August 17, 19 16] 



NATURE 



499 



in 1876 — 36'3 per looo population — and has gradu- 

 ally fallen since then to about 23 at the present 

 time, and this in spite of the marriage-rate having 

 remained almost constant. The decline of the 

 birth-rate has not oj>erated uniformly throughout 

 the country, but is more marked among the 

 middle and upper classes. Thus in Hampstead 

 the corrected birth-rate fell from 30'oi in 1881 to 

 I7'55 in 191 1, while the corresponding^ rates for 

 Shoreditch are 3i'32 and 30' 16. 



The general conclusion of the committee 

 seems to be that the decline in the birth-rate is 

 due to the deliberate limitation of families by anti- 

 conceptives and other means. At the same time 

 it is to be noted that the result of a census — a com- 

 paratively small one, it is true — taken by the Com- 

 mission of those who employed anti-conceptive 

 measures and of those who did not showed that 

 the size of the families was slightly larger among 

 fhe former I The conclusion arrived at by the 

 Commission seems to be based upon the unani- 

 mous opinion of the witnesses of the extensive 

 and increasing use of anti-conceptive measures, 

 particularly among the more well-to-do classes of 

 the community. Two of the witnesses, however, 

 Dr. Chalmers and Dr. Brownlee, maintained that 

 there are cycles in fertilit] , and that now we 

 happen to be in a cycle of low fertility. Among 

 the lower classes, especially in industrial areas, 

 the use of abortifacients appears to be rife, and 

 this may be a not unimportant factor in reducing" 

 the birth-rate. 



Various topics bearing on the question are dealt 

 with in the evidence, such as the influence of finan- 

 cial circumstances, housing, religious belief, etc. 

 One point of interest brought out is that the fer- 

 tility of " college " women seems to be as great 

 as that of "non-college" women, though, as might 

 be expected, the age at marriage of the former is 

 somewhat higher than that of the latter. 



The Commission is unable to formulate any 

 measures for arresting the decline beyond the use 

 of moral suasion to induce the married to fulfil 

 their responsibilities. 



The volume is an intensely interesting one, and 

 should be in the hands of all who are interested 

 in this national question. R. T. Hewlett. 



I S^.VG'S SEVEN-PLACE LOGARITHMS. 

 A A'ett' Table of Seven-Place Logarithms of all 

 numbers from 20,000 to 200,000. By Edward 

 Sang. Reprinted from the original stereotype 

 plates now in the custody of the Royal Society 

 of Edinburgh. Pp. xviii + 365. (London : 

 C. and E. Layton, 1915.) Price 215. net. 

 "^T^HIS table was originally printed in 1870 from 

 ^ the stereotype plates in the custody of the 

 , Royal Society of Edinburgh. The present book 

 ! is a reprint published in 191 5. 



Edward Sang (1805-90) was perhaps the 



^^[reatest calculator of logarithms. An excellent 



I account of the extraordinary energy that he 



I brought to bear upon this work is to be found in 



j a paper by Dr. C. G. Knott, of the Royal Society 



of Edinburgh, which forms part of the Napier 



XO. 2442, VOL. 97I 



memorial volume published in connection with 

 the Xapier tercentenary held in Edinburgh in 

 July, 1914. Sang computed, independently of all 

 previous work, the logarithms to twenty-eight 

 places of all primes up to 10,037, each prime 

 beine put into relation to at least three others. 

 By combination of these primes he tabulated the 

 logarithms to twenty-eight places of all integral 

 composite numbers from i to 20,000, a few gaps 

 due to uncalculated primes being left. From this 

 table he calculated by interpolation a great table 

 of logarithms to fifteen places of all integral 

 numbers from 100,000 to 370,000. Dr. Knott 

 considers that Dr. Sang was justified in assuming 

 the absolute accuracy of these tables to the four- 

 teenth place. 



This material, which may be regarded as a 

 fundamental basis for all future tabulations, has 

 never been published. All mathematicians would 

 agree that publication should take place, and Dr. 

 Knott discusses at length different methods of 

 procedure. As the manuscripts, are beautifully 

 written he inclines to the opinion that it would 

 be simple and a guarantee of accuracy to repro- 

 duce them as line engravings by photography. 

 He considers that a quarto volume of some 1200 

 pages would suffice for the fundamentally im- 

 portant parts of the manuscripts, and he estimates 

 that the cost of reproduction by photography 

 would be about one-third or one-fourth the cost of 

 setting them .up in type in the usual way. It 

 would, indeed, be a fitting outcome of the Xapier 

 tercentenary if this could be brought about, and 

 the writer is convinced that if Dr. Knott and his 

 colleagues in Scotland will persevere with the idea 

 they will be astonished at the support they will 

 receive even in these strenuous times. 



This reprint is perfectly and conveniently 

 printed with the usual description and examples of 

 computation. P. A. M. 



OUR BOOKSHELF. 



Mentally Deficient Children: Their Treatment and 

 Training. By Drs. G. E. Shuttleworth and 

 W. A. Potts. Pp. xix + 284. Fourth Edition. 

 (London: H. K. Lewis and Co., Ltd., 1916.) 

 Price 75. 6d. net. 

 We welcome very heartily the fourth edition of 

 Drs. Shuttleworth and Potts's excellent hand- 

 book on mentally deficient children. The book 

 has been very carefully revised, and a chapter 

 added concerning the mental troubles of youth. 

 The main new feature of the present volume is 

 an extremely interesting account of the Mental 

 Deficiency Acts of 191 4 — these being the ultimate 

 result of the Royal Commission of 1904. 



The Acts now enable the authorities to deal 

 with all mental defectives : (a) if under twenty- 

 one years, at the instance of parent or guardian ; 

 or (b) at any age if found neglected, abandoned, 

 destitute, or cruelly treated, criminal or inebriate, 

 or being the pauper mother of an illegitimate 

 child — and Dr. Shuttleworth states that "with 

 the judicious administration of the new Acts it 

 i is hoped that Great Britain will stand ahead of 



