254 SECTION MECHANICS. 



pressed one into another, which reach the same flat side, and the lower 

 parts of which have variable thicknesses, which become extremely 

 thin at a certain point of the axis of the " debouchure." 



This point is the principal centre of the flow which has been pro- 

 duced from the axis to the circumference by the pressures caused and 

 transmitted by the punch to the very interior of the mass. When this 

 flow has been able to take place, the virtual resistance of the partition 

 to be punched through was necessarily greater than the latteral resis- 

 tance ; but these two resistances will, on the contrary, be of the same 

 force when the " debouchure " begins to detach itself, and the effort 

 necessary to continue the punching will go on, after this, quickly 

 decreasing to the end of the operation. 



The mode of action of these resistances, which we can determine 

 from the facts themselves, has furnished us with the true knowledge of 

 the action of the transmitted pressures, and we have been able to 

 formulate the laws of the transmission of pressures in a solid mass in 

 course of deformation, in a zone more or less extended which we have 

 named the zone of activity. And, finally, by proving the force necessary 

 to be exerted at the moment when the " debouchure " separates itself, 

 we have been able to determine the true co-efficients of transversal 

 cuttings. They are as follows, for each square centimeter : 



Kilog. 



Lead 182 



Tin 209 



Alloy of Lead and Tin ... 230 



Zinc 900 



Copper 1893 



Iron 3757 



It is worthy of remark that these numbers come very near those of the 

 resistance to rupture by extension for each of the metals experimented on. 

 The results ot the calculations, with regard to the transmission of 

 mechanical work, from one layer to another next to it, allow us to 

 lay down the mathematical law for the distribution of pressures, not 

 only for punching, but also for the various methods of deformation 

 previously studied. The formula arrived at by this method have been 

 subsequently justified by M. de Saint Venant and by M. Levy ; quite 

 lately M. Boussinescq, of the Faculty of Lille, announced to us that he 



