256 



KNOWLEDGE. 



[November 2, 1896. 



heartiest thanks from every ornithologist in the land. 

 There yet remains a vast amount of information to be 

 culled from tlio schedules so carefully and keenly kc\it by 

 the lighthouse and lightship keepers. We hope, and 

 indeed believe, that Mr. (Uarke is going to continue his 

 labours ; and in the near future, when he has worked out the 

 migration phases of individual species, we may look lor a 

 monumental and trustworthy account of the fascinating 

 subject of the migration of birds in the British Islands. 



Harry F. Witherhv. 



,'^Co))it'9 of till' ]{i')iort on Binl Mijinitiiiii can bo obtiiined iit tlii> 

 British .Vstociiition, Burlington House, London, price (Jd.J 



FORECASTING BY CURVES. 



By Alex. ]>. MacDowall, j\[.A. 



THERE are some curves of social data which, ex- 

 tending through a series of years, are approxi- 

 mately straight lines. There are others not so 

 regular, but the general course of which, after 

 some smoothing or averaging process has been 

 applied, is shown to be approximately a straight line. 

 One is tempted to extend such curves in the same direction, 

 by way of seeing what may happen in the future. 



I propose to apply this rough-and-ready method of 

 forecasting to such unlike things as the following : — 

 Lunacy, the army death rate, coal mine explosions, acreage 

 under crops, illiteracy, and suicide. 



The degree of confidence (or difBdenee) with which one 

 makes these conjectures is, of course, difl'erent in difierent 

 cases. Thus it is, perhaps, easier to forecast the future of 

 illiteracy than that of agriculture. Even if a forecast be 



rejected as worthless, it may still be instructive to study 

 the unextended curve. 



In our very promiscuous diagram it is to be understood 

 that each curve stands by itself, having its own vortical 

 scale, indicated by a letter («, h, c, etc.). A smoothing 

 process has been applied in the case of h, c, and c 



A few words on each of the curves. Commencing with 

 lunacy [a), we have a curve showing the nniuber of insane 

 persons under restraint in England and Wales in each year 

 from 1800 to 1894. This has risen with steady rapidity 

 from about thirty-eight thousand to ninety four thousand, 

 a rate of growth much more rapid than that of population ; 

 a lower line, drawn from IHGI to 1801, shows what the 

 growth would have been at the population rate. 



Does this mean that insanity is increasing among us ? 

 Not necessarily ; and certainly the curve does not measure 

 such growth (if there be growth). It is well known that 

 more lunatics are now put under restraint than formerly, 

 and a process of accumulation has been going on in 

 asylums, owing to removals, by death or discharge, being 

 generally less in number than the admissions. On 

 the other hand, the growing tension of modern life, and 

 the growth of nervous diseases, seem to render an increase 

 of insanity very probable, and some figures relating to 

 lunacy might be cited which favour the belief in its increase. 



Extending this curve with a dotted line, we come, by 

 about the end of the century, to a figure equal to the popu- 

 lation of Norwich (one hundred and one thousand); twenty 

 years later to a Sunderland of lunatics ; and about 193C to 

 a Portsmouth ! 



Whatever the future growth, it is in any case an ugly 

 fact that we have nearly one hundred thousand " officially 

 known lunatics, idiots, and persons of unsound mind " 

 among us, i.e., about one in three hundred (and how many 

 free?). 



As to the causes of insanity, hereditary influence bulks 

 most largely. To intemperance is attributed 20 9 per cent, 

 in males, and 8'1 per cent, in females. 



In curve b, the dotted one, we have the fluctuation in 

 the death rate of the army in the United Kingdom since 

 1866. This has been brought down to 4-2 per thousand 

 in 1895 (from 12-6 at the outset). The continuous curve 

 is the result of smoothing with averages of ten, /.(., each 

 year's point represents an average of ten years. 



Now it would be a mistake to attribute this rapid decline 

 wholly to sanitary and medical improvement. Part of it 

 is no doubt due to the fact that the army has been growing 

 younger on the short-service system. Thus, the number 

 of men over thirty has declined steadily in the last twenty 

 years. 



If we extend the smooth curve we find it to reach the 

 zero line about 1911. It seems impossible to suppose the 

 army death rate quite extinguished, though it may very 

 likely continue to decline for a tiine. A death rate of only 

 one would mean over one hundred deaths in this country. 

 The curve may be usefully compared with general death- 

 rate curves as showing what has been accomplished with 

 a segregated class of men of a given age-group under strict 

 regulations. 



Our next curve, '■, relates to coal mine explosions in the 

 United Kingdom. The annual numbers of these since 

 1858 have been smoothed with averages of five. These 

 explosions numbered seventy in 1858, but only twenty- 

 two in 1894, and the figure has been as low as twelve. 

 Extending the curve, it would appear that by the beginning 

 of next century, if the same rate of progress is maintained, 

 this destructive form of accident should at least be reduced 

 to a very small figure, if not wholly prevented. 



The shrinkage of land under the plough in Great Britain 



