82 



NATURE 



[Nov. 28, 1889 



"drawn by Dr. Huggins in 1866 {Phil. Trans., vol. clvi. 

 •p. 393) ; it has been amply confirmed since, and cannot 

 ■be too forcibly insisted upon. We are unable to place 

 "either an upper or a lower limit to stellar dimensions or 

 intrinsic emissive intensity. Until Arcturus was proved 

 to be immeasurably remote, few would have been disposed 

 to credit the existence of a sun in space at least six 

 thousand times as effiulgent as ours is ; but we know no 

 reason why Arcturus itself should not be as vastly 

 exceeded by some giant orb at the outskirts of the Milky 

 Way ; while we are equally debarred from asserting that 

 among sixth, seventh, twelfth magnitude stars, there may 

 not be found some minute bodies at half the distance 

 from us of a Centauri. 



But when we pass from particular to general reasoning, 

 the aspect of the matter changes. No cause has yet 

 been shown why the stars should be exempt from 

 obedience to the " law of large numbers " which provides 

 (as Prof. Edgeworth has ably shown) a clue to other 

 labyrinths of facts. Statistics, it is true, are often mis- 

 leading, but only when they are wrongly employed. The 

 frequent misuse of a method does not justify its total 

 rejection. And the statistical method is peculiarly liable 

 to misuse. Attempts to get from it more than it will 

 properly give inevitably fail ; and what it will properly 

 give are general statements which should only be gener- 

 ally applied. An average result may not be the less 

 instructive because it is by its nature incapable of 

 furnishing specific data. 



The stars then must, on the whole, decrease in brightness 

 as their distances increase, and they must do so according 

 to an underlying fixed law which will be more and more 

 closely conformed to the larger the number of instances 

 included in the generalization. Each descent of one 

 stellar magnitude represents a falling off in light in the 

 proportion of 2| to i ; it represents, accordingly, an 

 augmentation of distance in the proportion of the square 

 root of 2|, or r59 to i. Theoretically, that is to say, 

 stars of any given magnitude are i"59 times more remote 

 than those one magnitude superior, 2^ times (1*59 X i"59), 

 where the gap is of two magnitudes, and so on. This 

 would be strictly and specifically true if all the stars were 

 equal ; but since they are enormously unequal, the rule 

 may be grossly misleading in particular instances, and 

 can only, by taking wide averages, be brought to approxi- 

 mate closely to actual fact. 



The determination of individual parallaxes has always, 

 with astronomical thinkers, been subordinate to the 

 higher aim of obtaining a unit of measurement for sidereal 

 space. Hence continual attempts to fix the " average 

 parallaxes " of classes of stars, which, however, remained 

 futile so long as precarious assumptions supplied the 

 place of direct information. Nor could this be obtained 

 until the exigencies of the research had evoked improved 

 means of practically meeting them. The earlier observers 

 chose the subjects of their experiments entirely with a 

 view to their successful issue. Stars likely, owing to their 

 brilliancy, their swift motion, or both combined, to be 

 nearer the earth than most others, were picked out for 

 measurement, with results, each by itself of high interest, 

 but woithless for generalizing purposes. It is only a few 

 years since increased skill in the handling of methods 

 authorized an extension of the range of their application. 

 The first systematic plan for investigating " mean 

 parallax" was proposed by Dr. Gill in 1883, and is now 

 in course of combined execution at Yale College and 

 the Cape. The completion last year of a section of the 

 work enabled Dr. Elkin to deduce an average distance of 

 thirty-eight light-years for the ten first magnitude stars 

 of the northern hemisphere ; but it would of course be 

 folly to regard this avowedly " provisional and partial " 

 result as a satisfactory basis for definitive conclusions 

 about the distances of more remote classes of stars. At 

 the most, it makes a useful temporary starting-point for 



some trial-trips of thought through snace. Before long, 

 however, through the exertions of Dr. Gill and Prof. 

 Pritchard, direct measures, not only of all the first, but 

 of most of the second magnitude stars all over the sky, 

 will have been executed ; and the proportion between 

 distance and brightness thus established may with some 

 confidence be used as a fathom-line for sounding otherwise 

 inaccessible sidereal abysses. A. M. Clerke. 



DR. H. BURMEISTER ON THE FOSSIL HORSES 

 AND OTHER MAMMALS OF ARGENTINA.^ 



'T^HIS handsome volume is a continuation of the author's 

 ^ monograph on the fossil horses of the Pampean 

 beds of Argentina, of which the first part was published 

 at Buenos Ayres in 1875, ^nd is stated to have been 

 specially brought out for the Paris Exhibition. The 

 author has, however, not done himself justice as regards 

 the title of this portion of the work, since, in addition to 

 the description of remains of the horses of the Pampean, 

 he also describes and illustrates the osteology of Mega- 

 therium, Mastodon, and MacraucJienia, so that a better 

 title for this volume would have been " The Fossil Horses 

 and other Mammals of the Pampean Deposits." 



Like the former part, the text of this volume is printed 

 in parallel columns of Spanish and German ; and the 

 execution of the plates leaves nothing to be desired, so 

 far as a clear delineation of the essential features of the 

 specimens portrayed is concerned. All the specimens 

 forming the subject of this monograph, are, as we learn 

 from the introduction, preserved in the National Museum 

 at Buenos Ayres, of which the learned author is the 

 Director ; and, so far as we may judge from the descrip- 

 tion and figures, that collection of fossil mammals must 

 be unrivalled in the excellence and completeness of its 

 specimens. 



The first section of the work, or that to which the title 

 alone properly applies, is devoted to the horses ; and 

 the author commences his description by observing that 

 the Equida differ from all other Ungulates in that the 

 premolars are larger than the true molars. For the more 

 generalized species of the Pampean deposits, like Equus 

 principalis of Lund, Dr. Burmeister adopts the Owenian 

 genus Hippidium {Hippidion), remarking that these 

 forms are distinguished from the modern horses by the 

 shorter and more curved crowns of their cheek-teeth, 

 which are of a more simple general structure, and also by 

 a difference in the form of the narial aperture, as well as 

 by their shorter limbs and stouter limb-bones. In the 



Fig. I. — Three right upper cheek-teeth of H ipparion, a, posterior, and b, 

 anterior outer crescent ; c. anterior, and (/, pjsterior inner crescent ; e, 

 anterior, and/, posterior pillar. 



Structure of their upper cheek-teeth the horses of this 

 peculiar South American group make, indeed, a decided 

 approach to the more generalized representatives of the 

 family, such as Hipparion. In the litter the anterior 

 pillar of these teeth (Fig. i, e) forms, as is well known, a 



' " Los Caballos Fdsiles de la Pampa Argentina," Supleinento. (" Die 

 fossilen Pferde der PampasformaUon, " Nachtrags Bericht.) By Dr. Hermann 

 Burmei>ter. Folio, pp. 65, pis. 4. (Buenjs Ayres, 1889.) 



