November 22,' 1917] 



NATURE 



223 



The outstanding- features of the lectures may 

 be summarised as follows : — Barrow regards a 

 curve as the locus of a movingf point, and makes 

 its velocity at any moment the resultant of two 

 velocities parallel lo two fixed axes ; one of these 

 \elocities is taken to be constant, and then the 

 nature of the curve determines the other com- 

 ponent velocity for any position of the moving- 

 point. Barrow does not, like Newton, consider 

 the calculation of the variable velocity (y) ; he 

 constructs an infinitesimal triangle, and from 

 this determines, generally by a sort of method 

 of "exhaustion," the value of the subtangent, or 

 ^ome such finite segment, from which the posi- 

 tion of the tangent can be inferred. Barrow's 

 rule for differentiating a product accordingly 

 appears in a form equivalent to 



d(uv)fuvdx = du/udx + dv/vdx, 

 ap.d similarly for a quotient. It may be added 

 tliat Barrow gives (Lect. x., ex. 5) an analytical 

 proof of a proposition equivalent to 



d tan x/dx = sec^ x, 

 and in this he neglects small quantities of higher 

 order than the first. It is, therefore, practically 

 certain that, if he had chosen to do so, Barrow 

 could have written an algebraic treatise on the 

 differential calculus ; and to this extent Mr. 

 Child's contention seems to us to be fully justi- 

 lied. Barrow was probably too enamoured of 

 the old geometry to wish to do anything of the 

 kind; and we may venture to think that he had 

 no conception of the immense importance of^ an 

 abstract, arithmetical calculus for mathematics in 

 general. It is here that the value of Leibniz's 

 -contributions becomes so manifest, and it 

 matters little how far he was really indebted to 

 Barrow^ 's lectures, of which he was known to 

 have had a copy. 



Mr. Child gives paraphrases (in modern nota- 

 tion) of the most important parts of the lectures, 

 with notes of his own in different type. At the 

 end we have a reduced facsimile of two pages 

 of the original, and of a sheet of the original 

 diagrams. So far as we have tested it, the 

 paraphrase is satisfactory; p. 57, 11. 14, 16, 

 "decreasing " and " decrease " should be " in- 

 creasing " and "increase," and p. 66, last line, 

 " that I know " should be "so far as I know," 

 and there may be other similar slips. Altogether, 

 Mr. Child may be heartily congratulated on the 

 result of his six months' research. G. B. M. 



OUR BOOKSHELF. 



The Distavces, Absolute Magnitudes^ and Spectra 

 of 734 Stars. Arranged for Use with Ordinary 

 Star Maps by T. E. Heath. Pp. iv + 52. 

 (Tenby: Sold by Miss Crealock, South Cliff 

 Street, Tenby, n.d.) Price 2s. 6d. net. 



The determination of the distance of a star, by 

 measuring its minute change of position when 

 seen from opposite points of the earth's orbit, is 

 :in extremely laborious work. According to Mr. 

 NO. 2508, VOL. 100] 



Heath's pamphlet, the parallaxes of about 700 

 stars constitute the total output up to now from 

 the various observatories of the world ; and for 

 many of these the only information obtained is 

 that the star is at a great but unknown distance 

 beyond the reach of the method. The general 

 fate of these data is to fall into the hands of some 

 mathematical astronomer, apparently actuated by 

 an irresistible impulse to add things up and take 

 the mean ; then comes a sudden jump to mathe- 

 matical formulae ; integrals gather in formidable 

 array, and the error-function makes its inevitable 

 appearance ; and so the riddle of the universe is 

 slowly disentangled^ — or knots itself tighter — to 

 the great satisfaction of those who have any 

 notion what it is all about. 



Mr. Heath is one of those who would rescue 

 the precious knowledge from this socialistic use. 

 For him the stars each have their individuality ; 

 they are personal acquaintances, not mere items 

 on a census-form. When he looks at the Great 

 Dog, in his mind's eye he sees Sirius a modest 

 star of 30 sun-power eight miles away (to use 

 his "Road-Book " scale), and its less conspicuous 

 neighbour Beta, a brilliant globe of 750 sun-power 

 223 miles distant. Then turning to the gleaming 

 belt of the Milky Way, on the same scale, " if we 

 took ship to America we might probably come to 

 the beginning of the Milky Way before we arrived, 

 and get through it before we came to the Pacific." 

 And so he places out the stars at their different 

 distances and gives the true measure of their 

 brightness. 



There must be many watchers of the skies to 

 whom the stars will acquire a new interest from 

 the information here set out. It has hitherto been 

 practically inaccessible except to specialists. Mr. 

 Heath does not conceal the fact that the individual 

 results are often very uncertain ; they are taken 

 from the best authorities, but it is only for excep- 

 tionally near stars that the distances are known at 

 all closely. But we can agree with him that on 

 the whole a true general view is conveyed. AVe 

 are glad to learn that the author has presented a 

 large number of copies to the Admiralty for dis- 

 tribution among the Fleet. A. S. E. 



The Road and the Inn. By James John Hissey. 



Pp. xviii + 435. (London: Macmillan and Co., 



Ltd., 1917.) Price los. net. 

 The latest addition to Mr. Hissey 's already long 

 list of travel books will delight every lover of 

 English byways. In a small motor-car, provided 

 with camera and brush, Mr. Hissev went from lane 

 to lane from Eastbourne to the Dukeries, Rugby 

 being his most westerly, and Dunwich his most 

 easterly, visit. There was no hurry and no bustle ; 

 and he preferred the country inn to the town hotel, 

 for his " aim was to get into the heart of the real 

 country." The serenity and charm of his gossipy 

 narrative show how well he succeeded in securing 

 the quiet holiday he desired ; and the beauty of 

 his pihotographs and drawings indicates his 

 re-discovery of some of the hidden glories of the 

 English countryside. 



