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XXV. On the Artificial Production of Hail, and on a new Theory 

 of this Meteoric Product. By P. J. M. Sanna-Solaro*. 



THE following is an extract from a memoir by Sanna-Solaro, 

 read before the French Academy of Sciences in April last. 



Meteorologists and natural philosophers concur without excep- 

 tion in the belief that hail is formed in the atmosphere by an 

 act of successive incrustation. The hailstones have hitherto 

 been considered to consist of a central nucleus around which 

 the several component layers are deposited ; and the prevalence 

 of this hypothesis has on the one hand proved an obstacle to the 

 discovery of the true origin of this meteor, and on the other 

 leaves unexplained several phenomena which accompany it. For 

 our part, we believe that hailstones are produced, from the first, 

 such, very nearly, as they are when precipitated to the earth. 

 Admitting that the congelation commences externally, it becomes 

 easy to explain all the peculiarities met with in their centre, and 

 all the other phenomena which these meteoric products exhibit. 



The external envelope having been formed (how this takes 

 place will be presently shown), that portion of liquid in contact 

 with the crust begins to congeal, bubbles of air are disengaged 

 from it and converge towards the centre. From this an amount 



appears to me perfectly clear, and will become so, I think, to the reader 

 with the aid of a few words of explanation. 



Let Q be a closed curve of the kind supposed lying in a plane which will 

 be treated as a constant plane of projection ; and for greater simplicity, and 

 in order to steady the ideas, imagine that the vanishing plane (meaning 

 thereby the plane* passing through the eye and the vanishing line), and the 

 plane of the object to be put in perspective, are retained at a constant 

 distance from each other and always perpendicular to the picture plane, 

 and also that the height of the eye above the vanishing line is invariable. 

 Take any fixed line and point in the picture Q, and determine the equation 

 to the curve boundary of its primitive O corresponding to a given distance k 

 between the fixed point and the variable vanishing line and to a given angle 

 of inclination ec between the fixed line and this variable line. Then by 

 hvpothesis the area of O, say M, is known in terms of its coefficients, 



dM dM 

 which will be known functions of ec and h ; hence -7— and -tt are known, 



and consequently the position of the perspective of the centre of gravity of 

 O on the picture is known ; and from this the position of that centre in its 

 own plane can be constructed, and therefore will have been found by aid 

 of algebraical and differentiation processes onty, as was to be shown. 



The above explanation may be made still more distinct if we suppose 

 that we begin with an object €1 (the curve for which is expressed by an 

 equation in its most general form), wherein we have, say, «=0 and h=\ ; 

 that from this we deduce the equation of P in the preceding investigation, 

 and from P pass to O as before ; then, having found the coordinates of the 

 perspective of the centre of gravity of O as functions of h and a, make a=0, 

 h=\, and pass back to the coordinates of the centre of gravity in Q, of 

 which the centre of gravity last named then becomes the perspective. 



* Translated by J. T. Arlidge, A.B., M.B. Lond. 



