unknown with its chilling effects. At the end of the fall term they have a very satisfactory knowledge of the fundamental laws and theories; are familiar with oxygen, hydrogen, nitrogen, carbon, and some of their compounds; and have mastered their chemical arithmetic with less difficulty than usual, and without requiring supplementary problems which I have previously had to prepare. While your reviewer says that the book has "None of the 'rub it in element," my experience has been just the opposite, in fact, it is that element that most excites my admiration. The properties of acids, bases, and salts, after being briefly treated in the early pages, are enlarged upon and thoroughly "rubbed in" for twenty-six later consecutive pages, besides being frequently alluded to by reference and question throughout the remainder of the text. Your reviewer states that the "index" has "one reference each to chemical equilibrium and explosives." Had he studied the text as well i s the index he would have noted that chemical equilibrium is constantly kept before the pupil by careful explanation and sumptuous use of the reversible reaction equation, and that explosives are not only treated individually in logical order, but are repeatedly mentioned when their components or constituents are discussed. The theory of the subject is explained in a convincing manner and industrial applications are stressed in a way to make the student realize the value, to him, of a thorough knowledge of the science. The laws of chemistry are connected to the theories that explain them with a clearness that should satisfy the most exacting. The wealth and variety of material meets the requirements of all, and one may omit what he does not consider essential. (I shall omit seireral chapters because my course has for its primary object preparation for college entrance examinations.) The extensive use of bold type and italics, the splendid illustrations, the clear and logical presentation, supplemented with summaries and questions and references at the end of every chapter, make it the nearest my ideal as an interesting, sound, and teachable text that I have used or examined. LAWRENCEVILLE HIGHSCHOOL. LAWRENCEVILLE. N. J.
H. W. HEATH
THE LAW OF AVOGADRO Under the above caption I published a brief paper in the November EDUCATION, giving what I was pleased number of the JOURNAL OP CEEMICAL to call a deductive proof of Avogadro's law from the empirical and firmly established laws of Gay-Lussac and the law of Combining Masses.
I n the January number of the same JOURNAL a letter appears which attacks my "deductive proof" (the quotation marks are those of the writer of the letter). I would have welcomed the opportunity t o reply t o this criticism sooner, but this was impossible as i t came to my notice only after its publication in the JOURNAL. I shall pass over the writer's claim that "It is thoroughly familiar to all how this principle arises out of Gay-Lnssac's Law of Combining Volumes and (as the mthor correctly points out) from the Law of Combining Weights," with this observation, that neither in Avogadro's memoir, nor in any text-book that I recall has the law of Combining Weights been explicitly stated, much less applied in establishing Avogadro's Hypothesis. However, his claim that "it is thoroughly familiar to all" may explain the uniformly obscure and scant treatment it receives a t the hands of textbook writers and teachers of chemistry. But i t is in the next paragraph of his letter that my critic clearly discerns "the fly in the ointment." Thus he says "in the author's 'deductive proof' (quotation marks to this phrase are the critic's) the equation V l / V s = %/nl X N 1 / N 2 is used, where V l / V 2 , the ratio of combining volumes and Nl/N2 the ratio of total molecules reacting, are both whole numbers (the italics are mine. May I interject a t this point that the ratios are not whole numbers; i t is the terms of the ratios that are whole numbers) whence, the author suggests n, cannot be not equal to nl (the number of molecules in equal volumes)." Then follows this, "The mathematical fallacy of this is apparent, however, for to fulfil the conditions it is only required that nz = bnl, where b is any whole number not necessarily one." Of course; but by what right does he confine the values of b to whole numbers? Why may not b be any number whatsoever, whole or fractional? Does he wish to claim, taking any two gases a t random, that the number of molecules in unit volume of one of them determines the number of molecules in unit volume of the other. That is what he is doing when he writes n, = bnl. Such a view is absurd. nl and nz are independent. We cannot say, for example, that the number of molecules in unit volume of hydrogen is proportional t o (or indeed any function of) the number of molecules in unit volume of oxygen. Surely it is unnecessary to elaborate this further. I showed in my paper that if nl is not equal to nz the conditionrequired, uiz., that V 1 / V zfollow Gay-Lussac's law could not be satisfied in all cases, i. e., for all values that n, and m could assume (and I cited a possible particular pair of values of n, and n2 to illustrate this point). It should be realized that Avogadro's Law is a limit law just as are those of Charles, Boyle, and Gay-Lussac as, in fact, I stated in my paper.
Therefore I hold that my "deductive proof" is neither "erroneous" nor "ambiguous," and that the mode of presentation employed does get us somewhere with respect to this fundamental law (not "assumption") of Avogadro. ABRAHAM HENWOOD
CENTRAL Hxca Scaoo~, PA. P~LADELPRIA.
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