494 



NATURE 



[June 17, 1920 



though partial, index of the density of the air at 

 any height. From this the third step followed — 

 the idea of a ballistic temperature such that when 

 used in conjunction with surface pressure the bal- 

 listic density was arrived at. Methods of com- 

 puting density weighting factors were developed 

 by the A.A.E.S., M.I.D., and by using these 

 factors temperature weighting factors were com- 

 puted (which allowed for the variations in the 

 vertical pressure distribution coiisequent on any 

 variation in the temperature distribution). Here, 

 again, the factors vary for each trajectory, but 

 the differences between trajectories are consider- 

 ably less than in the case of winds, and there 

 was little difficulty in arriving at the best average 

 factors to employ for field use. 



By the employment of wind and temperature 

 weighting factors, very numerous meteorological 

 observations were made available for the use of 

 gunners in the most convenient form. Ballistic 

 winds and temperatures for several selected times 

 of flight were telegraphed to the batteries at 

 frequent intervals, and the information given in 

 the meteorological telegrams, in conjunction with 

 the barometric pressure measured at the battery, 

 gave the gunner data which required no reduction, 

 but could be used directly for applying cor- 

 rections from the range table. It is, of course, 

 essential that the results of meteorological ob- 

 servations should be provided " red hot " to the 

 gunners, and methods of computation were so 

 perfected, and so high a degree of skill was at- 

 tained, that the calculation "of ballistic winds 

 from pilot-balloon observations kept pace 

 with the observation of the balloon itself, and 

 no time was lost in putting the information in 

 the form in which it was readily usable by the 

 gunner. 



A single concrete example may suffice to illus- 

 trate the importance of the methods which were 

 introduced by the meteorologists. 



If a projectile were fired due south, with a time 

 of flight of 50 sec. (i.e. rising to a height of about 

 10,000 ft.), under the following weather condi- 

 tions, viz. : — 



Wind 



Height in ft. Velocity Direction Temperature Barometer 



f.s. " p. 



Surface 8 no 50 



2,000 40 175 40 d-rt 



4,000 45 185 30 o S 



6,000 50 190 19 P o 



8,000 45 'OO X 2^^ 



10,000 60 



190 



-2 



Then, if surface conditions are used for arriving 

 at the appropriate corrections to apply, we have 

 for a certain gun that the wind will reduce the 

 range of the gun by 13 yards and deflect the pro- 

 jectile towards the west 60 yards. The surface 

 temperature being 10° F. below the range table 

 normal of 60° F., the range will be further reduced 

 by 42 yards — a total loss in range of 55 yards. 



But the ballistic wind for the above conditions 

 is a wind of 44 f.s. from direction 185°, and the 

 ballistic temperature is 36° F. For the same gun 

 and projectile this wind would produce a deflection 

 towards the east of 35 yards, a decrease in range 

 due to wind of 600 yards and to abnormal 

 temperature (and density) of 407 yards — in all 

 more than 1000 yards. Thus the corrections 

 applied by pre-war methods would have entailed 

 in this case an error in range of about 1000 yards, 

 and in line of about 100 yards. 



Instead of anti-aircraft gunnery being con- 

 sidered as a special department of gunnery, it is 

 more logical to consider fire on the flat as a 

 specially simple case of the more general science 

 of gunnery. In a very real way the development 

 of the science was due to the researches of the 

 A.A.E.S., M.I.D., and to the methods employed 

 by that department in the analysis of fuse trials 

 and in the calibration of guns. For anti-aircraft 

 fire under active service conditions the application 

 of meteorological corrections did not reach the 

 same degree of organisation as for fire on the flat, 

 for the application of corrections is a much simpler 

 problem in the latter case. But in experimental 

 work full account was taken of all the meteor- 

 ological information available. Thus one of the 

 main sources of errors in shooting was eliminated, 

 and the investigation of many ballistic problems 

 made possible. 



Obit 



S. RAMANUJAk, F.R.S. 



SRINIVASA RAMANUJAN, whose death was 

 announced in Nature of June 3, was born in 

 1888, in the neighbourhood of Madras, the son of 

 poor parents, and a Brahmin by caste. 1 know 

 very little of his early history or education, but 

 he became a student in Madras University, and 

 passed certain examinations, though he did not 

 complete the course for a degree. Later he was 

 employed by the Madras Port Trust as a clerk 

 at a salary equivalent to about 25L a year. By 

 this time, however, reports of his unusual abilities 

 had begun to spread, and, I believe owing to the 

 intervention of Dr. G. T. Walker, he obtained a 

 small scholarship which relieved him from the 

 NO. 2642, VOL. 105] 



uary. 



necessity of office work and set him free for 

 research. 



I first heard of Ramanujan in 191 3. The first 

 letter which he sent me was certainly the most 

 remarkable that I have ever received. There was 

 a short personal introduction written, as he told 

 me later, by a friend. The body of the letter con- 

 sisted of the enunciations of a hundred or more 

 mathematical theorems. Some of the formulae 

 were familiar, and others seemed scarcely possible 

 to believe. A few (concerning the distribution of 

 primes) could be said to be definitely false. There 

 were no proofs, and the explanations were often 

 inadequate. In many cases, too, some curious 

 specialisation of a constant or a parameter made 



