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descriptions and explanation were free from the exaggerations and contra- 
dictions of his predecessors. He showed the illusion to a pupil of his, a 
small schoolboy of thirteen ; and since then, following the instructions of 
my beloved master, I have seen the Fata Morgana again and again every 
springtime, some four or five hundred times in all. I can therefore speak 
of it as a familiar friend. 
In my monograph, Le Leman (Lausanne, 1895), and in my note of 1896,* 
I have endeavoured to lay down the determining conditions of the 
phenomenon. Since then I have taken a further step in the co-ordination 
of the facts, and I propose to give to-day the principal features of the 
mirage, which may perhaps serve as a better foundation for the mathe- 
matical study of the phenomenon, which I leave in the care of my mathe- 
matical and physical friends.*)* 
The physical conditions which determine the appearance of the Fata 
Morgana are always the same. When, under the bright skies of spring 
or early summer, the lake lies calm or slightly rippled by light and inter- 
mittent puffs of air, there appears at times during the afternoon when 
the air is warmer than the water a phantom-like transformation of the 
scenery of the opposite coast. Over a horizontal stretch of twenty 
or thirty degrees, the familiar details of the coast-line, which may be 
from ten to thirty kilometres distant, become strangely transformed. 
Resting on the water horizon, and bounded above by another horizontal 
line at a height of a few minutes of arc, there comes into view a verti- 
cally striped band or striated zone {zone stride ), seemingly composed of 
rectangles placed side by side, of varied tints and hues. It might be 
compared to the distant cliffs of Dover as seen by travellers crossing 
the Channel ; or to a great city built on the shore, with blocks of houses 
ranged along the quays, a Genoa, a Naples, or a Constantinople, 
miraculously rearing itself in a region known to be occupied by a few 
* “ Refractions et Mirages : passage d’un type a l’autre,” Bull. Soc. Vaud. Sc. nat., xxxii. 
271, Lausanne, 1898. 
t Refraction phenomena are not always presented in nature so clearly or so simply as 
might be desired. There may be no doubt as to the general nature of the mirage, which 
may nevertheless be difficult to interpret. The phenomena originate at a far distance, in 
air more or less saturated with water vapour, and frequently masked by a veil of fog. The 
observations are beset with great difficulties. Had it not been so I should not have spent 
more than fifty years in arriving at the present explanation. The observation of refraction 
phenomena over the surface of a lake demands an intimate acquaintance with all its 
characteristics. An occasional traveller spending a few days on its shores cannot be familiar 
enough with the lake scenery to enable him to know what changes, if any, may have 
occurred. Prolonged residence in the neighbourhood of the lake and a keen interest in the 
ever-shifting illusions are essential to a complete study of the phenomena. 
