42 



NATURE 



[September ii, igig 



ings exceeded 80° over the whole of England. The 

 total rainfall for the three summer months at Green- 

 wich was 603 in., which is 06 in. less than the normal 

 for sixty years. The wettest month was July with 

 226 in., and in August the fall was 220 in.' The 

 summer rainfall was 3 in. less than in 1918, and 

 47 in. less than in 1917; it was more than in 1911, 

 1913, and 1914. In 1903 the summer rainfall amounted 

 to 16-17 in- Rain fell in all on thirty-four days, and 

 of these July had fifteen wet days. The dura'tion of 

 bright sunshine at Greenwich for the three months 

 was 591 hours. July was the least sunnv with 

 119 hours, which is less than one-half of the sun- 

 shine in June and very little more than one-half of 

 that in August. 



"Newton's Interpolation Formulas," by Mr. 

 Duncan C. Eraser, originally published in the Journal 

 of the Institute of Actuaries, has been issued as a 

 separate pamphlet. It brings together the whole of 

 Newton's work on interpolation by means of formula; 

 of finite differences. The throe main sources are 

 Newton's short treatise, " Methodus Differentialis," 

 a letter written in 1875 to J. Smith, and Lemma 

 No. 5 in Book iii. of the "Principia." These are 

 supplemented by a letter from Leibnitz to Oldenburg 

 (1672-3) and two letters from Newton to Oldenburg 

 to be communicated to Leibnitz (1676). These letters 

 show that Newton was in possession of the methods 

 of calculation manv vears before 17 1.1, when the 

 "Methodus Differentialis" was first published. Mr. 

 Fraser_ gives an English translation of the treatise, 

 correcting some errors and adding useful comments. 

 The pamphlet should be in the hands of all interested 

 in the theory of series and in their use for calculation. 

 It demonstrates that Newton at the age of twenty- 

 three had worked out for himself all the methods of 

 computation now in use, with the exception of cal- 

 culating machines; and the idea of these, we are 

 reminded, originated with Newton's contemporary, 

 Pascal. 



Prof. D. E. Smith has successfully "filled a gap " 

 by writing a booklet on the early history of numbers 

 that will be the delight of the young, and will prove 

 a "mine of interesting information " to many of their 

 elders. Even as a mere "reader" his charmingly 

 written and beautifully illustrated " Number Stories of 

 Long Ago" (Messrs. Ginn and Co., 48 cents) is well 

 calculated to sow the good seed. Where it falls on 

 fruitful soil the results may not indeed be immediately 

 manifest, but may ultimately astonish that large sec- 

 tion of the comnriunity who hold that all that deals 

 with number is inherently unattractive, or even repul- 

 sive, to mortals. The text also contains problems and 

 tricks designed to amuse and instruct. To these a 

 key, "Number Puzzles before the Log Fire," has been 

 issued by the publishers, price di. Here we find in 

 disguise many friends, both old and new— echoes from 

 Diophantus, Achilles, and the "turtle," down to pro- 

 ducts of our modern civilisation, such as: — "A man 

 with $1 wanted $1.25. He pawned the $1 for 

 7"; cents, and then sold the pawnticket for i;o cents. 

 Who lost?" Or again: — "In a certain town 3 per 

 cent, of the inhabitants are one-legged, and half of the 

 others go barefoot. How manv shoes are necessary?" 

 It is no doubt well for the civilisation of the future 

 that the answer is " As many shoes as there are 

 people in the town." 



In the Journal of the Franklin Institute for July 

 Prof. \. E. Kennelly and Mr. E. Vclander describe 

 a new form of rectangular component alternating- 

 current rotentiometer which consumes little power 

 and avoids the use of electromagnetic phase-shifting 

 devices. It is constructed on the principle Introduced 



NO. 2602, VOL. 104] 



by Larsen in 19 10 — that is, it measures the alternating 

 potential required by balancing it against the fall of 

 potential down a non-inductive resistance through 

 which an auxiliary alternating current is passing, and 

 a mutual inductance the primary of which is in series 

 with the resistance. The balance is obtained by means 

 of a vibration galvanometer. The mutual inductance 

 consists pf forty-one double coils arranged to form a 

 toroid with a wooden core. The resistance Is wound 

 so as to be free from inductance and capacitance. The 

 instrument may be used up to a frequency of 2000. 

 During its use by the inventors the importance of 

 reducing the mutual capacitance between the two 

 windings of the Inductance coil has been emphasised. 



Although the greatest care is used in the selection 

 of wood for the spars of aeroplane wings, it is not 

 always possible to detect the presence of a "pocket" 

 of resin in the place of sound wood-fibre in some 

 important pgrt of a spar. On this account the United 

 States Forest Service has instituted at its laboratory 

 at Madison a series of tests of the effects of such 

 "pockets, on the strength of spars, and the results 

 of the work already done are summarised in an article 

 by Mr. J. R. Watkins in the .'\ugust issue of the 

 Journal of the Franklin Institute. Spars 6 ft. long 

 of spruce and Douglas fir of I section, with 

 "pockets" of known size in flanges or web, were 

 tested under load against sound spars. A " pocket " 

 5-6 in. long, J In. wide, and i in. deep in the com. 

 pression flange diminishes the strength considerably. 

 " Pockets " up to 4 in. long in the tension flange have 

 little effect on the strength, but in the web produce 

 a serious decrease of the strength of the spar in 

 horizontal shear. On the whole, the author con- 

 cludes that small "pockets" produce effects less than 

 has been supposed. 



.■^MONG the forthcoming science books in the new 

 announcement list of Messrs. Longmans and Co. 

 are: — "The Feeding of Nations: A Study in .Applied 

 Physiology," Prof. E. H. Starling; " Modern Science 

 and Materialism," H. Elliot; "The Elements of 

 Physics," R. A. Houstoun ; "Life in Earlv Britain: 

 A Survey of the Social and Economic Development of 

 the People of England from Earliest Times to the 

 Norman Conquest," N. Ault, and a new impression of 

 "The Profitable Culture of Vegetables, for Market 

 Gardeners, Small Holders, and Others," T. Smith. 



Messrs. Macmillan and Co.'s autumn list of an- 

 nouncements which has just been issued contains many 

 books of scientific interest, e.g. "Catalysis in Theory 

 and Practice," E. K. RIdeal and Dr. H. S. Taylor; 

 ".Alcohol: Its Production, Properties, Chemistr\, and 

 Industrial Applications; with chapters on Methyl 

 Alcohol, Fusel Oil, and Spiritous Beverages," C. Sim- 

 monds ; "Science and Fruit Growing. Being an ac- 

 count of the results obtained at the Woburn Experi- 

 mental Fruit Farm since its foundation in 1894," the 

 Duke of Bedford and S. Pickering; a new edition — 

 the fourth— of "Mendelism," Prof. R. C. Punnett; 

 "Essays on the Surgery of the Temporal Bone," Sir 

 Charles .A. Ballance, with the assistance of Dr. C. D. 

 Green, 2 vols.; ".An Introduction to .Anthropology: A 

 General Survey bf the Early History of the Human 

 Race," Rev. E. O. James; "The Ila-speaking Peoples 

 of Northern Rhodesia," Rev. E. W. Smith; ".Among 

 the Natives of the Loyalty Group," Mrs. E. Hadfield; 

 "Through Deserts and Oases of Central Asia," Miss 

 E. Sykos and Sir Percy S>kes; "Implication and 

 Linear Inference," Dr. B. Bosanquet; "The Idea of 

 Progress: .An Inquiry into its Origin and Growth," 

 Prof. J. B. Bury; "Mind Energy," Prof. H. Berg- 

 son, translated, in collaboration with the author, hv 

 Prof. H. Wildon Carr; "Geolog\ of India for Stu'- 



