No. 1070, Vol. 42] 



NATURE 



13 



fewer than 50,000 buffaloes have been killed for their 

 tongues alone, and the most of these are undoubtedly 

 chargeable against white men, who ought to have known 

 better." Over three and a half million individuals are 

 estimated to have been slaughtered in the southern herd be- 

 tween 1 872 and 1 874. 1 n the latter year the hunters became 

 alarmed at the great diminution in the number of the 

 bison, and by the end of 1875 the great southern herd had 

 ceased to exist as a body. The main body of the sur- 

 vivors, some 10,000 strong, fled into the wilder parts of 

 Texas, where they have been gradually shot down, till a 

 few years ago some two or three score remained as the 

 sole survivors of the three or four millions of the great 

 southern herd. Bison-hunting as a business definitely 

 ceased in the south-west in 1880. 



Almost equally brief, and equally decisive, is the 

 history of the great northern herd. The estimated 

 number in this herd in 1870 is roughly put at a 

 million and a half, ranging over a much wider area 

 than the southern herd. The portions of the herd in 

 British North America appear to have been extermin- 

 ated first. Previously to 1880, the Sioux Indians had 

 made an enormous impression on the numbers of this 

 herd in the States of Dakota and Wyoming ; but the 

 beginning of the final destruction of the herd may be said 

 to date from that year, which was signalized by the open- 

 ing of the Northern Pacific Railway, running right through 

 their area. In that year the herd was hemmed in on three 

 sides by Indians armed with breechloaders, who enor- 

 mously reduced its numbers. A rising market for " buffalo- 

 robes," in 1881, stimulated a rush on this herd, till "the 

 hunting-season which began in October 1882 and ended 

 in February 1883 finished the annihilation of the great 

 northern herd, and left but a few small bands of stragglers, 

 numbering only a very few thousand individuals all told." 

 It was long thought that a large section of the herd was 

 still surviving, and had escaped into British territory, but 

 this proved to be a mistake. 



"South of the Northern Pacific Railway, a band of 

 about three hundred settled permanently in and around 

 the Yellowstone National Park, but in a very short time 

 every animal outside of the protected limits of the Park 

 was killed ; and whenever any of the Park buffaloes 

 strayed beyond the boundary, they too were promptly 

 killed for their heads and hides. At present the number 

 remaining in the Park is believed by Captain Harris, the 

 Superintendent, to be about two hundred, about one-third 

 of which is due to the breeding in protected territory." 



It is curious to notice that even the bison hunters them- 

 selves were unaware of the extinction of the northern 

 herd in the spring of 1883 ; and costly expeditions were 

 actually fitted out in the autumn of that year to arrive at 

 the bison country and find that the " happy hunting- 

 grounds " existed no longer. 



Such very briefly is the mournful history of the exter- 

 mination of the two great herds of American bison. 

 Scattered individuals or small droves still exist here and 

 there in the more secluded parts of the country, in addi- 

 tion to those preserved in the Yellowstone. The pursuit 

 of them is, however, unremitting, and the author considers 

 that the final disappearance of every unprotected indi- 

 vidual is but a question of time. In 1 889 some twenty bison 

 were seen grazing in the Red Desert of Wyoming, which 

 narrowly escaped destruction. We have already men- 

 tioned the survivors of the southern herd still lingering 

 in Texas ; but there is strong evidence of the exist- 

 ence in the British district of Athabasca of a herd of 

 " wood-buffalo," estimated at upwards of 550 in number. 

 Exclusive of those in the Yellowstone, the number of 

 wild bison existing in the United States on January i, 

 1889, is given as 85. Finally, the whole census of living 

 examples of the American bison — both wild and tame— 

 at the date mentioned, gives only 1091 individuals. 



That the Government of the United States will do all 



they can to increase and preserve the herd in the Yellow- 

 stone Park goes without saying ; but the warning of the 

 author that without great care, and unless (if this be 

 possible) crossed, they will gradually deteriorate in sire, 

 should not be overlooked. 



The account of the Smithsonian Expedition into 

 Montana, which forms the concluding portion of the 

 volume, although well told, is not of sufficient general 

 interest to need further notice here. 



In conclusion, we have to congratulate the author on 

 having brought together such a number of facts in 

 relation to the extermination of the bison, which, if they 

 had not been recorded while they were fresh in men's 

 memories, would probably have been entirely lost. 



R. L. 



DICE FOR STATISTICAL EXPERIMENTS. 

 ■pVERY statistician wants now and then to test the 

 -*--' practical value of some theoretical process, it may 

 be of smoothing, or of interpolation, or of obtaining a 

 measure of variability, or of making some particular 

 deduction or inference. It happened not long ago, 

 while both a friend and myself were trying to find appro- 

 priate series for one of the above purposes, that the same 

 week brought me letters from two eminent statisticians 

 asking if I knew of any such series suitable for their own 

 respective and separate needs. The assurance of a real 

 demand for such things induced me to work out a method 

 for supplying it, which I have already used frequently, and 

 finding it to be perfectly effective, take this opportunity 

 of putting it on record. 



The desideratum is a set of values taken at random out 

 of a series that is known to conform strictly to the law 

 of frequency of error, the probable error of any single 

 value in the series being also accurately known. We 

 have (i) to procure such a series, and (2) to take random 

 values out of it in an expeditious way. 



Suppose the axis of the curve of distribution (whose 

 ordinates at 100 equidistant divisions are given in my 

 " Natural Inheritance," p. 205) to be divided into n equal 

 parts, and that a column is erected on each of these, of a 

 -f or a - height as the case may be, equal to the height 

 of the ordinate at the middle of each part. Then the 

 values of these heights will form a series that is strictly 

 conformable to the law of frequency when n is infinite, 

 and closely conformable when n is fairly large. Moreover 

 the probable error of any one of these values irrespectively 

 of its sign, is I. 



As an instrument for selecting at random, I have 

 found nothing superior to dice. It is most tedious 

 to shuffle cards thoroughly between each successive 

 draw, and the method of mixing and stirring up 

 marked balls in a bag is more tedious still. A tee- 

 totum or some form of roulette is preferable to these, 

 but dice are better than all. When they are shaken and 

 tossed in a basket, they hurtle so variously against one 

 another and against the ribs of the basket-work that they 

 tumble wildly about, and their positions at the outset 

 afford no perceptible clue to what they will be after even 

 a single good shake and toss. The chances afforded by 

 a die are more various than are commonly supposed ; 

 there are 24 equal possibilities, and not only 6, because 

 each face has four edges that may be utilized, as I shall 

 show. 



I use cubes of wood \\ inch in the side, for the dice. 

 A carpenter first planed a bar of mahogany squarely and 

 then sawed it into the cubes. Thin white paper is pasted 

 over them to receive the writing. I use three sorts of 

 dice, I., II., and III., whose faces are inscribed with the 

 figures given in the corresponding tables. Each face 

 contains the 4 entries in the same line of the table. The 

 diagram shows the appearance of one face of each of the 

 3 sorts of dice ; II. is distinguished from I. by an asterisk 



