114 



SCIENCE. 



[N. S. Vol. XXIV. No. 604. 



hope there soon may be demand, the author 

 might perhaps better satisfy a larger number 

 of students by a thoroughly digested epitome 

 of the present book, while the teacher should 

 welcome another volume that would still fur- 

 ther elaborate all but the anatomical part of 

 the present book. For the teacher there might 

 be added a consideration of the geographical 

 distribution of frogs, with maps; a full dis- 

 cussion of the remarkable breeding and brood- 

 ing habits of some exotic frogs; more ample 

 reference to the field of regeneration in frogs; 

 an account of the genesis of the eg^ and the 

 sperm; and original illustrations. He would 

 then have a fit complementary volume to 

 Gaupp's ' Ecker.' E. A. A. 



Easy Mathematics, chiefly arithmetic; being a 

 collection of hints to teachers, parents, self- 

 taught students and adults, and containing 

 most things in elementary mathematics use- 

 ful to he Tcnown. By Sir Oliver Lodge^ 

 r.E.S. Macmillan and Co. 1905. Pp. 

 XV -I- 436. 



When a man like Sir Oliver Lodge writes 

 on arithmetic we naturally expect an unusually 

 high motive. In the present case this motive 

 is set forth in such forceful terms as follow: 

 The mathematical ignorance of the average edu- 

 cated person has always been complete and shame- 

 less, and recently I have become so impressed with 

 the unedifying character of much of the arithmet- 

 ical teaching to which ordinary children are liable 

 to be exposed that I have ceased to wonder at the 

 widespread ignorance, and have felt impelled to 

 try and take some steps towards supplying a 

 remedy. The object in writing the book has been 

 solely the earnest hope that the teaching of this 

 subject may improve and may become lively and 

 interesting. Dulness and bad teaching are 

 synonymous terms. A few children are born 

 mentally deficient, but a number are gradually 

 made so by the efforts made to train their grow- 

 ing faculties. 



To read an arithmetic written in a breezy 

 style yet thoroughly sane from cover to cover 

 is a surprisingly interesting experience for 

 most people who try it. While those who are 

 familiar with elementary mathematics may not 

 learn any new facts by reading this book, yet 

 there will probably be few who will not have 



a more cordial attitude towards the subject. 

 It works a change of feeling and clearness of 

 vision rather than a deeper insight into the 

 more abstruse parts. 



The charm of many illustrations lies in their 

 extreme simplicity. For instance: 



It is very often a mistake for teachers to sup- 

 pose that some things are easy and other things 

 are hard; it all depends on the way they are pre- 

 sented and on the stage at which they are intro- 

 duced. To ascend to the first floor of a house is 

 difficult if no staircase is provided, but with a 

 proper staircase it only needs a little patience to 

 ascend to the roof. The same sort of steps are 

 met with all the way, only there are more of them. 

 To people who live habitually on the third floor 

 it is indeed sometimes , easier to go on the roof 

 than to descend into the basement. Educators 

 should see that they do not forcibly drive children 

 in shoals up an unfinished or ill-made stairway, 

 which only the athletic ones can elimb.^ 



The first part of the volume is partly his- 

 torical. In some of this the imagination is 

 explicitly allowed to wander beyond the estab- 

 lished facts. In addition to most of the ques- 

 tions which are met in arithmetic and ele- 

 mentary algebra, there are chapters on Easy 

 Mode of Treating Problems that require a 

 Little Thought, dealing with Very Large or 

 Very Small Numbers; Pumps and Leaks, Dif- 

 ferentiation, etc. The work is divided into 

 forty-seven brief chapters and throughout im- 

 presses one with the fact that the greatness of 

 a man is perhaps most strikingly exhibited by 

 his treatment of common subjects. The au- 

 thor with a narrow outlook would not make 

 such a wise choice of subject matter and would 

 not be apt to refresh the reader with such 

 broad views as ' Real living arithmetic is the 

 same in any country; and most important of 

 all is that which must necessarily be the same 

 on any planet,' and ' An equation is the most 

 serious and important thing in mathematics.' 



While the book naturally appeals most 

 strongly to the teacher, yet it seems to be 

 eminently suitable for those who desire - to 

 get a clear view of the subject matter which 

 has been employed in their early training. 

 The sub-title has a quaint eighteenth century 

 flavor, but the book itself is thoroughly modern 



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