The distinction between the aliphatic and the aryl free radia l s of Gomberg is so big that the authors confine their brief mention of these latter compounds to the historical treatment which makes up the introduction to the subjeet. In several aspects this book shows a marked parallelism to that of "The Free Energy of Organic Compounds," Parks and Huffman, Chemical Catalog Co , although the two books deal with entirely different, but equally important fundamental fields of chemistry. Both books deal with transformations in the field of organic chemistry; both emphasize pyrogenic reactions (this book more than that of Parks and Huffman): both have a marked similarity in construction: and both are of fundamental importance to the organic chemist. While the one book deals with energy relationships, the other is concerned with the velocities of chemical reactions and the rBle that aliphatic free radicals play in the interpretation of these reactions. Both books deal with chemical "reactivity" but from entirely different points of view. I n this hook one finds complete chapters on the preparation, identification, properties, and reactions of aliphatic free radicals. and a chapter on the activation energies of elementary organic reactions with their interpretation in terms of bond strengths. The later chapters deal with the application of these principles to the pyrogenic reactions of the paraffin hydrocarbons, ketones and aldehydes, olefins, alicyclic compounds, and other compounds of larger and complicated molecules. The last chapter deals with reactions in the liquid phase and the possible place of aliphatic free radicals in the interpretation of these reactions. A valuable table of the activation energies of some 200 reactions constitntes one of the aonendices. .. llesides making a compihtion of the systemalic work that has bwn wnied out in pyrogcnic and rclatcd reactions the authors have made it one of their purposes t o give reasonable mechanisms b y which the products of most pyrogenic reactions can be predicted. Not the least of the authors' purposes has been to point out the possible importance of free radicals as intermediaries in many organic reactions that are now interpreted in other ways. As a textbook this volume can oulv be used advantaewuslv , in more advanced and specializd courses. As a general referrncr book for the chemist the reviewer regards it as one of the noteworthy achievements of chemical litrraturc.
T o continue, "For example, potassium amide, which is a derivative of ammonia in the same sense that potassium hydroxide is a derivative of water, shows all the properties of a base. Acetamidine, as the nitrogen analog of acetic acid, meets our expectations in its behavior as an acetic acid. Acetamide shows the properties of a mixed acetic acid derived simultaneously from water and ammonia. Calcium cyanamid and cslcium cyanate are just as certainly calcium carbonates as is the familiar limestone. The first salt belongs to the nitrogen system, the second is derived a t the same time from ammonia and water, the third belongs to the oxygen system. Acids, bases, and salts, alcohols, aldehydes, and representatives of other classes of compounds containing nitrogen as their dominating element exhibit all the familiar properties of their analogous oxygen compounds." A thorough study of the monograph demonstrates beyond any doubt to the reader that these relationships are not formal in character, but real and significant. Thus a primary amine in ammonia solution exhibits properties which are ch&acteristic of alcohols, and the amidines are really acids. An entirely new point of view is introduced here when one considers the chemistry of these nitrogen compounds in relation to a nitrogen system. I t enables one to predict the behavior of nitrogen compounds from the standpoint of their chemical properties; and it should serve to stimulate, as well as t o guide, investigators in this field. This paint of view alone is an important contribution to chemistry. In the &st chapter of the monograph the physical properties of ammonia solutions are discussed. A few chapters follow dealing with the inorganic nitrogen compounds and nomenclature. The following chapters are concerned chiefly with the chemistry of organic nitrogen compounds. Of especial interest t o the reader are the chapters on the ammono-carbanous. -carbonic, -nitric, and -phosphoric acids. An appendix of more than 20 pages illustrates and describes the manipulations in the handling of liquid ammonia solutions in the laboratory. Frequent references are made t o the literature throughout the monograph. O* CBICAOO TABUNIVBP~LIY c e ~ c m o ILL , WARRENC. JOENSON
TEE POETRYOP MATBEMATICS AND OTAER ESSAYS. David Eugene Smith, Professor Emerituq of Mathematics. Columbia University. Swipta Mathematica'Library, Yeshiva College. New York City, 1934. v 93 pp. 12.5 X 18.5 em. $0.50 in paper, $0.75 in cloth.
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SYSTEM OF COMPOUNDS.Edward Curtk FrankT m NITROGEN lin, Stanford University, California. American Chemical Society Monograph No. 68. Reinhold Publishing Corporation, New York City, 1935. 339, pp. 12 tables. 26 figs. 15.5 X 23 cm. $7.50. Those interested in the chemistry of nitrdgen compounds and, in particular, liquid ammonia solutions have been Looking forward to the appearance of this monograph for many years. An examination of the text reveals that the demands of even the most critical observer have been fulfilled. The monograph represents a scholarly presentation of the results of researches conducted by the author and his students, as well as by workers in other laboratories, in this field during the past forty years. These researches are interpreted on the basis of a nitrogen system of compounds being quite analogous to the mare familiar compounds of the oxygen system. As a solvent ammonia takes the place of water in this system, and the compounds may be regarded as derived from the parent solvent. Thus Franklin states, "Of all known liquids ammonia most closely approaches water in all those properties which give to water its outstanding place among solvents. In its capacity as a solvent for salt liquid ammonia is secondary to water. though some salts, for example the iodides of mercury, lead, and silver, which are insoluble in water, dissolve abundantly in liquid ammonia. It approaches water in its power of ionizing electrolytes. Solutions of salts in liquid ammonia are excellent conductors of electricity. It unites with salts as ammonia of crystallization, ,even surpassing water in its capacity for forming solvates. Like water it is an associated liquid."
It is only fair t o prefacecomment on this Littlevolume of essays with the statement that it suffered the handicap of rather high expectations on the part of the reviewer. The title essay, in particular, elects one phase of a topic In which the reviewer has always felt a warm and sympathetic ihrest-the esthetic aspects of science. Unfortunately, the reviewer's own powers of expression are incommensurate with his capacity far appreciation in this field, and he hopes, all the more eagerly on that account, to find sometime that someone has said well a few of the things which he despairs of saying. One of the paramount difficulties which confronts any commentator on esthetics is that of selecting words which may be used in their dictionary senses or which, indeed, may be used consistently in any one sense throughout the course of a discussion. We have become reconciled to this difficulty in connection with esthetic criticism in music and the graphic arts and t o some extent in literature, and we make concessions to the commentatarconcessions which are often abused to the end that much solemn nonsense is perpetrated and solemnly applauded. As we progress from those branches of esthetics which are predominantly sensory in their appeal toward those whose beauties are purely intellectual, it becomes increasingly more difficult for the commentator to choose his language with precision, and correspondingly more =cult for the reader to overlook or condone errors of choice. The present author has been particularly unfortunate (or misguided) in making the same collection of letters do duty for two different (and sometimes it seems to the reviewer two totally unrelated) ideas. The effect is sometimes as shocking as that of
a very bad and tasteless pun. The mention of poetical "numbers" in the sense in which Longfellow uses the term in the opening lines of his Psalm of Life by way of pointing out a mathematical element in poetry is a flagrant example. Another example, not quite so obvious in outward form, but closely related in essence occurs in the discussion of "points of contact" between poetry and mathematics. Voltaire is quoted to the effect that: "One merit of poetry few will deny; it says more and in fewer words than prose." I n instance Professor Smith quotes Dr. Nitobe's translation of that exquisite little Japanese lament of a mother for her dead child. "How far, today. upon the chase, I wonder. Has gone my little hunter of the dragon fly-" He then paraphrases Voltaire t o the effect that mathematics says more and in fewer words than any other science. Mathematics and poetry therefore have in common the quality of brevitythat beauty of economy which is the consequence of casting out all dross. To the reviewer this common quality of brevity establishes only the most superficial likeness between poetry and mathematics. Contemplation of it leads to a far more profound conviction of difference than of likeness. Paetrycan be economical because it actually says so little-because i t leaves the sensitive and experienced reader the opportunity of reading so much into it. The mathematical equation is economical because its extremely condensed symbolism enables it to set down a great deal in a very small space. Any reader who has learned the symbolism can read precisely what is i n i t but he must beware of reading anything a t all into it. I n short the basis of poetical brevity is subjective; that of mathematical brevity is objective. Further, the author maintains that poetry and mathematics are akin in that both embody truth. Now truth is a treacherous word a t best and one is often puzzled t o know what it may mean in any connection. Most of us would maintain. however, that i t cannot mean the same thing in application t o mathematics that i t does when applied to poetry. I t may seem a trille harsh t o criticize one writer for a fault that thousands exhibit. Yet there is something in the nature of the subject matter of this essay which makes that fault glaringly obvious. One cannot ignore the sense of incongruity in the spectacle of a mathematician who would carefully distinguish between 2 and 2' using the same symbol t o represent ideas which might better be designated b and y, and indeed implying that they are identities. I n consideration of the family resemblance between poetry and religion, it is not surprising that the essay modestly entitled "Religio Mathematici" should exhibit much of the style and method we have noted in the essay an "The Poetry of Mathematics." There is the same tendency t o make words do double duty and t o obscure the fact that they are doing so. The author appears t o have been so diverted hy the pretty pastime of arranging phrases in formal patterns that he only hints occasionally a t what the real meat of his subject might have been. The parallel sets of mathematical and religious postulates which he draws up may serve t o illustrate. MATHEMATICS
1. The Infinite exists. 2. Immortal laws exist. 3. The laws relating to finite magnitudes do not hold respecting the in6nitely large or the infinitely small. The existence of h .v ~ e r-s ~ a ciseentirely reasonable. No factor is ever lost. Time may be a closed curve. RELIGION
God exists. God's laws exist. God's laws are entirely m e r e n t from ours. There are spaces beyond ours. The soul exists and is eternal. God looks a t time as a whole.
"The Call of Mathematics" deals with the place of mathematics in a general education. The utility of the subject, its minimum essentials, its cultural aspects, and the present status of elementary instruction are discussed. Here the author handles his subject more straightforwardly. Teachers of elementary mathematics and science should read what he has to say. The historico-biographical notes on "Thomas Jefferson and Mathematics" and on "Gaspard Monge, Politician" are interesting and well written. I n spite of the criticisms offered, the reviewer recommends the reading of this little collection of essays. He recommends, however, that much of it he read like poetry-not so much for what is set down as for what may be suggested t o the mind of the reader in the process. Ch70 REnraavrn
FUNDAMENTALS oa DAIRYSCIENCE. By Associat~sof Lore A. Rogns. American Chemical Society Monograph No. 41. Second edition, Reinhald Publishing Company, New York City. 1935. 616 pp. illus. 15 X 22 em. $6.00. The first edition of this book was reviewed in TnIs JOURNAL,
5, 6 3 H (1928). The present second edition follows the same general plan as the original issue, although the persons responsible for the revision of the various chapters are not in every instance the original authors of the sections being revised. The list of contributors has been expanded and the size of the hook has increased by 73 pages. To those whose work even remotely touches upon some phase of dairy science it is useless t o detail the merits of this volume. Most of them probably already have the new edition on their shelves, or will have it as soon as they are aware of its availability. To those who have no knowledge of the scientific aspects of the dairy industry the reviewer can recommend this volume as a mine of authentic information dealine resoectivelv with the chemistry, physical chemisuy, and ttvhnology of the constituents of milk, the microbiology of milk and milk products, the nutritive value of milk and milk products, and lhc physiology of milk secretion. Written as i t is by a group ofcollaborators, all of whom have a t some time been associatedwith Lore A. Rogers, it presents the integrated views of many specialists in the field of dairy science. I n snite of the diverse authorshin of chanters and sections there is a remarkable continuity of thought. Tme, there is some repetition o l ideas and suhject matter, but perhaps these may well serve to emphasize important facts. .\lore than 2250 citations are given to literature sources. The dairy industry is fortunate to have available such an uhaustive and authoritative uade mccum add the American Chemical Society is t o be congratulated for providing in its series of monographs one which will so well serve one of America's major industries.
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UNnrsenrY os M m ~ s s o r ~
ST.PAW+,
MRINBSOTA
Ross AIDN GORTNBR
BRITISH C H E M IAND ~ THBIEM A ~ A C T U R E R Association S. of British Chemical Manufacturers, 166 Piccadilly, London, W.1, England, 1935. 459 PP. 13.5 X 21.5 em. Gratis t o genuine purchasers of &emicals upon direct application t o the Association a t the address noted. OF ENGINEERING EDUCATION AND RELATED T m INVESTIGATION A c ~ ~ v r n E s 192S1923. . SUMMARY OF RESULTS. Charles F. Scott, Chairman, Board of Investigation and Co&dination, Society for the Promotion of Engineering Education. 1934. ii 37 pp. 15 X 21.5 cm. $0.10. Pamphlet summary of the Society's two-volume, 1700-page report. The original report and the summary can be obtained from the Society's secretary, F. L. Bishop, University of Pittsburgh. The report is $3.00per single volume or $5.00per set.
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