596 



NATURE 



| January [6, 1 9 19 



1, in Stonyhurst and Bootham School. Prof. 

 Nunn's lecture, which was a departure from the usual 

 presidential address, was an unqualified success. The 

 Astronomer Royal, in the course of the discussion, 

 testified to his appreciation of Prof. Nunn's presenta-i 

 lion of the subject. 



A paper on " [Tie Teaching of Geometry to First- 

 year Pupils" was introduced by Mr. Basil A. Howard. 

 There was a vigorous discussion, from which il was 



abundantly evident thai teachers do not even yet 

 regard the leaching of elementary geometry as in a 

 satisfactory condition, It seems likely that a cleavage 

 in the near future will be established between "prac- 

 tical experimental geometry" and "theoretical geo- 

 metry," as the attempt to mix up these two aspects 

 of the subject throughout the school course has not 

 led to the best results, they being neither coincident 

 nor contradictory, hut distinct and complementary. 



BIOLOGY OF .1 LIFE-TABLE. 



AT a meeting of the Royal Statistical Society on 

 December 17 a paper was read by Dr. J. 

 Brownlee entitled "Notes on the Biology of a Life- 

 Table." Dr. Brownlee pointed out that a life-table 

 contained a record of the natural history of the life- 

 processes of man from birth to death. As man must 

 be looked upon in the light of a physico-chemical 

 engine with the power of working for a certain time, 

 it should be possible to obtain from the different life- 

 tables some indication of the rate at which the engine 

 works and the manner in which the power of working 

 is altered by different environments. That some law- 

 exists is shown by the relationship between environ- 

 ment and ill-health advanced by Dr. Farr forty years 

 ago. He established a relationship for the decade 

 1861-70 that D = c&P, where D is the death-rate, <5 the 

 number of persons living per sq. m., and c and p are 

 constants. Unfortunately, Dr. Farr could only use 

 crude death-rates, and his law was not found to apply 

 in the subsequent decades. Now, however, it is pos- 

 sible to use life-table death-rates. 



It is found, when the different areas in the country 

 are arranged in groups according to their different 

 death-rates, the groups being so large that the effects 

 of different local conditions are averaged out, that the 

 death-rate increases directly as the tenth root of the 

 densitv of the population as measured by the number 

 of persons on each square mile. The equations for the 

 three decades for which statistics exist are as 

 follows : — 



D=i2-428- 10018 

 D=ii-4sS-° 9850 

 D=io-82c. 10179 



1S61-70 

 1881-90 

 1891-1900 



It follows from this that there must be some definite 

 law underlying the life-processes, and that between the 

 different life-tables close relationships should exist. In 

 :m endeavour to find these relationships Dr. Brownlee 

 had made various experiments. In the first instance 

 il was found that if a suitable upper limit to life were 

 assumed, the expectations of life at all ages between 

 ten years and venty-five years, and the differences 

 of the upper limit of life and the actual age when 

 plotted on double logarithmic paper, lay on a straight 

 line. This gives a relationship E, = a(C — x)«, where C 

 is the upper limit of life, E the expectation at age v, 

 and a and n are constants. It is further found that 

 n, 1 ', and logn used as co-ordinates are collinear. The 

 limited range through which the formula could 1" 

 applied, however, and the fart that the upper limit of 

 life was in most tables quite ridiculously low sug- 

 I a search for a better expression. He found on 



NO. 2568, VOL. I02] 



trial that the formula 1 which represents the reaction 

 between a substance and a ferment, when the reaction 

 is such that combination takes place between the sub- 

 stance and the ferment, followed by dissociation as 

 the alteration of the substance proceeds, gave an 

 adequate graduation. Taking the amount of the 

 original substance to be represented by the , spi 

 of life, the relationship between age and expectation 

 is thus given in the following form : 



---v- 



When this formula is used, c and a are collinear for 

 all life-tables, and c and >i are collinear for each 

 definite epoch, the epochs investigated being the 

 decades 1861-70, 1881-90, 1891-1900, and the three 

 years 1910-12. Further, it is found that all the lattet- 

 lines are parallel. The constant direction of these may 

 be assumed to be associated with the fact that the 

 exponential relation of the death-rate to the density 

 given by Farr's law is constant. The changing posi- 

 tion of the line may also be associated with the change 

 in the multiplying factor, which, as has been se< n, 

 has been continuously decreasing. A theoretical draw- 

 back to using the formula as given above is that it 

 assumes that the expectation of life is an adequate 

 measure of vitality. This assumption implies that 

 each year of life is of equal value, and therefore 

 equates a year of life lived between twenty and twenty- 

 one with a year of life lived between seventy and 

 seventy-one, though the rate of action of life-processes 

 must be verv much greater in the former case than in 

 the latter. This difficulty, however, can be got over 

 when it is noted that the same formula graduates, not 

 only the expectation of life, but also the life insurance 

 premiums, so that it may be taken that any simple 

 law of decay expressible by a geometrical progression 

 acting as life goes on mav be included in the argument. 

 Dr. Brownlee thought that the relationships first 

 given by Dr. Farr, and now found to apply for forty 

 years in England and Wales, as also the relationship 

 between the constants in the formula used for 

 graduating the expectations in the life-tables, showed 

 that the response of the human engine to different 

 conditions was not arbitrary, but governed by very 

 special laws. 



UNIVERSITY AND EDUCATIONAL 

 INTELLIGENCE. 



Glasgow. — The faculties of science and medicine 

 have lately received important benefactions, which 

 will enhance the resources of the University for in- 

 struction and research. Messrs. W. G. Gardiner and 

 F. C. Gardiner, shipowners in Glasgow, have made a 

 gift of 6o,oooZ. to the University for the foundation 

 of three professorships, at a stipend of 1000!. a year 

 each, in bacteriology, in organic chemistry, and in 

 physiological chemistry. The "Gardiner" chairs will 

 be associated with the existing departments of patho- 

 logy, chemistry*, and physiology respectively, in which 

 the several subjects have been represented by endowed 

 lectureships. 



The Right Hon. Sir Joseph P. Ma. lav, Bart., has 

 provided for five vears a lectureship for clinical and 

 practical instruction in tuberculosis at the Bridge of 

 Weir Sanatoria. The instruction will be open to 

 medical practitioners and students. Dr. James 

 Crocket, D.P.H., has been appointed the first lecturi r. 



A professor in the faculty of medicine has founded 

 an " Arbroath " bursary of 40/. a year for medical 



' Chemical Statics and Dyr 



' P- 376. 



