662 



NATURE 



[January 20, 192 1 



from the India Office in London, but my efforts had 

 succeeded before this reached Madras. 



Throughout his life Ramanujan kept religiously to 

 a diet of vegetables, fruit, and rice, and in England, 

 outside his own rooms, food and clothing were a 

 continual trial to him. I have known him ask with 

 unaffected apologies if he might make his meal of 

 bread and jam because the vegetables offered to him 

 were novel and unpalatable, and with a pathetic con- 

 fidence he has appealed to me for advice under the 

 discomforts of shoes and trousers. His figure was 

 short, and until his health gave way it was stout. 

 His skin, never of the darkest, grew paler during his 

 Stay in England. His head gave the impression, 

 which photographs show to have been false, of 

 broadening below the ears, which were small. His 

 face was clean-shaven, with a broad nose and a high 

 forehead, and always his shining eyes were the con- 

 spicuous feature that Mr. Rao observed them to be 

 in 1910. 



Ramanujan walked stiffly, with head erect, and his 

 arms, unless he was talking, held clear of his body, 

 with hands open and palms downward. In conversa- 

 tion he became animated, and gesticulated vividly with 

 his slender fingers. He had a fund of stories, and 

 such was his enjoyment in telling a joke that often 

 his words struggled incomprehensible through the 

 laughter with which he anticipated the climax of a 

 narrative. He had serious interests outside mathe- 

 matics; he was always ready to discuss whatever in 

 philosophv or politics had last caught his attention, 

 and Indians speak with admiration of a mysticism 

 of which his English friends understood little. 



Perfect in manners, simple in manner, resigned in 

 trouble and unspoilt by renown, grateful to a fault 

 and devoted beyond measure to his friends, Ramanu- 

 jan was a lovable man as well as a great mathe- 

 matician. By his death I have suffered a personal 

 loss, but I do not feel that his coming to England 

 is to be regretted even for his own sake. Prof. Hardy 

 speaks of disaster because of the hopes he entertained. 

 If he pictures Ramanujan as he might have been 

 throughout a long life, tormented by a lonely genius, 

 unable to establish effective contact with any mathe- 

 maticians of his own class, wasted in the study of 

 problems elsewhere solved, Prof. Hardy must agree 

 that the tragedy averted was the greater. Shortly 

 before he left England, at a time of great depression, 

 Ramanujan told me that he never doubted that he did 

 well to come, and I believe that he would have chosen 

 as he did in Madras in 1914 even had he known that 

 the choice was the choice of Achilles. 



E. H. Neville. 



University College, Reading, December 7. 



The Mechanics of Solidity. 



The letters under this title from Mr. R. G. 

 Durrant, Mr. V. T. Saunders, and Dr. H. S. 

 Allen (Nature, December 2 and 23 and January 6) 

 are very interesting and suggestive, but melting 

 points are of little value in discriminating be- 

 tween the hard and soft varieties of the sarne steel, 

 and molecular weights, volumes, and frequencies have 

 not yet any very definite significance in relation to 

 solid metallic mixtures. My initial proposal that 

 certain simple measurements might with advantage 

 be substituted for the complicated tests now used by 

 engineers and metallurgists was a "practical," if 

 myopic, one; it has evidently been misunderstood, 

 so perhaps I may be allowed to state the case in 

 greater detail. 



By "solidity" I meant to imply all the properties 

 covered by the adjectives strong, elastic, stiff, fiabby, 



NO. 2673, VOL. 106] 



tough, hard, mild, brittle, and many others. Solidity 

 may eventually be specified in terms of atoms and 

 molecules, but the specification would be very com- 

 plicated, and I cannot at present " take sanctuary 

 among the atomists " ; solidity may be referred to 

 its origins or to its manifestations, and for the 

 moment the latter course seems to be the only prac- 

 ticable one. Solidity may be analysed in various 

 ways, but Hertz has explained the meaning of 

 "strength" very clearly, and it is convenient to take 

 strength as the starting point ; solidity seems to 

 comprise elasticity, strength, and something more, 

 namely, the variation of elasticity and strength with 

 deformation. Isotropic solidity appears to be a con- 

 tinuum which fades into fluidity ; it would be very 

 desirable to know how many dimensions define this 

 continuum, but the problem of mechanical testing is 

 rather simpler, viz. How many dimensions are im- 

 portant, and what is the best way to measure them? 

 For the convenience of readers of Nature who 

 are unfamiliar with current engineering practice I 

 may refer to the recent report of the Steel Research 

 Committee of the Institution of Automobile En- 

 gineers ; this, of course, is primarily a report on 

 certain metals, but incidentally it serves as a report 

 on the tests employed. The procedure is as follows : 

 Test pieces are cut to three standard shapes and 

 broken under prescribed conditions; four different 

 measurements are made on the first piece and one 

 measurement on the second and third pieces. The 

 second and third tests are each repeated three times, 

 and Brinell measurements are made on all test pieces. 

 The report represents practice of a very high standard, 

 and the foregoing programme is carried out thrice for 

 each of some two hundred mechanical varieties of 

 twenty chemically distinct steels ; the report records 

 about ten thousand measurements in all, each of them 

 involving considerable care and labour. I feel sure 

 the committee would endorse my view that in certain 

 tests the concordance of nine individual measure- 

 ments leaves a great deal to be desired ; whatever 

 these tests may determine, they do not determine 

 anything very accurately. 



To obviate all possibility of misconception, I should 

 state the proposed alternative plainly. Six simple 

 mechanical properties of a metal — density, two elas- 

 ticities, and their temperature coefficients — can be 

 measured fairly easily and with some precision ; the 

 temperature coefficient of intrinsic energy makes a 

 doubtful seventh. The connection between these 

 properties and practical engineering is admittedly 

 obscure, but in the writer's limited experience this 

 is true also of some of the other tests. None of the 

 six properties referred to are customarily measured, 

 but the single one that is well known — the thermal 

 coefficient of density — bears a decided general 

 resemblance to a strength, the particular strength to 

 which Hertz has appropriated the word " hardness." 

 Mv suggestion is that these six properties, and pos- 

 sibly others, would be worth investigating, and that 

 some of them may prove convenient indicators of 

 mechanical consistency ; they would certainly serve 

 as indicators of uniformity, and it may be doubted 

 whether the other tests do much more. 



Both Mr. Durrant and Mr. Saunders refer to the 

 question of definitions, and these are certainly 

 required for many of the attributes of solidity ; 

 hardness, however, appears to be an exception, and 

 has been defined by Locke, Hertz, and Clerk- 

 Maxwell. K definition established in the seventeenth 

 century and supported bv such hifh authorities cannot 

 lightly be set aside ; it seems that Mr. Saunders is 

 right, and that "Brinell hardness" is not hardness. 

 Verbal difficulties of this kind beget confusion, but, 



