which can predict effects from known 

 causes. 



No statement of evidence is really a fact until all 

 the factors are known, and, therefore, statistics 

 cannot predict, and man cannot forestall disease or 

 economic distress, in spite of the sciences of biology 

 and medicine and the " science of economics." 



W. Wilson Leisenring. 



In a notice (Nature, May 6, p. 596) of an address 

 by Dr. Hoffman, the words are used : " Imagination 

 is what the mathematician is ever trying to get rid 

 of." As such misconceptions as this are unfortun- 

 ately rather widespread, it may be useful to protest 

 against them. Imagination is essential to mathe- 

 matics. The work of the great mathematicians 

 affords many striking examples of creative imagina- 

 tion, and for the proper understanding and apprecia- 

 tion of even the elementary parts of the subject the 

 use of imagination is necessary. One of the most 

 important qualities of a good mathematical teacher 

 is the power of stimulating the pupils' imagination, 

 and it is, perhaps, the neglect of this faculty by some 

 teachers which is responsible for the dulness and life- 

 lessness of what is too often taught in schools under 

 the name of mathematics. F. E. Cave. 



Girton College, Cambridge, May 10. 



Dr. Hoffman's charge against the mathematicians 

 was not that they lack imagination but that they 

 set before them as the ideal of their science the getting 

 rid of it. The quotation from Prof. Whitehead, who 

 certainly is not lacking in that faculty, makes the 

 meaning clear. There is, however, a drawback in 

 our language in the fact that we use the same word 

 for imagination when we mean aesthetic creation, 

 what the Italians call fantasia, as we do when we 

 mean the anticipation which is pure reproduction, 

 what the Italians call immaginazione. It is of course 

 the aesthetic creation the mathematician aims at 

 dispensing with in order to preserve the purely 

 logical character of his ideas. Even Kant repre- 

 sented it as a kind of handicap that mathematical 

 concepts should require sensuous intuition for their 

 expression. The Writer of the Article. 



The Elliptic Logarithmic Spiral— a New Curve. 



If, in an elastic system with one degree of freedom, 

 and friction proportional to the velocity, the relation 

 of the " free " force to the displacement be considered, 

 an interesting curve results. 

 Thus if the displacement be 



x = ae-^* cos nt 

 the force is given by 



F = &(?-** cos {nt + e), 

 and by eliminating the cosines we have 



2Fx , F2 



-T-COS e+T^ 



ah b^ 



sm'' e. 



which may be termed an elUptic logarithmic spiral or 

 a damped Lissajous' curve. 



If the vibrations are maintained or forced by a 

 fprce of harmonic character, the force displacement 

 curves become ellipses. 



NO. 2744, VOL. 109] 



The same equations, hold for the compounding of 

 two damped harmonic motions of equal periods at 

 right angles, so that the path of a body at the lower 

 part of an oiled sphere or of the bob of a conical 

 pendulum in a viscous medium would be, in plan, an 

 elliptic logarithmic spiral. H. S. Rowell, 



Director of Research. 



Research Association of British Motor 

 and Allied Manufacturers, 



15 Bolton Road, Chiswick, W.4, May 3. 



Intelligence Statistics. 



I WAS interested in a short note in Nature of 

 February 16, p. 218, on the dependence of the 

 standard of intelligence of individuals on the part of 

 the year in which they were born. Statistics appear 

 to show that the standard of intelligence is higher in 

 individuals born in the autumn (say October) than 

 in those born in the spring (say April) . At first sight 

 this result may seem rather unexpected, as one might 

 expect that the influence of summer would be 

 beneficial to a child born in the spring, whereas, in 

 the case of a child born in the autumn, it would not 

 be surprising if the succeeding winter were to have a 

 deleterious effect on the mental growth. 



It appears to me that the chances of a child sur- 

 viving the first year of life are greater for a child born 

 in the spring than for one born in the autunin, and 

 I do not doubt but that statistics have shown that 

 this is so. Coupled with this one would expect that 

 the general " fitness " of the survivors of the first 

 year of life would be greater for individuals born in 

 the autumn, because the weaklier members have 

 been weeded out by the severity of winter in the first 

 few months of life. This would appear to be sufficient 

 to explain the result mentioned at the beginning of 

 this letter. We should thus expect that, in the 

 southern hemisphere, children born in the spring 

 (April) would in later life have a higher average 

 standard of intelligence than those born in the later 

 months of the year. Statistics from the southern 

 hemisphere would thus be of value in this connection. 



It is possible that this aspect of the problem has 

 already been dealt with. As the papers on this 

 work are not accessible to me, however, I have not 

 seen the explanations offered for the above-mentioned 

 interesting phenomenon. Robert W. Lawson. 



The University, Sheffield. 



A Rainbow Peculiarity. 



In Nature of March 9, p. 309, Major Lockyer 

 asks if it is a fact of general observation that " the 

 whole area of the inside of the primary bow is brighter 

 than the region outside," and he refers to the pheno- 

 menon as " a fact in Nature which appears to have 

 been rarely noticed visually." The following quota- 

 tion from " The Divine Adventure," by Fiona 

 Macleod (William Sharp), shows that the mystic 

 poet not only saw clearly into the heart of Nature,.. 

 but was also a keen observer of her outward mani-, 

 festations : 



It is not Love that gives the clearest sight : 

 For out of bitter tears, and tears unshed, 

 Riseth the Rainbow of Sorrow overhead, 

 And 'neath the Rainbow is the clearest hght. 



Probably the phenomenon was commonly known 

 amongst the Western Isles he loved so well. 



John P. Dalton. ; 

 University of the Witwatersrand, Johannesburg. 



