146 FELIX savart's researches on the 



that, in reference to the transversal motion, the numbers of the vibra- 

 tions are as the square roots of the resistance to flexion, or, wliich is 

 the same thing, that the resistance to flexion is as the square of the 

 number of oscillations. 



Fig. 6 shows the results of an experiment of this kind which was 

 made upon the same piece of beech-wood from which I cut all the 

 plates which I shall mention hereafter. In this figure I have, to impress 

 the mind more strongly, given to these rods directions parallel to the 

 edges A X, A Y, A Z of the cube fig. 5, and I have supposed that the 

 faces of the rods are parallel to those of the cube. It is to be remarked 

 that two sounds may be heard for the same mode of division of each 

 rod, according as it vibrates in ab ov cd; but when they are very thin 

 the difference which exists between them is so slight that it may be 

 neglected. The inspection of fig. 6 shows, therefore, that the resistance 

 to flexion is the least in the direction A Z, and is such, that being re- 

 presented by unity, the resistance in the direction A Y becomes 2'25, 

 and 16 in the direction of A X. It is evident that the elasticity in any 

 other direction must be always intermediate to that of the directions we 

 have just considered. 



This being well established, we shall proceed to the examination in 

 detail of the different series of plates we have mentioned above. 



First Series Plates taken round t/ie axis A Y and perpendicular to 



the face AXBZ of the cube. 

 In the plates of this series, one of the modes of division remains con- 

 stantly the same. (See figs. 5, 7 and 8.) It consists of two lines crossed 

 rectangularly, one of which, a y, places itself constantly on the axis A Y 

 of mean elasticity ; but although this system always presents the same 

 appearance, it is not accompanied, for the different inclinations of the 

 plates, by the same number of vibrations ; this ought to be the case, 

 since the influence of the axis of greatest elasticity ought to be more 

 sensible as the plates more nearly approach containing it in their plane: 

 the sound of this system ought therefore to ascend in proportion as the 

 plates become more nearly paraUel to the plane C Y A X. As to the 

 hyperbolic system, it undergoes remarkable transformations, which de- 

 pend on this circumstance, that the line a y remaining the axis of mean 

 elasticity in all the plates, the line c d, which is the axis of least elasti- 

 city in No. 1, transforms itself gradually into that of the greatest elas- 

 ticity, which is contained in the plane of the plate No. 6. It hence 

 follows that there ought to be a certain degree of inclination for which 

 the elasticities, according to the two directions ay, c d, ought to be 

 equal: now, this actually happens with respect to the plate No. 3; and 

 this equality may be proved by cutting in this plate, in the direction 

 of a j^ and its perpendicular, two small rods of the same dimensions : it 



