ON THE FLOW OF SOLID BODIES. 253 



the perfectly geometrical position of the natural phenomena be explained 

 in any other way ? It is always as you see, when the regularity could 

 not be more perfect, it appears to us like the most absolute evidence. 

 The indefinitely reducible molecular formation, could not, assuredly, 

 be better justified than by means of these parallel walls, which preserve 

 to a microscopic thickness natural tissues, and an equality of appear- 

 ance and movements which are very remarkable. 



These experiments in concentric flow have, with regard to the 

 relative displacements, been submitted to calculations, and we are 

 now able, in such a deformation, to lay down the trajectory passage of 

 each one of the molecules of the mass, and establish with certainty the 

 final places which they will occupy, compared to those in which they 

 were at first ; and also, by the same means, the transformed of any 

 line or of any surface to their first position. 



These experiments became far more convincing when the shape and 

 position of the apertures are varied ; tubes still replace the slabs, but 

 the relative thickness of these tubes, the juxtapositions and the con- 

 volutions which result are just as instructive with regard to the clearness 

 of their shapes and the distribution of the pressure in the whole extent 

 of the mass which is escaping. But this question will occupy our atten- 

 tion more especially in the study of "punching." 



If a punch be driven into a plate of metal, it will propel before it the 

 material of which the plate is composed, which, at a given moment 

 begins to form a protuberance on the opposite site, and finally detaches 

 itself in the form of a cylinder of the same diameter as the punch, and 

 to which the very characteristic name of " debouchure " has been 

 given. Under certain thicknesses the "debouchure" preserves a 

 height equal to the thickness of the plate, but this is no longer the case 

 when the thickness of the plate is very high. 



A "debouchure" one centimeter high has been made by a block 

 five centimeters thick. If the block be formed of several plates laid one 

 over the other, all these plates will be represented in the " debouchure." 

 The lower plates, pretty nearly, by their original thickness ; the superior 

 plates by a kind of convex lens, of which the curved side has for basis 

 the flat side which has remained in contact with the punch, and which 

 has kept, according to the common axis, almost the whole of its 

 original thickness ; the intermediate plates by a number of cups 



