I2i 



NATURE 



[April 17, 19 19 



the screws of the Maxwell top, the analytical com- 

 plexity in chap. xvii. defied a Weierstrass, who 

 handed his difficulties over to the young" Kowa- 

 levski, to break her teeth over the problem. 



The ardent spirit is not deterred, but, on the 

 contrary, rather stimulated, to tackle a question 

 declared intractable ; so Prof. Gray gives a resume 

 in chap. xvii. of the progress made so^ far by other 

 daring mathematicians — Russians for the most 

 part — although we miss a figure and descrip- 

 tion of the Maxwell top, to be placed on the table 

 in front and twirled by a finger and thumb. 



The spherical pendulum of chap. xv. was 

 early to receive attention as a problem in 

 mere particle dynamics, realised in swinging 

 a plummet about at the end of a thread. 

 This is a case of gyroscopic-top motion where 

 the component ang-ular momentum (A.M.) about 

 the axle is zero, and is realised in the 

 apparatus of Fig. 3o(&) by projecting the wheel 

 without rotation. But this limitation makes the 

 motion very uninteresting analytically, except as 

 illustrating a solution of a Lame equation of the 

 second order. The simple case of holding out the 

 axle horizontal, and projecting it horizontally with- 

 out any rotation of the wheel, is of interest as 

 giving a state of motion that has a simple ana- 

 lytical solution, which may be written down here : 



sin ecos (;^-/z/) = -v/(sece3-cosftj)v'(cos0), 

 sin Q sin (i^ - ht) = \/{co% % - cos e.cos 6 + sec a,), 



where 2}i denotes the precession when the axle is 

 horizontal, and ^3 is the extreme angle of the axle 

 tvith the downward vertical, to which the axle 

 sinks and then rises up again to the horizontal. 



This can serve as a penultimate case where the 

 spherical pendulum is whirled round swiftly, 

 apparently in a horizontal circle, as with the 

 lariat or Sola, as on p. 302, contrasted with swift 

 whirling in a vertical circle, penultimate case of 

 pendulum motion, and an extreme contrast to 

 small plane oscillation near the vertical. 



Lagrange came to grief over the small 

 conical oscillations of the spherical pendulum (c/. 

 § 5) P- 302), yet he could have saved himself and 

 detected his error but for the self-imposed restraint 

 of excluding the diagram from his " M6canique 

 analytique. " So it is curious to find the same 

 fashion coming again in the modern school of pure 

 analytical treatment, of doing away with an appeal 

 to the visual sense of a geometrical figure. 



In swift rotation about an axis in the neighbour- 

 hood of a principal axis, as the axis of figure of a 

 symmetrical top, the instantaneous axis does not 

 wander far from the principal axis, and the axis of 

 A.M. keeps close by also, even when the body, like 

 the top, is acted on continuously by a force or 

 couple which causes the A.M. vector to move. 



The kindergarten explanation of top motion, in 

 considering only the rotation about the axis, can 

 then be made more exact, when it is assumed that 

 the divergence of the axis of A.M. and angular 

 velocity from the axis of figure is always small, so 

 that one may be used indiscriminately for the other. 



In this way, by calling CR the A.M. above the 

 NO. 2581, VOL. 103] 



axis of figure, and gM.h sin Q the couple of gravity 

 on the top when the axis points up at an angle d 

 with the upward vertical, the simple formula is 

 obtained for ^, the precession : 



mCR sin e=^o-M/5 sine, m=^', 

 CR 



provided Q is not too small. 



Poinsot applied the same principle in his treat- 

 ment of precession and nutation (" Connaissance 

 des temps," 1858), assuming the divergence of 

 the axis of rotation and of A.M. from the axis of 

 figure of the earth as insensible ; otherwise we 

 should see the stars dancing about. The treat- 

 ment here in chap. x. could be simplified in. 

 Poinsot 's method. The Glasgow problem on p. 13 

 of the calculation of the diameter of the earth's 

 axis at the pole may be cited as a justification of 

 Poinsot's assumption. 



It was a mathematical genius who changed in 



A C 



precession to the reckoning in w'-i =304, 305, or 



some say 305, 306, instead of the usual reciprocals 

 in small decimals, indistinguishable numerically. 

 And we venture to put in a plea for the sidereal 

 day as the unit of time in these measurements^ 

 and not the solar year, thus making R = 27r for 

 the earth. 



The effect of precession is to shorten the year 

 about twenty minutes, and thus the period is 

 26,000 years of a complete revolution of the equi- 

 nox through the stars. The classical scholar may 

 be encouraged to take up the study of Astronomy 

 when he hears that stray references tO' the stars 

 by Homer are a guide to us in assigning limits 

 to the age in which he lived and wrote. Astro- 

 nomy was a much more living, actual interest in 

 the days before clock and watch was so plentiful. 



G. Greenhill. 



A PHYSIOLOGIST'S CONTRIBUTION TO 

 WAR SURGERY. 



Intravenous Injection in Wound Shock. Being 

 the Oliver-Sharpey Lectures delivered before 

 the Royal College of Physicians of London in 

 May, 1918. By Prof. W. M. BayHss. Pp. xi-+- 

 172. (London : Longmans, Green, and Co.,, 

 1918.) Price 95. net. 

 'T^HE war has brought into touch with directly 

 ■'- practical problems many whose interests, 

 before its outbreak, lay in fields of investigation 

 which were pKjpularly regarded as purely aca- 

 demic and remote from contact with everyday 

 needs. In no department of research has the 

 value of "pure" science been more finely vindi- 

 cated than in that of physiology ; and the gain 

 to both physiology and practical medicine from 

 this closer alliance of theory and application has 

 been the subject of general remark. There could 

 scarcely be a better example of this recent tendency 

 than Prof. Bayliss's book on the treatment of 

 "wound shock," which embodies, with much 

 added detail and illustration, the substance of his 



