October i6, 1890] 



NATURE 



;87 



wheel and wheeled carriage, and of the ballistic pendulum. 

 Prof. Price calls the inventor Captain Robins ; but, 

 according to the preface of his " Mathematical Tracts," 

 Robins was of Quaker extraction (like so many other 

 students and inventors of warlike instruments), and his 

 only military employment was as chief engineer of the 

 East India Company, in planning and carrying out their 

 fortifications. 



In chapter vi. the rotation of a rigid body about a 

 fixed point is discussed, with applications to the three im- 

 portant problems of motion under no forces with Poinsot's 

 geometrical representation, the motion of the top or 

 gyrostat, and the precession and nutation of the earth's 

 axis. These problems illustrate very strikingly the great 

 increase in complication when we go from plane motion 

 to motion in space. The figure of the herpolhode, on 

 p. 251, shows points of inflexion ; but, as the author men- 

 tions in § 295, these points of inflexion cannot exist in 

 Poinsot's herpolhode. An elegant geometrical demonstra- 

 tion is given on p. 379 of Sylvester's extension of Poinsot's 

 representation, where confocals to the momental ellipsoid 

 are made to roll upon parallel planes ; and now it is 

 possible in certain corresponding herpolhodes for points 

 of inflexion to make their appearance ; the analytical and 

 geometrical discussion of this problem has engaged the 

 attention of de Sparre and Hess. 



We mentioned at the outset that the author did not 

 permit himself the use of elliptic functions ; but appa- 

 rently he could not resist the temptation of introducing 

 them in the complete solution of Poinsot's motion, the 

 simplicity and elegance of the representation being so 

 great. In the separating case, when the modulus of the 

 elliptic functions becomes unity, the introduction of the 

 corresponding hyperbolic functions would have exhibited 

 an analogous symmetry. 



By considering the elliptic functions as defined by plane 

 pendulum motion, some of the results in the motion of 

 the top or gyrostat could have been exhibited by com- 

 parison with a plane pendulum ; but it must be confessed 

 that the simplicity is not maintained when we investigate 

 the projection of the motion on a horizontal plane, with- 

 out we introduce functions invented by Hermite, of a 

 higher degree of complication. 



In the discussion of precession and nutation, a simpli- 

 fication can be introduced by making use of the observed 

 fact in determining the latitude, that the deviation of the 

 axis of rotation from the axis of figure, although certainly 

 existing, is quite inappreciable in the case of the earth ; 

 so that the axes of figure, of rotation, and of angular 

 momentum may be taken as coincident. With this ap- 

 proximation the pole of the earth follows a point 90° in longi- 

 tude behind the sun or moon with a certain velocity ; and 

 now the rest of the calculation of precession and nutation 

 becomes a kinematical problem. 



Chapter vii. discusses interesting and important prob- 

 lems of small oscillations and of bodies rolling on each 

 other, e.g. of a billiard ball on the table ; and chap- 

 ter viii., on relative motion, is important as showing how 

 far we are justified in applying our dynamical equations 

 to the problems going on around us, considering that 

 they take place on the surface of the earth, which is 

 moving in a complicated manner in space. The corre- 

 sponding elementary discussion in Maxwell's " Matter and 

 NO 1094, VOL. 42] 



Motion," on the ideas of relative motion, and the modifica- 

 tion of the principles of dynamics to make them rigorous, 

 is well worth attention at this point. 



The deviation from the vertical of a body let fall down a 

 deep mine, of a projectile from the vertical plane of fire, 

 and the rotation of the plane of oscillation of Foucault's 

 pendulum, are discussed as illustrations of the influence of 

 the earth's rotation in modifying a dynamical question ; 

 but considering how slight a disturbing cause, such as 

 a current of air, would be sufficient to mask the eff"ect, 

 we believe that these effects have not yet really been 

 observed. 



In Foucault's pendulum a very slight jockeying can 

 make the thing go as we wish ; while with artillery fire at 

 long ranges the disturbing cause of deviation or drift 

 quite overpowers any deviation due to the rotation of the 

 earth. Theoretically, Foucault's pendulum, if set swinging 

 in a plane- through the rising moon, should continue to 

 follow the moon ; and roughly speaking, a shot fired at 

 the rising moon should keep moving in the moving 

 vertical plane through the moon, and would thus fall to 

 one side of its original vertical plane of fire ; in a range 

 of twelve miles, and a time of flight of one minute, this 

 deflection would, in the latitude of Shoeburyness, amount 

 to about 71 yards, out of about 1000 yards observed 

 average lateral deviation. 



A few simple problems on the vibration of elastic 

 threads and plates are given in chapter ix. ; and 

 chapter x., as already mentioned, is occupied by Prof. 

 Donkin's contribution on Theoretical Dynamics. 



Throughout the work good collections of illustrative 

 examples are introduced, to test the student in his grasp 

 of the principles given immediately before. If we might 

 make a slight criticism, we should suggest the introduction 

 of some arithmetical exercises on these problems, taken 

 from examples in real life ; for, as Sir William Thomson 

 insists, it is from arithmetical applications that the student 

 obtains a real grasp of dynamics ; the examples given 

 here only testing his algebraical and geometrical power. 



In conclusion, we congratulate the student of mathe- 

 matics at Oxford on the possession of such an admirable 

 text-book, fully brought up to date in the latest 

 developments. A. G. Greenhill. 



ANNALS OF THE ROYAL BOTANIC GARDEN, 

 CALCUTTA. 



Amtals of the Royal Botanic Garden, Calcutta. Vol. I. 

 Appendix— (i) "Some New Species of Ficusfrom New 

 Guinea," by George King, F.R.S., &c.. Superintend mt 

 of the Royal Botanic Garden, Calcutta. (2) " On the 

 Phenomena of Fertilization in Ficus Roxburghii, Wall," 

 by D. D. Cunningham, F.L.S., &c., Surgeon-Major, 

 Bengal Army. (Bengal Secretariat Press, 1889.) 



ABOUT a dozen new species of Ficus are added here 

 to Dr. King's valuable monograph of the figs of 

 the " Indo-Malayan and Chinese countries," which occu- 

 pies the whole of the first volume of the " Annals." It 

 may be remembered that Dr. King proposed a modified 

 classification of the species of Ficus, based upon 

 characters indicating, in his view, the direction of 

 evolution in the genus, beginning with a small group 

 having pseudo-hermaphrodite flowers {Pahcomorphe), 



