240 



SCIENCE. 



[Vol. XII. No. 302 



results produced by artificial selection are taken as examples of 

 what would take place in nature under the assumed circumstances ; 

 and this " natural selection " is proposed as a sufficient explana- 

 tion of the appearance of " a race which conchologists would call 

 a distinct species." 



The author states also, referring to Mr. Bakewell, " I have heard 

 him say, that he scarcely knew any assignable limits beyond which 

 these changes, both external and internal, might not be carried " 

 (p. 402). Another statement is interesting as showing that Charles 

 Darwin doubtless knew of this Mr. Bakewell, and may have heard 

 him discuss these matters in his boyhood. In a footnote (p. 403) 

 we read, " Mr. Bakewell of Dishley was in a considerable degree 

 self-educated ; but he possessed a strong original mind, which was 

 enlightened by study and meditation. He was also a man of great 

 moral worth, and was intimately acquainted with Dr. Priestley, Dr. 

 Darwin, and other eminent philosophers who inhabited the central 

 part of England, towards the close of the last century. The late 

 Countess of Oxford once asked the author of the present work, 

 ■whether he was ?-elated to the Mr. Bakewell who invented sheep- 

 He replied that he was of the same Leicestershire, or originally 

 Derbyshire family," 



It appears from these quotations that " the Mr. Bakewell who 

 invented sheep," and the Mr. Bakewell, author of ' Introduction to 

 Geology,' were true Darwinists before Charles Darwin. And who 

 can tell how much of Mr. Bakewell's theory of natural selection 

 was transmitted to the youthful Darwin through the delicious mut- 

 ton of the Leicestershire Downs ? H. S. WILLIAMS. 



Cornell University, Nov. 3. 



' Bi-daily.' 



The Monthly Weather Review of the Signal Service for August 

 contains the term 'bi-daily,' as applied to the present system of 

 indications, which are now made twice each day. That this is an 

 incorrect use of the prefix ' bi ' may be discovered by consulting a 

 dictionary, or by reflecting upon its derivation. 



The prefix ' bi ' doubles the word to which it is prefixed. A 

 biennial election is a two-yearly election, i.e., once in two years ; 

 and a bi-daily observation is an observation made every two days. 



An event occurring twice each day is half-daily or semi-daily, the 

 same as a semi-annual dividend or a half-yearly payment. 



The word ' tri-daily,' which is applied to the signal-service ob- 

 servations, has attained by usage the meaning ' three times a day,' 

 because of the lack of any other simple prefix. But the extension 

 of this improper usage to the prefix ' bi ' can have no warrant, 

 since we have the correct prefix ' half ' or ' semi,' both of which 

 are already in common use. Geo. E. Curtis. 



Topeka, Kan., Nov. i. 



Buffalo on the Texas Plains. 



The re-opened discussion of the buffalo question calls for a few 

 statements concerning these animals in Texas. Two hundred head 

 or more of these animals may be found in the Panhandle of Texas, 

 on the Llano Estacado, and in No-Man's Land. Some are on the 

 Palo Duro Caiion ranch, owned by Capt. Charles Goodnight ; 

 others in the Texas Capital Syndicate, or XIT pasture, especially 

 on the North Plains, i.e., north of the Canadian River ; still others 

 are at large. Probably twenty or more buffalo calves were captured 

 this spring in that region and driven to Kansas for mercenary and 

 breeding purposes. The cow-boy's ideal, like that of the more 

 ' refined ' sportsmen, is to shoot these cattle at sight, but the pro- 

 prietors of the ranches are doing much for their protection. 



There are also many buffalo on the South Plain. The antelope, 

 black-tailed deer, and many rare but smaller mammals, are found 

 in the same region — all of which I saw or heard of during a recent 

 visit to Plaza Larga, Tucumcarri Mesa, and the Texas Panhan- 

 dle. Naturalists desiring these forms should go to Tascosa, Tex., 

 near the New Mexican line, a place easily accessible from Kansas, 

 Denver, and Texas, via the Fort Worth and Denver Railway. The 

 capture of wild horses is a profitable pursuit in this region. 



ROBT. T. Hill. 



University of Texas, Austin, Nov. 7. 



AnsTvers. 



37. What Numbers does it take to make a Billion > 

 — Responding to Query 37 {Science xii. 204), ' What numbers make 

 a billion .'' ' I would offer the following remarks : The term ' billion ' 

 appears to have been introduced by the Italian arithmeticians early 

 in the fourteenth century. Peacock, in his admirable history of 

 arithmetic (Encyclopad. MetropoL. vol i.), states that the Italians 

 made " a great addition to their former numerical language by the 

 use of the word ' millione ' (which properly signifies ' great thou- 

 sand ') to denote the square of one thousand ; and which was fol- 

 lowed by the words 'billione.' ' trillione,' etc., deduced immediately 

 from the form by pursuing the natural analogies of the language : a 

 series of numerical terms was thus formed, proceeding not by tens, 

 but by millions." The new terms were slowly adopted by the 

 nations of Europe, but in every case in their original and etymologi- 

 cal sense. 



In Spain these terms were used probably not long after their 

 establishment in Italy ; in France they were adopted not much be- 

 fore the opening of the sixteenth century; in Germany, early in the 

 sixteenth century ; in England, not till the close of the seventeenth 

 century ; and in Russia, early in the eighteenth century. Locke, 

 who published his great essay in 1690, complains that his country- 

 men were accustomed to speak of millions of millions of millions 

 instead of using the more convenient term ' trillions ; ' and he gives 

 an example of the proper notation to sixty places of figures, divided 

 into sextuple periods, and duly named up to nonillions. " The ordi- 

 nary way of naming this number in EngUsh will be the often re- 

 peating of millions of millions of millions of millions," etc. {Htiman. 

 Understanding, book ii. chap. 16, sect. 6). It is important to 

 observe, that, wherever introduced, the term ' billion ' uniformly 

 designated the fo'j- power of the million, — a value, the prefix to 

 twelve places of figures. In the Italian dictionary of the Accade- 

 mici della Crusca, the word ' bilione ' (or ' billione ') is defined, " un 

 milione di milioni." In the Spanish dictionary of the Academia 

 Espanola, the word ' billon ' is defined, " un millon de millones," or 

 a million multiplied by itself. In the German dictionary of Dr. 

 Daniel Sanders, ' billion ' is defined, " millional million." And in 

 Littre's ' French Dictionary,' after defining the word, it is stated, 

 "The forms billion, trillion, etc., were devised in the sixteenth cen- 

 tury to signify periods of six to six figures : counting from the right, 

 units were represented by the first six places of figures, the millions 

 were represented by the figures from 7th to the 12th places, the 

 billions were represented by the figures from the 13th to the i8th 

 places, and so on." Est. De La Roche's ' Arithmetique ' is quoted 

 as stating, " A billion is equal to a million million." Littre adds 

 (without explanation), " It was not till the middle of the seven- 

 teenth century that the rule of separating into periods of six, was 

 changed to separating into periods of three figures, and the original 

 billion was divided by i.ooo.'i It is not a little surprising that our 

 compilers of school arithmetics (whether smitten with Franco- 

 mania or with Anglo-phobia) have almost unanimously adopted the 

 modern French perversion of the terms ' billion,' ' trillion,' etc. And 

 thus business-men are in the habit of numerating ' - illions ' by 

 places of three (after the million place), whWe astronomers and 

 mathematicians preserve the original and logical numeration by 

 places of six figures. It needs but a bare inspection of the terms 

 themselves to see that this French neologism (of the last two 

 centuries) is not only anomalous, but wholly irrational. The form 

 of the words ' million,' ' billion,' ' trillion,' ' quadrillion,'' quintillion,' 

 etc., necessarily denotes some co-ordination of numerical progres- 

 sion. What can it possibly be on the pedagogue's system ? The 

 expression i 000, 000 000 (one thousand million) does not admit any 

 logarithmic bisection. How can it, then, be in any sense a billion? 

 If it be any kind of a bis, what is its primary .' It is an impossible 

 second power, having a surd for its root. Had the French arith- 

 meticians cut down at the same blow the jnillion to the mille, the 

 scheme would at least have been consistent. A true billion is evi- 

 dently a second order of million, and the only rational order is the 

 second power. 



To any reflecting mind the school-book numeration is simply 

 absurd, and its prevalence is a very puzzling phenomenon. 



W. B. T. 



Washington, D.C., Oct. 30. 



