492 



NATURE 



[October 20, 1910 



note-books given in this volume show how little the 

 law was able to fill his mind. In January, 1652, he 

 began to occupy himself with various geometrical 

 problems leading to equations of the second or third 

 degree, of most of which he gave solutions in his 

 " Illustrium quorundam Problematum Constructiones," 

 which came out in 1654 as an appendix to his work on 

 the quadrature of the circle. Both the rough work 

 and the printed essay are reproduced in the present 

 volume, and it is interesting to follow the stages by 

 which he succeeded in submitting problems to 

 algebraical analysis which Archimedes, Nicomedes, 

 and other Greek mathematicians had treated by pure 

 geometry. 



The principal publication from this period of 

 Huygens' life is his book on the quadrature of the 

 circle, by which he took his place among the leading 

 mathematicians of the day. It was a time when circle 

 squarers flourished, several of them men of some dis- 

 tinction, such as Grf^goire de St. Vincent, whose bulky 

 work appeared in 1647 and called forth several 

 polemical writings. Huygens entered the field in 165 1 

 with his " 'El^tTKo-it Cyclometrioe " (reprinted in T. XI. 

 of the new edition), in which he showed the fallacy of 

 .St. Vincent's quadrature of the circle. In 1654 he 

 brought out a larger work, " De Circuli Magnitudine 

 Inventa." In this he developed further the use of the 

 properties of the centre of gravity on the basis of the 

 theorems he had published in 1651, and rigorously 

 proved some propositions used by Snellius without 

 proof, as well as a number of new theorems about 

 sums of polygonal perimeters and various quantities, 

 between which the length of the circumference of the 

 circle is intermediate. Finally he calculated -a by 

 means of a 60-sided polygon within the limits of three 

 units of the tenth decimal. The number of decimals 

 is, of course, inferior to that previously attained by 

 Van Ceulen and others, but the result was found 

 without the appalling labours which these had gone 

 through, and the investigation is valuable on account 

 of the theorems proved by Huygens. 



The lucidity and force of the arguments in the 

 " 'EfcVao-i? " had made its author hope that Ihey had 

 convinced Gri5goire de St. Vincent of his mistakes. 

 He esciianged a number of civil letters with St. 

 Vincent, but the latter could never be induced to enter 

 on a discussion of the matter, but always evaded it by 

 saying that some day he would answer all his critics 

 at the same time. But several of his pupils entered 

 the lists for him, among whom was the Jesuit 

 Ainscom, who in 1656 published what he imagined was 

 a refutation of all the adversaries of his master, and 

 did his best to convince people of the truth of the four 

 methods of squaring the circle set forth by St. Vincent, 

 but never put into practice by him. Huygens lost no 

 time in replying ; his " Epistola " to Ainscomb was 

 published at the Hague in the same year. It forms 

 the concluding portion of the present volume of his 

 works, and .in accordance with the praiseworthy rule 

 of the editors of this most valuable edition of Huygens' 

 works, the part of .\inscom's essay dealing with the 

 attack of Huygens is also reprinted. 



J. L. E. D. 



NO. 2138, VOL. 84] 



.1 PRIMER ON COAL MINING. 

 First Steps in Coal Mining. For Use in Supplemen- 

 tary and Continuation Classes. By .\lexander Forbes. 

 Pp. viii + 320. (London, Glasgow, and Bombay: 

 Blackie and Sons, Ltd., 1910.) Price 2s. 6d. 



THE present adds one more to the already long list 

 of primers on coal-mining that have been produced 

 so freely of recent years, and unfortunately it cannot 

 be said that it is sufficiently an improvement upon 

 some of its predecessors to justify its publication. It 

 is difficult to see to what class of student such a book 

 as the present one can address itself, or which it can 

 expect to benefit ; if it is intended for the instruction 

 of youths actually engaged in mining operations, such 

 definitions as "the men engaged in the excavation of 

 the material are termed sinkers," "the portion of the 

 twenty-four hours during which each set works being 

 called a shift," "the extreme end of the road ... is 

 called the face," &c., are surely superfluous, as these 

 expressions must be familiar to every boy about a pit. 

 If, on the other hand, the book is intended for those 

 who have no personal knowledge of coal-mining, the 

 amount of information afforded upon the majority of 

 mining operations cannot possibly be sufficient to en- 

 lighten them ; for instance, it is hopeless to expect 

 that the subject of coal-cutting by machinery can be 

 adequately taught in three pages ; in the same way, 

 only twenty pages are devoted to the whole subject of 

 shaft-sinking, including all the special methods, 

 entirely out uf ]jlace though these are in an elementary 

 book. 



Just about one-third of the book has been devoted 

 to an outline of geology, and this is the most, if not 

 the only, satisfactory part of it. The remainder is 

 made up of "scrappy " chapters on the various depart- 

 ments of mining, with some fragments of elementary 

 chemistry and physics distributed amongst them. Not 

 content with this wide range, the author has not hesi- 

 tated to include even mine surveying, to which he 

 devotes nearly four pages ! Of what use he imagines 

 that these can possibly be to anj'one it is hard to con- 

 ceive, even though he has inserted an illustration, 

 without a word of description, of an old-fashioned 

 theodolite, possibly with the object of giving an air 

 of completeness to his index. Had the author con- 

 tented himself with writing an elementary text-book 

 of geology for the use of miners, he might probably 

 have produced a work of greater use than the more 

 ambitious effort now before us ; at the same time, it 

 cannot but Jse admitted that not even in the geological 

 section has the author displayed the faintest evidence 

 of originality in thought or treatment. This want of 

 novelty throughout the book is shown very strikingly 

 in the illustrations, every one of which appears to 

 have been published before in other works. Their 

 •selection has, moreover, not always been a happy one, 

 as witness the picture of the theodolite already referred 

 to. For sheer futility it would be difficult to surpass 

 some of the illustrations to the chemical section, such, 

 for example, as Fig. 129, which represents water 

 being poured out of a jug. 



The very best thing that can be said of the book 

 is that it is comparatively free from serious mistakes. 



