BOOK REVIEWS proceedings v o l u m e s are a v o i d e d here, I still do n o t agree w i t h t h e publication of s y m p o s i u m proceedings as a book. T h e m a i n failure of proceedings books is t h a t the research t h e y contain tends to get lost in libraries; generally, w h e n looking for published results in a particular research area, one goes to t h e discipline's scientific journal and does n o t search for cont e m p o r a r y research in book form. I n this way, proceedings results are often ignored b y people from outside t h e field unless published or discussed in an appropriate journal. [This was done, for instance, w i t h t h e Oberwolfach Conference on Celestial Mechanics which t o o k place only two weeks before this s y m p o s i u m ; its proceedings appeared as an issue of The Journal of Celestial Mechanics (2, 1970, 271-447) m o n t h s before this book was published.] Besides this weakness, proceedings as books fail on m a n y o t h e r counts: (i) t h e proceedings in book form are v e r y expensive ; (ii) often there is duplication between papers w i t h i n a conference; (iii) inferior papers are f r e q u e n t l y published since little refereeing is done; (iv) usually there is a long delay before publication; and, lastly, (v) t y p o g r a p h i c a l errors are c o m m o n in the n o r m a l proceedings volume. I n conclusion, Periodic Orbits, Stability and Resonances is excellent for a proceedings volu m e ; it well summarizes where an e x p a n d i n g area of celestial mechanics stood two years ago. JOSEPH A. BURI~S
Department of Mechanics and Centsr for Radiophysics and Space Research CorneU University Ithaca, New York 14850 Introduction to Meteorological Optics. R. A. R. TRICKER. A m e r i c a n Elsevier, N e w York, 1970. 285 pp. Price $11.50.
Introduction to Meteorological Optic~ is an excellent introduction to a r e j u v e n a t e d field of physics. Much of t h e w o r k in t h e field occurred before t h e beginning of t h e 2Oth c e n t u r y and m a n y mistakes r e m a i n in m o r e recent work. The objective of this b o o k is to provide th~ basic concepts necessary for f u r t h e r s t u d y in t h e area while also presenting an e l e m e n t a r y s u r v e y of t h e present s t a t e of the art. The t r e a t m e n t is designed w i t h physical insights as t h e m a i n objective, t h e m a t h e m a t i c s being used m o r e as a descriptive tool t h a n as an analytical one so t h a t the physics is n o t clouded w i t h unnecessary m a t h e m a t i c a l rigor. T h e discussions often follow t h e logical
t h r e a d of historical i n t e r p r e t a t i o n s to build to present d a y viewpoints, t h e a u t h o r often choosing to introduce atmospheric p h e n o m e n a in t h e words of those who first recorded t h e observations. The book has been arranged so t h a t t h e physics and m a t h e m a t i c s necessary in later chapters is d e r i v e d in t h e c o n t e x t of t h e simpler p h e n o m e n a discussed in earlier chapters. M a t h e m a t i c a l results n o t derived in t h e t e x t are reserved for t h e six appendices. The first c h a p t e r on refraction in t h e a t m o s p h e r e introduces t h e application of Snell's law to mirages, t h e setting Sun, and l u n a r eclipses. The second c h a p t e r differs f r o m the subject m a t t e r of t h e r e m a i n d e r of t h e b o o k in t h a t it deals w i t h a g r o u n d p h e n o m e n o n - - t h e heiligenschein. The heiligenschein is t h e area of anomalous brightening surrounding the shadow of the h e a d of the observer on d e w y ground. This e v e r y d a y p h e n o m e n o n is explained r a t h e r simply as the result of w a t e r drops acting b o t h as lenses to focus t h e light on the surface and as m a g n i f y i n g glasses t h r o u g h which t h e image m a y be seen. Of interest is a photographic d e m o n s t r a t i o n of the increase in brightness of a water-filled flask as a b a c k g r o u n d surface is b r o u g h t near. Here, as elsewhere in t h e book, an effect is shown to be i m p o r t a n t in n o n m e t e o r o logical terms, as in the application of the heiligenschein to the cat's eye m a r k e r for traffic lanes. The n e x t five chapters cover the more c o m m o n p h e n o m e n a resulting f r o m single scattering f r o m ice and w a t e r particles in the a t m o s p h e r e - - t h e rainbow, ice particle halos, t h e corona, supern u m e r a r y rainbows, and t h e glory. The r a i n b o w is discussed first f r o m an historical perspective a n d f r o m the geometrical optics a p p r o x i m a t i o n . Secondary and higher order rainbows are discussed as well as the polarization of the p r i m a r y a n d secondary rainbows. Following this c h a p t e r the a u t h o r leaves t h e optics of t h e raindrop for a v e r y long c h a p t e r d e v o t e d to a careful description and e x p l a n a t i o n of the large v a r i e t y of ice particle halos observed in nature. The g e o m e t r y is formidable b u t so is the task, including as it does n o t only t h e 22 ° and 46 ° halos c o m m o n l y observed, b u t t h e m o c k sun, Lowitz arcs, sun pillars and m a n y o t h e r effects. T h e description of t h e corona introduces t h e concept of w a v e optics and diffraction used in the following chapters. The corona is t h e sometimes diffuse, sometimes m u l t i p l e ringed halo seen around t h e Sun and Moon w h e n the Sun or t h e Moon is seen behind a t h i n cloud. The discussion of supern u m e r a r y rainbows dispenses w i t h m u c h of the m a t h e m a t i c s usually found elsewhere a n d perm i t s writing d o w n A i r y ' s well-known " r a i n b o w i n t e g r a l " almost b y inspection. T h e d e v e l o p m e n t
BOOK R E V I E W S
is by concepts, not equations, although equations do play a major role. The bows are caused by diffraction effects arising from the nonspherical nature of the scattered wavefront. The derivation of the rainbow integral follows from the description of diffraction from a straight edge by showing t h a t both phenomena result from a nonspherical wavefront. The shape of the wavefront scattered from a raindrop is derived intuitively and the calculation of the Airy integral easily follows. The author refers to a method of measuring drop sizes in clouds by using the intensity distribution in the supernumerary bows. The glory, similar in appearance to the heiligenschcin, is the bright outline around the shadow of the observer projected on a cloud, often seen by the casual observer in an airplane. The book concludes with an introduction to the mathematical theory of waves and the Mie theory, a chapter on Rayleigh scattering, and one on visibility t h a t is particularly interesting to pollution ridden city dwellers. The discussion of the Mie theory is well arranged. The concepts of the wave theory are developed from an oscillating string through scattering of electromagnetic waves by a sphere. Vector calculus is not required. I t is unfortunate t h a t the discussion stops just short of presenting any Mie theory
results since such a large body of theory exists in this area. The major shortcoming of the book is its failure to relate the various scattering phenomena to the phase functions derivable exactly in the Mie theory. As the book is organized it is not clear t h a t rainbows, the corona, and glory are prominent features in the scattering diagram of water drops and t h a t all the various features can be related to a single theory. There is little discussion of the geometrical optics approximation and the effect produced by particles which are not very large compared with the wavelength. Although the avoidance of this complication is in line with the author's stated objective, the book would be far more complete if more references were made to the range of validity of the approximation and the effect of smaller particles on the scattering phase function. The book also suffers from a lack of a larger bibliography on the recent extensive literature on scattering by spherical particles, the author preferring to cite more classical references. LAIRD WHITEHILL
Laboratory for Planetary Studies CorneU University lthaca, New York 14850