416 



♦ KNO\VLEDGE 



[Nov. 21, 1884. 



inhabitants, while still retaining all its original ethnical 

 peculiarities. 



In short, the relative numbers at starting of any two 

 races which occupy the same country are comparatively 

 unimportant, ethnologically speaking ; what it really im- 

 ports us to know is how fast or how slowly each of the two 

 elements tends to increase. A constant supplanting of 

 families by families is always going on — an absorption of 

 one family by the other ; and this often in a way that 

 completely misleads us as to the true result. For, suppose 

 a stock with a Norman name — call it De Montmorency — 

 to settle down among a Saxon population, and, from 

 generation to generation, to have one son only, who always 

 marries a Saxon woman. At the fifth generation, there 

 will still apparently be a De Montmorency, who will pass 

 current with all of us for a genuine unadulterated Norman. 

 But, in reality, though he traces in the direct line by heir 

 male back to the original De Montmorency, he will have 

 only Jj- of Norman blood, and f^ of Saxon. Put a negro 

 for the ancestor, and this truth will be immediately 

 apparent. For the first generation will be a mulatto, the 

 second will be a quadroon, the third an octaroon, and the 

 fourth will so entirely have lost the traces of African 

 descent as to be (in the old slave phrase) " white by law." 

 Nobody on earth could possibly detect in the fifth remove 

 the very slightest tinge of negro ancestry. 



And this last example leads us up to the final point, to 

 prove which I have ventured to adduce the imaginary case 

 of Barataria. It seems to me that while historical data are 

 in the very highest degree misleading (because we can never 

 really ascertain for distant times the relative rates of in- 

 crease), the one certainty upon which the ethnologist can 

 repose is physical peculiarities. These, it has abundantly 

 been shown, do really repeat themselves with great persis- 

 tency, being truly characteristic of races and of their inter- 

 mixture, even down to the very fractions of each involved. 

 Nobody has any practical difficulty in distinguishing a 

 mulatto from a negro or a white man ; a quadroon from a 

 mulatto ; or an octaroon from a quadroon. One can say at 

 once, " This man is a pure-blooded Chinaman; this one is 

 half-Chinese and half-Malay ; this one is Malay with a 

 slight Chinese intermixture," and so forth. The physical 

 peculiarities of both races persist in the hybrids ; and 

 when we find a remote hybrid (like our person of negro 

 descent in the fifth degree) in whom one stock has com- 

 pletely overborne the other, it is because the remaining 

 fraction of the weakest blood has been practically bred out. 

 Such a person is, in fact, essentially a white man. In 

 British ethnology (to take a home case) the differences of 

 race are, of course, far less marked, but they are equally 

 persistent ; and the best way, therefore, to arrive at a just 

 conception of what blood preponderates in our modern 

 British people is not to follow the procedure of Professor 

 Freeman and the historical school, but to follow that of 

 Professor Huxley, Dr. Beddoes, and the scientific anthro- 

 pologists. Look not at the ethnical composition of Britain 

 in the ninth century, but at the skull and bones of the 

 modern Englishman, compared with those of the purest 

 discoverable old Celts and the purest discoverable old 

 Teutons. 



Hek Majesty the Qneen has accepted a copy of Mr. Fayle's new 

 work entitled " The Spitalfields Genins ; a" Memoir of William 

 Allen," who was the coDfidential friend, the trustee, and the 

 executor of her Majesty's father. 



Messrs. Hachette & Co., of Paris, will publish very shortly a 

 popular illustrated French editions of Dickens's works. The majority 

 of the illustrations are those by Barnard, but every volame will 

 contain a certain number of original designs by various English and 

 foreign artists residing in England. M. Joseph Tonnean will supply 

 the greater number of these. — Athencviim. 



CHATS ABOUT GEOMETRICAL 

 MEASUREMENT. 



By Richard A Proctob. 



( Continued from p. 383.) 



A. But can we always get a neat set of chords, like 

 AC, OD, DE, &c., in Fig. .3, or of tangent-lines like 

 AH, H K, K L, (fee, in the same figure, and so determine 

 the length of our arc ? 



L 



Fig. 3. 



M. Unfortunately we cannot. We usually have to be 

 content with another device, the consideration of which ia 

 of some importance, since it brings before us the true idea 

 of tangent-lines. Indeed, I am not sure but that the 

 measurement of direction at difierent points of a cvm'e 

 ought not to have been the first point to l)e considered. 

 However, as we have been naturally brought to it along 

 the line we have followed, we may take it now as well as 

 earlier. 



Fig. 6. 



A. I am all attention. 



3f. 'Tis well Let A D B (Fig. 6), be a small part of 

 some arc, A T the tangent at T. Join A B, AC, AD. 

 Then it is clear that these lines lie nearer and nearer in 

 direction to the tangent line A T. Moreover, since the 

 curve ha.s the direction A T at the point A, and changes 

 continuously in direction from A to D, C, B, &c., it is 

 evident that by taking points as C, D, and thence, along 

 the curve, successively nearer and nearer to A, we get 

 chords as A B, A C, A D, ic, drawing nearer and nearer 

 in direction to the tangent A T, until they differ from it in 

 direction by an angle less than any angle, however small, 

 that can be indicated. The angle like BAT made between 

 one of these chords and A T grows less and less up to 

 nothing as the other end draws nearer and nearer to A, 

 passing continuously through all values between the angle 

 BAT with which it may be supposed to have begun, and 

 the evanescent angle when the moving point merges 

 into A. 



A. All this is clear ; but what this has to do with the 

 measurement of the length of an arc I fail utterly to see. 



M. Nay, did I say you could see the connection ? But 

 I think you will as I proceed. 



A. Again, I am all attention. 



M. Suppose now that from B, C, D a series of parallel 

 lines are drawn making some finite angle B K T, C L T, 

 DMT with A T ; and produce the various lines as shown 

 in Fig. C. Then it is obvious that the ratios A B to A K, 

 AC to AL, AD to AM draw nearer and nearer to 

 equality as we take points B, 0, D nearer and nearer to A 



