148 FELIX savart's researches on the 



It is almost useless to observe that the plates taken in the directions 

 I, II, III, inclined on the other side of the axis A X the same number 

 of degrees as the plates 1, 2, 3, would present exactly the same phEeno- 

 mena as these latter. This observation being equally applicable to the 

 following series, we shall not mention it again. 



Second Series. — Plates taken round the axis A Z of least elasticity 

 and perpendicular to the plane C Y A X ; figs. 9 and 10. 



As in the preceding case, one of the nodal systems of the plates of 

 this series consists of two lines crossed rectangularly, one of which, a z, 

 corresponds with the axis A Z ; whence it follows tJiat the second may 

 be considered as the projection of the two other axes on the plane of 

 the plate, which, whatever its inclination may be, ought consequently 

 to possess a greater elasticity in the direction fff than in the direction 

 a z : thus the hyperbolic system of this series cannot present the trans- 

 formations which we saw in the preceding series, where erf, fig. 8, possesses 

 sometimes a less, at other times a greater elasticity than that of a y. 

 In the present case, a z remaining constantly the axis of least elasticity, 

 the resistance to flexion in the direction y^ goes on gradually increasing 

 from the plate No. 1 to the plate No. 6 parallel to the plane A X B Z, 

 and the branches of the hj^erbola straighten themselves in proportion as 

 the plates more nearly approach this last position. As to the soundswhich 

 correspond to each of these nodal systems, it is observed that they ascend 

 gradually from No. 1 to No. 6, and that the sound of the hyperbolic 

 system is sharper in a part of the sefries than that of the system of crossed 

 lines, whilst they become graver in the other part. There is therefore a 

 certain inclination for which the sounds of the two systems ought to be 

 equal ; and this evidently would have taken place in the present expe- 

 riment for a plate intermediate to No. 4 and No. 5. 



The interval between the gravest and the sharpest sound of each 

 series was an augmented fifth. 



Third Series. — Plates taken round the axis A X of greatest elasticity, 

 and perpendicular to the plane A Y D Z ; figs. 1 1 and 1 2. 



The elastic state of these plates cannot present such remarkable dif- 

 ferences as those we have observed in the preceding series ; for, being 

 all cut round the axis of greatest elasticity, they can only contain in 

 their plane that of least or that of mean elasticity, or lastly, those in- 

 termediate between these limits, which do not vary greatly from each 

 other. Thus it is seen that their modes of division differ very little from 

 each other, and that the sounds which correspond to them present 

 rather slight differences, although they go on ascending in proportion 

 as the plates more nearly approach containing the axis of mean elas- 

 ticity in their plane. Here, as in the other series, one of the nodal 



