ELASTICITY OF REGULARLV CRYSTALLIZED BODIES. 151 



experiments made with a substance the three axes of which shall be 

 accurately perpendicular to each other, which is not entirely the case 

 in wood. 



It would now remain for us to examine two other series of plates, 

 one taken round the diagonal A B, and the other round the diagonal 

 A C ; but as it is evident that the arrangements of nodal lines which 

 they would present would differ very little from those of the fourth 

 series, we may dispense with their examination. 



Such are, in general, the phaenomena wliich are observed in bodies 

 which, like that we have just examined, possess three axes of elasticity: 

 collected into a few propositions, the results we have obtained are re- 

 ducible to the following general data. 



1st. When one of the axes of elasticity occurs in the plane of the 

 plate, one of the nodal figures always consists of two straight lines, which 

 intersect each other at right angles, and one of which invariably places 

 itself in the exact direction of this axis ; the other figure is then formed 

 by two curves which resemble the branches of a hyperbola. 



2nd. Wlien the plate contains neither of the axes in its plane, the 

 two nodal figures are constantly hyperbolic curves ; straight lines never 

 enter into their composition. 



3rd. The numbers of vibrations which accompany each mode of di- 

 vision are, in general, higher as the inclination of the plane to the axis 

 of greatest elasticity becomes less. 



4th. The plate which gives the sharpest sound, or which is suscep- 

 tible of producing the greatest number of vibrations, is that which 

 contains in its plane the axis of greatest elasticity and that of mean 

 elasticity. 



5th. The plate which is perpendicular to the axis of greatest elasti- 

 city is that from which the gravest sound is obtained, or which is sus- 

 ceptible of producing the least number of vibrations. 



6th. When one of the axes is in the plane of the plate, and the elas- 

 ticity in the direction perpendicular to this axis is equal to that which 

 itself possesses, the two nodal systems are similar ; they each consist of 

 two straight lines which intersect each other rectangularly, and they 

 occupy positions 45° from each other. In a body which possesses three 

 unequal axes of elasticity there are only two planes which possess this 

 property. 



7th. The transverse axis of the nodal curves always occurs in the di- 

 rection of the least resistance to flexion ; it hence follows, that when in 

 a series of plates this axis places itself in the direction at first occupied 

 by the conjugate axis, it is because the elasticity in this direction has 

 become relatively less than in the other. 



8th. In a body which possesses three unequal axes of elasticity, there 

 arc four planes in which the elasticity is so distributed that the two 



