Dec. 6, 1888] 



NATURE 



135 



■F(J>^+'«,'«+I,a') 



the investigations relating to the partial differential 

 juation of Hamilton and Jacobi, where the author de- 

 ices Lambert's important theorem concerning the rela- 

 )ns between the time of describing an arc of the orbit, 

 le chord of the arc, the bounding radii of the sector, and 

 major axis. This last-mentioned theorem for the 

 »cial case of the parabola was first discovered by Euler, 

 point on which the late Prof. Oppolzer used to insist ; 

 extension of the theorem for any value of the 

 centricity of the orbit being due to Lambert. A short 

 istorical sketch of the matter contained in this section, 

 ferring chiefly to the labours of Lagrange, Hamilton, 

 ' Jacobi, concludes this portion of the subject, and we 

 )me to the third section of the book. 

 This last section of the work treats of the theory of 

 Sneral perturbations. Here, of course, Lagrange's theory 

 'the variation of constants plays an important part, and 

 re have that part fully dwelt upon by the author. The 

 "jvelopment of the disturbing function is given, and here 

 ^nd there a simplification in the symbols might, we think, 

 with advantage be introduced. In the expansion of 



_s_ 



r,- - 2;-,r2 cos 6 -f r/)"^ we have given the simple ex- 

 ression for half the coefficient of cos mQ in terms of 

 I iauss's hypergeometric series, viz. — 



-^ j(.y+2)(j-t-4)---( -y+2?;? - 2) 



im . m\ V 2 2 



The secular and periodic changes in the elements of the 

 •orbit receive the usual treatment, the stability of the solar 

 system is discussed, and also the influence upon the 

 results of terms in the higher powers of the eccentricity 

 and inclination 



A few pages are also devoted to a point which 

 writers are accustomed to say never occurs in the solar 

 system— viz. commensurability of the mean motions of 

 two planets. The importance of the subject treated in 

 this section induces the author to extend the limits o'f the 

 historical sketch with which he has concluded the two 

 previous sections, and to give a little more fully the history 

 of the important theory of perturbations ; and he adds, 

 in conclusion, that the best proof of the truth of Newton's 

 law is in the discovery of the cause "of the observed 

 irregularities in the motion of Uranus," a cause sus- 

 pected by Bouvard and by Bessel, and a problem which 

 death prevented the latter from undertaking, but which 

 was " von zwei anderen Astronomen Leverrier und Adams 

 gelost." Speaking of the latter, the author remarks that 

 " er seine Resultate einige Monate friiher dem Astrono- 

 men Airy mittheilte " ; the want of a " Durchmusterung," 

 however, placed the optical discovery of Neptune in the 

 hands of Dr. Galle. 



At the end of the book are given a few small tables 

 chiefly Leverrier's elements of the orbits of the major 

 planets, except for Uranus and Neptune, Newcomb's 

 more correct values of these quantities being adopted. 



We note a few misprints.. On p. 5, at the bottom, re- 

 ferring to the rotation ofthe axes, "-f- ;ir nach + ^" should 

 ■obviously read "-f j/ nach -f z." On p. 11, for k^ read 

 k\ On p. 45, in differentiating V, a homogeneous func- 

 tion of degree - i, the factor z of is omitted. On 



az 

 p. 46 it might be mentioned that M = 2///. In the copy 

 before us, pp. 225 to 240 are omitted, and pp. 273 to 288 

 have been bound in their place. 



Regarding the whole book, we may say that there is 

 much that may be found in any ordinary text-book on 

 the subject. But the author has endeavoured to do more 

 than give a mere sketch, as writers of the present day 

 usually do, leaving the reader to search the pages of 

 Crelle's Journal, the Comptes rendus, or some similar 

 publication, for important papers connected with the sub- 

 ject. Where these have appeared useful, they have been 

 introduced in a modified form if necessary ; and where 



such papers are interesting, but beyond the scope of the 

 present work, full references are given— a practice much 

 to be commended. The author expresses a hope that he 

 will be able to deal later with the theory of the rotation 

 of bodies about their centres of gravity, the figure of the 

 earth, &c., and with the theory of the tides ; and we wish 

 him the success which the present work augurs. 



R. B. 



. NOTES. 

 Dr. Alfred R. Wallace has in the press a new work on 

 Darwinism, which aims at establishing the theory of natural 

 selection on a firmer basis, and also deals with the various sup- 

 plementary theories which have been put forth since the publica- 

 tion ofthe sixth edition ofthe "Origin of Species." The book 

 will be published early next year by Messrs. Macmillan and Co. 



Prof. Giard's first lecture at the Sorbonne is pubHshed in 

 the Revue Scientifique (December i). It was delivered before a 

 large audience, and many hundreds of persons had to be content 

 to stay at the door. The Thursday lectures of M. Giard are 

 devoted to an historical sketch of embryology in its relation to 

 the theory of evolution. The Saturday lectures are devoted to 

 embryological phenomena, considered generally. 



On the 19th inst. a monument of the astronomer Leverrier 

 is to be unveiled by the French Minister of Public Instruction, 

 in the Cour d'Honneur of the Paris Observatory, The likeness 

 of Leverrier is said to be very striking. The statue of Arago 

 is finished, and has been sent to the foundry. It will be 

 situated close to the Observatory Gardens, but is not to be put 

 in its place until after the Exhibition. 



The well-known botanist. Dr. C, J. de Maximowicz, 

 writing from St, Petersburg to Kew about Prjevalsky, whose 

 last book we review to-day, -says: — " Ves, poor Prjevalsky 

 is dead, and I mourn for him like a brother. He was a 

 splendid character and a highly gifted man. He died with 

 his Expedition fitted out and ready to start. Under these 

 circumstances, the Russian Geographical Society intends to 

 appoint, as head of the Expedition, Colonel Pentsow, a good 

 topographer, who has already twice been in Northern Mongolia. 

 Lieutenant Roborofski, Prjevalsky's associate, and a very capable 

 officer and good collector, who did the botanical work during 

 the two last journeys, is to go also. The plan is to remain the 

 same, perhaps with the exception of Lhassa and the investiga- 

 tion of Northern Tibet. But the Society will appDint this time 

 a geologist, which it is indeed high time to do." 



We learn that the Hon. John Collier has just completed a 

 portrait of Dr. A. W. Williamson, For. Sec. R,S. This portrait, 

 which is to commemorate the thirty-eight years of Dr. William- 

 son's professorial work at University College, will be presented to 

 the College by Sir Henry Roscoe, on behalf of the subscribers, 

 on Wednesday, December 12, at 4.30 p.m. The subscribers to 

 this portrait will give a dinner to Dr. Williamson on the same 

 evening at the Freemasons' Tavern, 



Last Saturday, a very large meeting, convened by the Council 

 of the Teachers' Guild of Great Britain and Ireland, was held 

 at the rooms of the Society of Arts, Adelphi, to consider a 

 subject which is likely soon to attract much serious attention — 

 the organization of secondary education. The Guild numbers 

 among its Presidents some of the most eminent authorities on 

 higher education, as Heads of Colleges, Professors of the English, 

 Scotch, and Irish Universities, the President of the Royal 

 Academy, Prof. Huxley, and Mr. Mundella, Sir Philip Magnus, 

 who presided, said that at present no public body was resix)ns- 

 ible for the secondary education of the country. There was no 



