Augtist 1 8, 1881] 



NATURE 



357 



facts which induced him to consider those layers at St. John's as 

 belonging to the Lower Carboniferous. Therefore naturalists 

 will scarcely agree that such a statement, made by a prominent 

 and acknowledged authority, can be cancelled by a simple nega- 

 tion not supported by facts. Till this is done in a reliable 

 manner, those oldest insects will have to be considered as 

 belonging to the Lower Carboniferous. 



Cambridge, Mass., July 25 H. A. Hagen 



The True Coefficient of Mortality 



The very interesting and suggestive lecture of Alexander 

 Buchan on "The Weather and Health nf London" (Nature, 

 vol. xxiv. p. 143 et scq.") reminds me of the propriety of calling 

 the attention of writers on "vital statistics" to a point in rela- 

 tion to the ti-ue method of discussing the mortuary data. The 

 specific point to which attention is drawn is the necessity of 

 estimating the relative tendency to special diseases by comparing 

 the number of deaths from the given cause with the numljer of 

 persons living at the ages embraced in the record ; instead of 

 making the comparison (as is usually done) v\ith the total deaths 

 from all causes, or with the total number living at all ages. 



In like manner, in discussing the influence of age on the 

 mortality from any given disease, it is veiy common to prepare 

 tables of the number of deaths at each age, and in some in- 

 stances these numbers have been assumed to represent the 

 relative tendency to the disease at different ages. It is scarcely 

 necessary to say that this is a very serious en'or, for it must be 

 borne in mind that the number of persons living at different ages 

 is very unequal. Indeed it is self-evident that the true co- 

 efficient of mortality for any given disease at any given age is 

 expressed by the ratio of the number of deaths from the specified 

 disease at the given age to the number of persons living at the 

 same age : or, as it may be otherwise indicated, the number of 

 deaths from the given disease at the given age per 1000 persons 

 living at the same age. 



In illustrating this point I shall select cancer, because, in 

 relation to the influence of age, it furnishes an extreme case, 

 and thus affords a glaring instance of the fallacy of taking any 

 basis of comparison other than the number of persons living at 

 each age. The mortuary records of the Department of Seine 

 in France, during the eleven years, from 1830 to 1840 inclusive, 

 furnish a total of 91 18 deaths from cancer, 2163 males and 6955 

 females. The following table relating to the mean amiual 

 mortality from this disease among females will illustrate this 

 point : — 



The foregoing table demonstrates the inaccuracy of the popu- 

 lar impression that the tendency to cancer attains its maximum 

 between the ages of 35 and 50 years. The numbers in columns 

 (3) and (4) might seem to support such an opinion ; but, as we 

 have seen, tho^ein column (5) are evidently the true indices of 

 the tendency to this disease at different ages ; and it will be 

 observed that the mortality goes on steadily augmenting with 

 each succeeding decade of age up to 90 years. The fact likely 

 to be most strongly impressed on the reader by the numbers in 

 column (S) is the remarkable regularity of increase of the co- 



efficient of mortality for cancer with advancing life amonf 

 females after the age of 25 or 30 years. Between the ages oi 

 25 and 75 the mortality increases n^..rly in arithmetical progres- 

 sion as the age advances in arithmetical progression, the average 

 increment being about 1-30 per 1000 living at each age for each 

 decade. Assuming this to be the law of mortality from cancer 

 among females, it admits of very simple mathematical expres- 

 sion. Thus, let 



A = the age at which liability to cancer begins. 



A' = any .age greater than A. 



C = constant coefficient, variable according to country, state 

 of civilisation, &c. 



Then we have— Annual mortality per 1000 living at age A' = C 

 (A' -A). 



In our table representing the mortality from cancer in the 

 department of the Seine from 1830 to 1840 inclusive, the value 

 of A may be taken = 25, and C = 0-13 ; hence we have — An- 

 nual mortality per 1000 living at age A' ^ 0-13 (A' -25). Thus 

 by the formula the mortality at 55 = 3 '90, and column (5) gives 

 4-00 between 50 and 60 ; at 75, formula = 6-50 ; table = 6-49 

 between 70 and So. 



The mortality from cancer seems to be vastly smaller in Eng- 

 land than it is in France, so that a less value must be given to 

 the constant C. The foregoing formula represents the law of 

 increasing mortality with advancing life in the simplest form, as 

 a function of the age. This extreme simplicity is probably 

 unique in the case of cancer, and seems to indicate that age is 

 so far the controlling element in the development of this disease 

 as to overpower all other causes. In the case of other diseases 

 we cannot expect to escape the necessity of employing those 

 exponential functions in investigating their laws of mortality, 

 which are essential when a multiplicity of causes are in 

 operation. 



Many years ago the attention of the medical profession in this 

 country was called to the fact that the available mortuar)' data 

 were not discussed in a manner which revealed the true value of 

 the facts contained in the numbers.' But there is reason to 

 believe that Prof. Francis A. Walker, the intelligent superin.- 

 tendent of the census of the United States for 1S80, will not 

 overlook this point when he comes to the discussion of the 

 mortuary statistics which have been collected. 



Berkeley, California, July 7 John Le Conte 



[Mr. Le Conte does not appear to have apprehended the point 

 discussed in the lecture on "The Weather and Health of 

 London " — that point in no part of the inquiry being the 

 tendency to the disease at different ages, but the manner of the 

 distribution of deaths in the case of each disease through the 

 weeks of the year, w ith the view of arriving at some knowledge 

 of the inlluence of season in determining that di^lril>ution. Only 

 in one case, viz., in discussing the rates of the mortality from 

 diarrhcea in .-everal large towns, was a reference to population 

 required, and in that case the curves were drawn, showing the 

 weekly rate of mortality per 1000 of the population of the 

 respective towns. — Ale.xander Buchan.] 



Bisected Humble Bees 



I TOO have frequently observed humble bees lying dead or stu- 

 pefied under lime-trees, sun-flowers, and some other plants, and 

 once I saw a Staphylinus, commonly known as Black Cock-tail, 

 or Devil's Coach-horse, nip a humble bee in two, and on pas-ing 

 that way later I found that it had cleared out the honey-bag and 

 left the tw lialves of the bee on the path, as described by your 

 correspondent. I have known boys catch humble bees and eat 

 the hor.ey in them ; and probably many other animals have 

 learned how to get at the sweet drop. 



Trinity College, Cambridge Thos. McK. Hughes 



At your request for information on the above I beg to say 

 that I have observed both the flycatchers alluded to by your 

 correspondent, and also the little blue tit {Parus cayiika) attack 

 the humble bees in the manner described, to extract the honey- 

 bag. Tills attacking the bees is not, so far as my experience 

 goes, a general characteristic of these birds, and what should 

 lead them to it occasionally I cannot ascertain. 

 Exeter, August 15 Edward Parfitt 



' Vide papers by the writer, entitled " Statistical Researches on Cancer.' 

 Southern Med. and S urg. J ourn. , new series, vol. ii. pp. =57-293. May' 

 1846. Als . " Vital Statistics," illustrated by the " Laws of Mortaliry from 

 Cancer," Western Lancet, vol. i. pp. 176-190, March, 1872 (San Francisco). 



