178 



SCIENCE, 



[Vol. XXI. No. 530 



I. Thorold, by Delesse. 



II. Napanee Mills, by W. M. Smith, Syracuse, N Y. 



in. Hull, by Delesse. 



IV. Quebec, by Delesse. 



As to the relative qualities and tensile strength of the various 

 Canadian cements, it has been thought best to say nothing, as 

 "comparisons are odious." Much information and many sched- 

 ules of testing operations may, however, be found in recent re- 

 ports of tlie City Engineers of Toronto and Montreal. In these 

 reports the various Canadian brands are shown in compaiison 

 with most of the prominent European and American natural and 

 artificial cements. 



LETTERS TO THE EDITOR. 



*** Correspondents are requested to be as brief as possible. The wriler'a name 

 is in all cases required as proof of good faith. 



Chi request in advance., one hundred copies of the number containing his 

 communication will be furnished free to any correspondent. 



The editor willbe glad to publish any queries consonant with the character 

 of the journal. 



Prehistoric Remains in America. 



There is one fact in regard to the prehistoric and protohistoric 

 remains of North America which does not appear to have re- 

 ceived the attention it deserves. 



If we examine carefully the descriptions and figures of these 

 remains so far as published and attempt to classify them, we 

 soon find ourselves forced to admit that there are two well- 

 marked, general classes of types, the one belonging to the Pacific 

 and the other to the Atlantic slope. The characteristics which 

 distinguish these two classes are botli numerous and well- 

 marked. Geographically, the Rocky-mountain range appears to 

 be the dividing line as far south as the Rio Grande, Mexico, and 

 Central America, belonging to the Pacific slope section. 



Although the remains of the Pacific division present many 

 types, varying in the different sections, yet there is such a 

 strong general resemblance, on the one hand, of those found 

 from Southern Alaska south to the Isthmus (excepting a gap in 

 California), and, on the other hand, such a strong contrast with 

 those of the Atlantic slope as to justify the conclusion that this 

 arises from ethnic distinctions and indicates different races. 

 Mr. Swan has long been calling attention to the resemblance be- 

 tween the types of the region inhabited by the Haida Indians and 

 the remains of Mexico and Central America, and no one who 

 will make the comparison will fail to be convinced. Professor 

 Dall, who has studied the manners, customs, and remains of the 

 Northwest Coast, reaches the same conclusion. I cannot enter 

 into details in this brief article, but ask any one who doubts the 

 correctness of this conclusion to compare the figures given by 

 Ensign A. P. Niblack, in his work on "The Coast Indians of 

 South Alaska anil Northern British Columbia," with those found 

 on the monuments of Mexico and Central America, and then with 

 the types of the Atlantic slope. It is true that the former are 

 modern, yet the resemblance both in general character and com- 

 bination to those of Mexico and Central America is too marked 

 to be overlooked, while no such resemblance to those of the At- 

 lantic slope is observable. 



Do not these resemblances on the one hand and differences on 

 the other have an important bearing on the question. '-From 

 whence did America (or rather North America) derive its origi- 

 nal immigrants ? " That the works of the two slopes present two 

 distinct classes of types cannot be denied. That there is in Cali- 

 fornia a break in the continuity of the types of the Pacific slope, 

 which seems to indicate an overflow from the Atlantic side, only 

 serves to emphasize the above conclusion. The marked similarity 

 between the types of the Pacific slope and the Pacific Islands 

 has been referred to by Professor Dall (3d Ann. Rep. Bur. Eth., 

 pp. 147-151), who finds that they have prevailed "from Melan- 

 esia to Peru and from Mexico to the Arctic." In summing up, 

 he remarks that ' ' the mathematical probability of such an inter- 

 woven chain of custom and belief being sporadic and fortuitous 

 is so nearly infinitesimal as to lay the burden of proof upon the 

 upholders of the latter proposition." Pi-ofessor Dall does not 

 argue from this a common origin of the people possessing these 



characteristics; but believes they have been " impressed "" upon 

 the inhabitants of the western coast from the Pacific side. Not- 

 withstanding this disclaimer, does not the evidence indicate two 

 streams of original immigration, one to the Atlantic and the 

 other to the Pacificcoast? Ensign Niblack, although disclaiming 

 any inference to be drawn therefrom as to relationship, gives a 

 list of resemblances between the customs and works of the New 

 Zealanders and Haida Indians that is certainly remarkable. 



The idea that America was peopled by way of Behring Straits 

 is somewhat losing its hold on the minds of students, and, as a 

 usual result, there is a tenilency to swing to the opposite extreme. 

 Drs. Brinton and Hale are inclined to believe, chiefly from lin- 

 guistic evidence, that the first settlers came from Europe to the 

 North Atlantic coast. The former says in his " Races and Peo- 

 ple,-," pp. 347-248, " Its first settlers probably came from Europe 

 by way of a land connection which once existed over the North 

 Atlantic, and that their long and isolated residence in this con- 

 tinent has moulded them into a singularly homogeneous race, 

 which varies but slightly anywhere on the continent and has 

 maintained its type unimpaired for countless generations. Never 

 at any titne before Columbus was it influpnced in blood, language, 

 or culture by any other race," 



Now it may be that settlers came from Europe to the North 

 Atlantic coast, but the evidence is decidedly against the remain- 

 der of the above quoted paragraph, which is, in fact, somewhat 

 self-contradictory. For, if the settlement was at one point, by 

 one race, and this race was never influenced by another, it is 

 difficult to imagine in what respect the moulding process acted. 

 However, the cliief objection is to the theory of a single original 

 element, and the assumption that it was never influenced in 

 pre-Columbian times by anv other race or element. The facts 

 set forth by Professor Dall and confirmed by Ensign Niblack are 

 too apparent to he set aside by any theory or mere declaration. 

 Even without the evidence presented by these parties, the differ- 

 ences between the archeeologic types of the Pacific and Atlantic 

 slope are suffi.cient to outweigh any argument that lias been pre- 

 sented against intrusive elements. Cyrus Thomas. 



Wasbington. D.C. 



Some More loiinitesimal Logic 



Professor Bowser, in his reply to me in Science, Mar. 10. does 

 not recognize the logic of his calculus in the example in question. 

 The only reasons given in his calculus that would permit the use 

 of cosdx = 1 are, the axiom (?), page 13 : — 



" An infinitesimal can have no value when added to a finite 

 quantity and must be dropped." 



And, page 37 : — 



"Because the arcdx is infinitely small, . . . its cosme equals 

 1. ' 



If, for these reasons, cos da; ^1, then, for the same reason-, 



^'3cos (~+dxj=l. 



Four out of the five axioms on page 12 are misleading, not to 

 say incorrect. The orders of infinitesimals or infinites to be re- 

 tained in an expression do not depend upon the expression, but 

 upon the use that is to be made of it. Sometimes we must use 



cos dec : 



1 - 



etc. Quite prominent 



— or = 1 — — 4- — , 

 2 2 34 



mathematicians have failed to do this properly in instances where 

 they would naturally use great care. Reasoning on infinitesimals 

 is at best of a slippery character. I have referred in my former 

 article to an example (Ex. 3, p. 335) where Professor Bowser 

 obtains a result that is easily verified to be incorrect: yet the 

 logic of his work seems correct, not only to the average, but to 

 the best students; and it must have seemed right to Professor 

 Bowser, or he would not have inserted it. 



The second proof of the differentialof the logarithm, pp. 39-31' 

 is another example of false logic. The same proof is found in 

 Olney, p. 25; Taylor, p. 24; Hardy, p. 31; and is the only proof 

 relied upon by some of these authors. This is quite a list of 

 mathematicians who have indulged in infinitesimal reasoning of 

 the value zero, and who will probably learn of it for the first time 

 through this article. It is easily seen that the logic is false by 



