302 SOCIETY OF PHYSICS AND NATUEAL HISTORY OF GENEVA. 



twenty-four liours amounted to 30 and 40 centimetres, (12 and 16 inches.) 

 The inundations occasioned by falls of water so exceptional cannot be 

 attributed solely to the removal of the forests from the mountains, how- 

 ever unfavorable such clearings may be. Lastly, mention was made of 

 the shower of mud observed at Naples by Professor Claparede. The 

 clouds, on that day, had a peculiar aspect and seemed to be formed of 

 dust; muddy spots were left on the windows by the drops of rain. Gen- 

 eral Dufour'had witnessed at Corfu showers of mud which the inhabit- 

 ants attributed to the wind of Africa. 



§ 3.— Mathematics and Physics. 



Pure mathematics has been the subject of but a single memoir, which 

 was read to us by Professor De La Harpe. It is the first part of a trea- 

 tise on the Ibrmation of powers, in which the author demonstrates that 

 the higher powers are formed by differences. He gives the formulas 

 designed for the calculation of high powers and designates them by the 

 general name of formula of the monome. This memoir vfas accomp-mied 

 by models intended to facilitate the understanding of the demonstrations. 



The geodesic labors undertaken by Swiss savants have been continued 

 duringthe year 1868. Professor Plantamour has communicated to us 

 the result of the Swiss levelings, which embrace the whole of the west- 

 ern part from Geneva to Basle. MM. Planta mour and Hirsch have been 

 engaged in determining for the ditiereut stations the numbers as referred 

 to the stone of Niton, which serves as the point of departure, while the 

 primitive data simply give the difference of level between two consecu- 

 tive stations. The number of points for w^hich the amounts have been 

 thus established is 626. To that end, it was necessary to make a com- 

 pensation for the errors in the system composed of a series of polygons, 

 each of which ought to be exactly closed. One of the causes of error in 

 a leveling of precision, the influence of which is very considerable in a 

 country so broken as ours, is the variableness in the absolute length of 

 the sights, according to atmospheric circumstances, the temperature, 

 hygrometric state; and, from direct and numerous comparisons, this 

 variation may amount to a ten-thousandth of their length, more or less. 



M. Plantamour gave an account of observations which he had made 

 during a sojourn of nearly two months at Weissenstein with a view of 

 determining the astronomical co-ordinates of that station. He also read 

 a memoir on the latitude of the Eighi Culm from observations made at 

 that locality in 1867. The latitude was determined as well by the circum- 

 meridian zenithal distances of stars as by observations of their passage in 

 the prime vertical. The number obtained is sensibly greater than that 

 indicated in the triangulation of Switzerland, which had been deduced 

 from the latitude of Berne by the calculation of triangles. The differ- 

 ence is easily explained by the attraction of the neighboring chain of 

 the Alps situated to the south of the Eighi. 



The effects of lightning on trees have been studied by Professor Col- 

 ladon in the case of sixteen poplars, three oaks, a fir tree, and a vine. 

 The poplars which were struck were seamed with furrows, greatly shat- 

 tered, and stripped of bark and liber in the two lower thirds of the tree, 

 the upper third being most frequently exempt from injury, probably in 

 consequence of the greater conductibility of that portion of the branches 

 and foliage. The poplar of Italy especially attracts lightning, for M. 

 Colladon has seen it struck in preference to neighboring oaks and elms, 

 though the latter were taller than the poplars. The effects of lightning 

 on oaks are very different from those just described : the upper parts 



