322 PETER GUTHRIE TAIT 



space close to a red-hot bar of metal, could be produced by natural rates of change 

 in some ten or twenty miles of the atmosphere: and he would have deserved the 

 credit of having completely solved the problem. 



Six months after my paper was read, another happy chance led me to seek for 

 a voluminous paper by Biot, of which I had seen no mention whatever in any of 

 the books I had previously consulted. The probable reason for the oblivion into 

 which this treatise seems to have fallen is a curious one. It forms a considerable 

 part of the volume for 1809 of the Mm. de I'Institut. But in the three first great 

 libraries which I consulted, I found this volume to be devoid of plates. In all 

 respects but this, each of the sets of this valuable series appeared to be complete. 

 Without the figures, which amount to no less than sixty-three, it is practically 

 impossible to understand the details of Biot's paper. The paper was, however, 

 issued as a separate volume, Recherclies sur les Refractions extraordinaires qui 

 ont lieu fres de Vhorizon (Paris, 1810), which contains the plates, and which I 

 obtained at last from the Cambridge University Library. I have since been able 

 to procure a copy for the Edinburgh University Library. Biot's work is an almost 

 exhaustive one, and I found in it a great number of the results which follow almost 

 intuitively from my methods : such as the possible occurrence of four images, under 

 the conditions usually assumed for the explanation of the ordinary mirage; the 

 effects of (unusual) refraction on the apparent form of the setting sun, etc. But it 

 seems to me that Biot's long-continued observations of the phenomena as produced 

 over extensive surfaces of level sand at Dunkirk have led him to take a somewhat 

 one-sided view of the general question. And, in particular, I think that his attempted 

 explanation of Vince's observations (so far as I am able to understand it; for it 

 is very long, and in parts extremely obscure and difficult, besides containing some 

 singular physical errors) is not satisfactory. His general treatment of the whole 

 question is based to a great extent upon the properties of caustics, though he 

 mentions (as the courbe des minima) the "locus of vertices" which I had employed 

 in my investigations, and which I think greatly preferable. There can be no doubt, 

 however, that Biot's paper comes at least next in importance to that of Wollaston : 

 though in his opinion Wollaston's work was complete only on the physical side of 

 the problem. " Sous le rapport de la physique son travail ne laisse rien a de'sirer." 



But, if the chief theoretical papers on the subject have thus strangely been 

 allowed to drop out of notice, the case is quite different with several of those which 

 deal with the observed phenomena. Scoresby's Greenland, his Arctic Regions, and 

 his Voyage to the Northern Whale Fishery, are still standard works ; and in them, as 

 well as in Vols. IX and XI of the Trans. R.S.E., he has given numerous careful 

 drawings of these most singular appearances. The explanatory text is also 

 peculiarly full and clear, giving all that a careful observer could be expected to 

 record. It is otherwise with the descriptions and illustrations in Vince's paper {Phil. 

 Trans. 1799). In fact the latter are obviously not meant as drawings of what was 

 seen ; but as diagrams which exhibit merely the general features, such as the relative 

 position and magnitude of the images : the details being filled in at the option of 

 the engraver. That such was the view taken by Brewster, is obvious from the 

 illustrations in his Optics (Library of Useful Knowledge), for while one of Scoresby's 



