SCIENTIFIC NEWS. 31 C 



ing examined by him with great attention, led him to new 

 inferences respecting the theory of these curves. 



Thus for example, if we take a rectangular parallelogram Examples. 

 of glass o inches long and 3 broad, fix it in the line of its 

 longer axis one sixth of its length from the end, and apply 

 the bow to one of the longer sides of the parallelogram at 

 one third of its length ; the lines in the sand, when come to 

 a state of rest, will divide the surface into eight equal rec- 

 tangles by a right line in the direction of the great axis, and 

 three equidistant right lines parallel to the shorter sides. 

 But Mr. Paradisi found, that on causing the plate to vibrate 

 by a succession of very little touches with the bow, 8 semi- 

 circles were first obtained, the centres and diameters of 

 which were placed symmetrically on the longer sides of the 

 parallelogram, and the point of application of the bow was 

 one of these centres. These semicircles gradually increase: 

 those on the same side from separate become tangents, and 

 afterward penetrate into each other, leaving between them 

 rectilinear lines perpendicular to the longer sides; and in 

 proportion as these lines increase in length, the arcs flatten 

 as they approach the greater axis of the parallelogram, with 

 which they are at length confounded. 



In other experiments Mr. Paradisi obtained whole initial 

 circles formed on the surface of the plate, and semicircles 

 with their diameters resting both on the longer and shorter 

 sides of the parallelogram. The velocity of the grains of 

 grains of sand placed in the perimeters diminished in pro- 

 portion as the radii increased. 



Mr. Paradisi applies the term of centre of vibration to the Centres of ?i- 

 centre of the circle that forms round the point to which the bratlon and 



r secondary 



bow is applied, and that of secondary centres to those of the centres. 

 other circles. Supposing afterward, that when the system 

 of curves is arrived at a fixed state, any given element of 

 these curves is directed by the result of several forces, the 

 actions of which emanate from these different centres of 

 vibration, and are functions of their distances from the ele- 

 ment of the curve in question, he arrives at a differential 

 equation between the coordinates of this element, the sum- 

 mation of which would require the form of the functions, 

 that represent the laws of the actions of the forces, to be 



known 



