=1557.= Of all the great subjects which belong to the province of his section, take that which at first sight is the least within the domain of mathematics--I mean meteorology. Yet the part which mathematics plays in meteorology increases every year, and seems destined to increase. Not only is the theory of the simplest instruments essentially mathematical, but the discussions of the observations--upon which, be it remembered, depend the hopes which are already entertained with increasing confidence, of reducing the most variable and complex of all known phenomena to exact laws--is a problem which not only belongs wholly to mathematics, but which taxes to the utmost the resources of the mathematics which we now possess.--SMITH, H. J. S. _Presidential Address British Association for the Advancement of Science, Section A; Nature, Vol. 8 (1873), p. 449._ =1558.= You know that if you make a dot on a piece of paper, and then hold a piece of Iceland spar over it, you will see not one dot but two. A mineralogist, by measuring the angles of a crystal, can tell you whether or no it possesses this property without looking through it. He requires no scientific thought to do that. But Sir William Roman Hamilton ... knowing these facts and also the explanation of them which Fresnel had given, thought about the subject, and he predicted that by looking through certain crystals in a particular direction we should see not two dots but a continuous circle. Mr. Lloyd made the experiment, and saw the circle, a result which had never been even suspected. This has always been considered one of the most signal instances of scientific thought in the domain of physics. --CLIFFORD, W. K. _Lectures and Essays (New York, 1901), Vol. 1, p. 144._ =1559.= The discovery of this planet [Neptune] is justly reckoned as the greatest triumph of mathematical astronomy. Uranus failed to move precisely in the path which the computers predicted for it, and was misguided by some unknown influence to an extent which a keen eye might almost see without telescopic aid.... These minute discrepancies constituted the data which were found sufficient for calculating the position of a hitherto unknown planet, and bringing it to light. Leverrier wrote to Galle, in substance: “_Direct your telescope to a point on the ecliptic in the constellation of Aquarius, in longitude 326°, and you will find within a degree of that place a new planet, looking like a star of about the ninth magnitude, and having a perceptible disc._” The planet was found at Berlin on the night of Sept. 26, 1846, in exact accordance with this prediction, within half an hour after the astronomers began looking for it, and only about 52′ distant from the precise point that Leverrier had indicated.