February 17, 1H93.] 



SCIENCE. 



95 



The fact that the exact age of each horizon referred to is clearly 

 established in the geological column should make these beds of 

 particular Interest to the paleobotanist and should contribute 

 materially to our facilities in correllating the much-discusfed 

 Interior Tertiaries. Daniel W. Langdon, Jr., F.G.S.A. 



Cincinnati, Ohio. 



Bowser's Mathematical Text-Books. 



I HAVE just read a note on "Bowser's Trigonometry" by Pro- 

 fessor Hodgkins in Science of Jan. 20. Permit me to add a few 

 words OD Bowser's series, both in the way of praise and criticism, 

 and, therefore, favoring both sides of the question. I used his 

 analytical geometry and calculus for two years with good results. 

 They are well adapted to the average student in arrangement, 

 examples, and general plan, and they are more modern than 

 most text-books of the same class. But the subject is sometimes 

 unnece.isarily complicated, as in solid analytics, where the beauty 

 of the method of direction-cosines is seriously marred. Also, in 

 respect to the details of accuracy of statement and logical demon- 

 stration, I am sorry to class the series among the free and easy 

 kind of which we have so many, although among the best of that 

 kind. The public is as much at fault for accepting and even de- 

 manding boobs in that style as are the authors for writing them. 



Let me illustrate by his treatment and use of the method of 

 infinitesimals. That method is at best a dangerous one, even in 

 the hands of the masters, let alone the average student. This is 

 suflScienlly well illustrated by the errors into which Professor 

 Bowser himself has fallen ; and he should read the scoring that 

 Clausius gave his mathematical critics on their use of infinitesi- 

 mals. He will find that he is in good company. Most anything 

 can be proved to the satisfaction of the average student, just as 

 Professor Bowser establishes the differentials of the trigonometric 

 functions. Thus, by trigonometry, 



sjji (X + djc) + cos{ X + dx) = sin as •»/ 2 cos { ^T -\- dx ) 



-f cos X cos dx + cos X sin dx 



= sin X -\- cos X + cos x dx, 



since i' 2 cos( r^ 4- dx )= 1, cosda3=l, sindx^dx. 



Hence d (sin x f cos x) = cos x dx, a false result. 

 Professor Bowser is more fortunate than the critics of Clausius, 

 since he happens upon a final result that is correct; but, farther 

 along, this good hick deserts him, in the case of a carefully- 

 worked example (Calc, ex. 3, p. 325). Another case is ex. 8, p. 

 338. In view of these facts, I hope Professor Bowser will revise 

 his demonstrations and eulogy on infinitesimals, to the decided 

 improvement of his valuable book. A. S. Hathaway, 



Professor of Ma hematics, Kose Polytechnic Institute. 

 Terre Haute, lad., Jan. 28. 



the twelfth day of the month Kayab, a somewhat peculiar orna- 

 mental sign, composed of two nooks, is seen between the two 

 dots of the number. 



In connection with these facts, I wish to mention that there 

 really exists an instance of a cross between the two dots of a 

 number in Dresden Codex 46, already mentioned by Professor 

 B'orstemann in Zeitsehrifl fiir Ethnologic, 23 (1891). p. 149, that, 

 unfortunately, I had overlooked. Dr. Seler. 



Steglitz, Germany, Jan., 1893 . 



Some Additional Remarks on Maya Hieroglyphic Writing. 



In a former communication, replying to some objection 

 brought forward by Professor Thomas, I noticed that in the 

 numerals, composed of straight lines and dots, which are seen 

 accompanying the hieroglyphs of the Maya inscriptions, the one 

 <3ot of the numbers 1, 6, 11, 16 always is supported and framed 

 by two ornamental signs filling up the space, vvhile no ornamen- 

 tal sign is seen between the two dots of the numbers 2, 7, 12, 17. 

 I noticed this for a Copan Stela published by Alfred Maudsley 

 (see the Figs. 1-16 in my former paper). I may add that the 

 same applies to the inscriptions of the Palenque tablets, only that 

 here the two dots of the number 2, like the one dot of the number 

 1, are framed by two ornamental signs, while the two dots of the 

 numbers 7, 12, and 17, as a rule, are standing alone. I wish to 

 state that although prevailing in most cases, this rule may allow 

 some exceptions. Alfred Maudsley, page 39 of the text, gives 

 drawings of the numerals, where an ornamental sign, similar to 

 the two ornamental signs of the numbers 1 and 6, is seen between 

 the two dots of the numbers 2 and 7. Maudsley does not men- 

 tion where be has taken these figures. But, for instance, on the 

 cross-tablet 1, of Palenque, in the hieroglyph V. 17, designating 



Languages of the Gran Chaco. 



I WAS very much gratified to see that Dr. Brinton thinks well 

 of my intention to publish all the material I can get hold of con- 

 nected with the languages of the Gran Chaco. The following 

 facts may be of interest to him and other Americanists on your 

 side of our continent. 



1. Dr. Brinton is quite right in giving the name of '"Guaycuru" 

 to the Abipone and other cognate dialects. The root word is 

 ary, which simply means "a fierce savage." Gu and cuni are 

 simply particles. 



2. The linguistic library of the La Plata Museum vrill comprise 

 two series: First, the Guaycuru; second, the non-Guaycuru 

 group. 



The Guaycuru Group 



a MocoBl. Father Tavolini's MS. faithfully reproduced; a 

 grammar founded on same, with a preliminary discourse and 

 other papers. An English version of the grammar. 



b. ToBA. Father Barcena's MS. complete, with supplementary 

 vocabularies by Carranza, Pelleschi, the editor, and others. A 

 preliminary discourse on the language. An English translation 

 of F. Barcenas Quires. 



c. Abipon. Father Dobrizhoffer's chapters on this dialect, 

 supplemented from MSS. supposed to be Father Brigniel's, with a 

 preliminary discourse, and most important vocabulary. 



d. Lengua. Cerviiio's MS. vocabulary. Evidently a cognate 

 dialect, with Mansfield's Pajagua. Preliminary discourse on the 

 same subject.. 



e. GuATCURU. An essay on Castelnan and Gibii's vocabu- 

 laries. 



Non-Guaycuru Group. 



a. A reproduction of Father Machoni's work on the Lule lan- 

 guage, with an essay on the suffixing dialects of the Chaco. 



b. An essay on the Vilela and Chulupi dialects, to accompany 

 Pelleschi's vocabulary. 



c. Mataco. Pelleschi's grammar and vocabularies, with notes 

 and preliminary discourse by the editor. 



d. Possible numbers in Mataguays, Nocten (Mataco dialects), 

 and Chiriguano (a Guarani dialect). 



Dr. Moreno, director of the La Plata Museum, is doing bis best 

 to push this work forward. Samuel A. Lufone Qdevedo. 



Pilciao, Catamarea, Argentine Republic, Dee. ly. 



Controversies in Science. 



It might be well for scientific controversialists to bear in mind 

 that undue heat is an indication — as in mechanics — of want of 

 that balance that should constitute a judicial mind. The world 

 generally views with amusement the frothy utterances of the 

 man on the wrong side who finds himself hard pressed by reit- 

 erated facts, and judges him to be in the wrong, frequently, 

 by his language, when he may be correct entirely. One without 

 any knowledge of the facts of the present controversy between a 

 few persons connected with the U. S. Geol. Survey — a survey 

 at present under a cloud from the disbelief of Congress as to its 

 need? and usefulness — and the upholders of " palfeolithic man," 

 would naturally incline to the side taken by Professor Wright, 

 merely from the perfect courtesy and evenness of temper which 

 he has preserved under exceptional circumstances. It is seldom 

 in the course of controversy that a clergyman of good character 

 has been so bespattered with epithets, inuendoes, and charges 

 that would render him — if true — worthy of abrupt expulsion 

 from any position of trust, or from any decent religious body. 



