ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 147 



will be seen, on causing them to vibrate in the same mode of trans- 

 versal motion, that they produce the same sound. It also follows, because 

 the elasticity in the direction ay is sometimes smaller and sometimes 

 greater than that which exists in the direction of c d, that the first axis 

 of the nodal hyperbola ought to change its position to be able to remain 

 always perpendicular to that of the lines a?/, cd, which possess the 

 greatest elasticity ; thus, in Nos. 1 and % cd possessing the least elas- 

 ticity, it becomes the transverse axis of the hyperbola, whilst in Nos. 4, 

 5 and 6, the elasticity being greater in the direction c d than in that 

 of a y, the transverse axis of the hyperbola places itself on the latter 

 line. As the ratio of the two elasticities varies only gradually, it is 

 obvious that the modifications impressed on the hyperbolic system ought 

 in the same manner to be gradual: thus the summits of these curves, 

 at first separated in No. 1 by a certain distance (which will depend on 

 the nature of the wood), will approach nearer and nearer, for the fol- 

 lowing plates, until they coalesce as in No. 3, at a certain degree of 

 inclination, which was 45° in the experiment to which I now refer, but 

 which might be a different number of degrees for another kind of wood. 

 At the point where we have seen that the elasticities are equal in the 

 direction of the axis, the two curves transform themselves into two 

 straight lines which intersect each other rectangularly, after which they 

 again separate ; but their separation is effected in a direction perpen- 

 dicular to that of their coalescence. The sounds of the hyperbolic 

 system follow nearly the same course as those of the system of crossed 

 lines, that is to say, they become higher in proportion as the plates 

 more nearly approach being parallel to the axis of greatest elasticity ; 

 but it deserves to be remarked, that the plate No. 3, for whlcli the elas- 

 ticity is the same in the two directions a y, c d, is that between the two 

 sounds [of which there is the greatest interval : this evidently depends 

 on the elasticity in the two directions ay, cd being very different from 

 that which exists in the other directions of the plate. 



Lastly, it is to be remarked that, in the four first plates, the sound of 

 the hyperbolic system is sharper than that of the system of crossed 

 lines, and that it is the contrary for the plate No. 6, which renders it 

 necessary that there should be between No. 4 and No. 6 a plate, the 

 sounds of which are equal, which in the present case is exemplified in 

 No. 5, although its two modes of division diff'er greatly from each other. 

 There is another thing remarkable in this plate; its two modes of di- 

 vision can transform themselves gradually into each other by changing 

 the position of the place of excitation, so that the two points c and c' 

 becoming two nodal centres, are in every respect in the conditions 

 indicated by fig. 4. 



The interval included between the gra\'est and the shai^pest sounds 

 of this series was an augmented sixth. 



l2 



