What does an ice crystal look like? You would think t h a t we would know bynow. W e do indeed know quite a bit about ice crystals, yet there is oneintriguing variety t h a t has remained obscure until recently. On occasion crystalsof this sort occur in t h e atmosphere by t h e billions, so in one sense they are notat all uncommon or exotic. Moreover, they leave a characteristic signature in t h esky, and their existence had therefore been conjectured, even in t h e nineteenthcentury. Nevertheless, for a long time nobody knew for sure what t h e crystalslooked like. T h e crystals were seen for t h e first time only a few decades ago, andthey have been seen well only recently. T h e shape of these crystals is determinedby the so-called angle x. T h e search for angle x is t h e effort to discover w h a t t h ecrystals look like.These crystals would not be so intriguing were it not for their signature in t h esky. By signature we mean atmospheric halos, something akin to t h e familiarring around t h e moon. But t h e halos associated with these special crystals areeasily recognizable as being different—especially in size—from t h e ring aroundthe moon; they are "odd radius" halos. For a long time t h e existence and n a t u r eof odd radius halos was as murky as t h a t of t h e crystals t h a t make t h e m . W e nowthink t h a t we are beginning to u n d e r s t a n d them, but much remains to be done.Some of what remains to be done is just a fleshing out of t h e photographicrecord of these halos. Here anyone can make a contribution, anyone who hasmodest camera equipment and is alert for w h a t to watch for. W e have no doubtt h a t with increased awareness new halos will be seen and photographed, and wehope t h a t some of you will be t h e ones to do so.viiviii A T M O S P H E R I C H A L O ST h e ultimate goal of this book is to tell what is known about odd radius halos.B u t as you read on, you will see t h a t t h e odd radius halos are partly just anexcuse for us t o talk about halos in general. One can even argue t h a t it is theodd radius halos t h a t are t h e "halos in general," because it t u r n s out t h a t it is theodd radius halos t h a t are in a sense typical, and it is t h e more traditional andmore common halos t h a t are exceptional—exceptional in t h e sense t h a t they havespecial properties. T h e general context demanded by odd radius halos is the bestsetting for thinking about even t h e common halos.T h e study of odd radius halos is very much a work in progress. There are stillhalo displays t h a t we do not understand very well, and there are halo displays t h a twe do not u n d e r s t a n d at all. Only recently have we begun to make the accuratemeasurements of halo radii t h a t are necessary for testing t h e theory. And onlyrecently have we begun t o get electron microscope photographs of the ice crystalst h a t m a y hold some of t h e secrets of odd radius halos.In writing this book, we have tried to present things in such a way t h a t you,t h e reader, can come to u n d e r s t a n d how we know what we know. T h e theory ofhalos is simple enough so t h a t this can be done, at least to a large extent. So youshould not have to take a lot on faith; we have tried to present enough of thereasoning so t h a t you can largely judge t h e logic of t h e theory for yourself, and wehave presented enough of t h e d a t a — m a i n l y halo and ice crystal photographs—sot h a t you can test t h e predictions of t h e theory yourself. W e have omitted sometopics t h a t we t h o u g h t were speculative or whose conclusions were hard to justifyin a short space.T h e level of difficulty of t h e book is uneven, we admit. Most of t h e book canbe followed by attentive readers with no special background, b u t p a r t s of it, suchas t h e t r e a t m e n t of crystallography, require some college level m a t h e m a t i c s .Obviously you do not need our permission to pick and choose what to read.A word about t h e halo photographs: Most of t h e m are scans of traditional35mm slides. Nearly all have been enhanced to some degree using digital unsharpmasking. W i t h a few exceptions, t h e resulting images still show less t h a n wasvisible in t h e halo displays themselves. T h e main exceptions are t h e lunar halodisplays, where, due to t h e long time exposures required, a slide will sometimesreveal more t h a n was seen at t h e time of t h e display. B u t never have we addedanything artificially to t h e halo photographs.T h e degree of enhancement varies from one photo to another throughout thebook, but on a given photo t h e enhancement has been applied uniformly over t h eentire image, rather t h a n to selected portions, and you will be able to estimatet h e degree of enhancement by looking for vignetting at w h a t would normally bewell-defined edges. In Figure 18.5, for example, t h e prominent white vignettingof t h e sun-blocking stick is a sign of strong enhancement.P R E F A C E ixWell developed halos—and not just t h e odd radius halos—are beautiful, and soare the atmospheric ice crystals t h a t cause t h e halos. W e think t h a t t h e sciencet h a t links t h e crystals with t h e halos is beautiful in its own right. W e hope youwill agree