?o6 



NATURE 



May 



1909 



of the Board of Education Examination, and to meet 

 the requirements of Army candidates. In the 

 ■chapter on parallel projection, the theory on which 

 it depends, viz. that it is the view, on the YZ plane, 

 of the solid and the various coordinates and the co- 

 ordinate axes, obtained by parallel rays inclined to 

 that plane at some specially chosen angle, is not put 

 quite so clearly as perhaps it might profitably have 

 been, but the author expressly says that the theory is 

 to be dealt with in the second volume, which is in 

 course of preparation, and the chapter in question 

 very clearly shows how the constructions are to be 

 made and used for measurements. The sentence on 

 p. 92, lines 13-16, contains an erroneous and incom- 

 plete argument, very unlike the author's usual careful 

 accuracy. The sentence as it stands implies that ver- 

 tical planes are necessarily perpendicular to horizontal 

 lines. 



There is a useful appendix on algebraic solid g^eo- 

 metry, dealing with planes and lines, as far as the 

 tangent plane to a sphere, and two other appendices 

 give the requirements of the Board of Education in 

 solid geometry and some sets of its papers. 



There are a good number of examples attached to 

 each chapter for the student to solve, and we are 

 glad to see a good index, which greatly facilitates 

 reference. 



(2) It is difficult for the writer of a geometrical 

 text-book for beginners to decide how much of the 

 philosophy underlying the subject should be given. 

 The author's treatment of the straight line and of 

 parallel straight lines is not satisfactory. He defines 

 a straight line as the shortest distance between two 

 points, but makes no use of that definition in the 

 text, and parallel straight lines are defined as straight 

 lines drawn in the plane in the same direction. It 

 may be contended that this is sufficient for voung 

 students, though it certainly will not satisfy all 

 teachers. It is, however, an appeal to common 

 notions, and, after all, a good many propositions do 

 depend on these, however carefully the philosophical 

 foundations may be laid. A more serious defect is 

 where the author, after proving, by means of oppo- 

 . site rotations, that lines are parallel when the alter- 

 nate angles are equal, promises another proof, and 

 eventually gives one which depends on a proposition 

 deduced from the previous one, a most flagrant case 

 of reasoning in a circle. 



The author has adopted the excellent plan of elevat- 

 ing a number of standard problems and theorems 

 into the text which are usually only given as riders, 

 and though occasionally we would have liked to see 

 slightly different methods of construction or of 

 proof, on the whole they are complete and 

 clear, and the propositions are accompanied bv 

 a good number of well-chosen exercises. The range 

 of the book is as far as the end of the sixth book 

 of Euclid, with the omission of one or two proposi- 

 tions at the end. We cannot, however, find the very 

 important proposition on which the proofs of the 

 properties of similar triangles depend, viz. that if one 

 transversal is divided into equal parts by a series of 

 parallel straight lines, all transversals are also divided 

 NO. 2063, VOL. 80I 



by them info equal parts. The nearest approach to 

 this is on p. 84, where a construction is given for 

 dividing a line into equal parts, but it is merely said 

 that " it is easy to show " the congruence of certain 

 triangles, &'C. The full proof should have been given, 

 or, better still, the construction should have been pre- 

 ceded by the general theorem. Of course, the teacher 

 can supply the omission, but it is notorious how 

 young students usually fail to remember proofs which 

 are not in their text-book. 



OUR BOOK SHELF. 



The Story oj Gold. By E. S. Meade. Pp. xv+206; 



illustrated. (London : Appleton and Co., 1909.) 



Price 2S. 6d. net. 

 The author of this book appears to believe that 

 all human progress depends on a continuous rise 

 in prices, that a rise in prices is always due to 

 a great addition to the stock of gold in the world, 

 and that consequently it behoves statesmen to see 

 that gold is produced from the mines in a rapid and 

 increasing stream. Rome decayed because the 

 Spanish mines stopped producing. Europe welteri-d 

 in misery until 1492 because the stock of precious 

 metals continued to diminish. Thereafter all went 

 well until about 1810. (N.B. — The price of wheat 

 in 1809 was 157.S. per quarter, with wages much lower 

 than now.) Then the revolt of the Spanish .-Xmerican 

 colonies cut off the production of the mines, and 

 began a period of stringency which was not relieved 

 until after 1849. From 1873 to 1896 the new gold 

 supplies were again inadequate, prices fell, trade was 

 bad, the human race languished. Then for a time 

 the enormous production of gold allowed progress to 

 be resumed. The pace, however, is rapidly becoming 

 hotter. Although the output of gold is even more 

 enormous now and is still increasing, the supply of 

 other commodities has overtaken it, and unless the 

 gold miners redouble their efforts there is little chance 

 of a revival of prosperity. 



The author is a professor of finance of the University 

 of Pennsylvania, and consequently his discussion of 

 geological, chemical, and engineering problems con- 

 nected with gold need not be taken seriously. Never- 

 theless, a long succession of careless misstatements 

 such as appear in the book becomes wearisome, and 

 creates an atmosphere of prejudice against the author, 

 so that his most lugubrious predictions and stirring 

 calls to action leave the reader unconvinced and 

 apathetic. Even when his information is correct, the 

 author's utterances are somewhat cryptic, e.g. " Gold 

 is remarkable for its freedom from corrosive solu- 

 tions." 



His main thesis is, of course, tinged with exag- 

 geration. There is no doubt that rising prices benefit 

 all those who buy to sell again, includinp;' speculators 

 as well as merchants. How far the whole community 

 benefits is not quite so certain. It is often contended 

 that a flat level of prices would be best of all. More- 

 over, it is hardly fair for the representative of almost 

 the only nation still addicted to frenzied finance to 

 attribute its disasters to those laggards the gold 

 miners. 



There is no need to be pessimistic as to the ade- 

 quacy of the supply of gold, but if it really became 

 scarce, it is perfectly obvious to unprcjudicf d ob- 

 servers that gold need not be retained as the sole 

 medium of exchanfre. In a sense most of its work 

 is done already by cheques, bank notes, silver, and tb^ 

 like. Althouijh in earlier times it was prized for itself 

 alone, it is now of very little intrinsic value. It 



