LAWS OF DECREMENT. 369 



RHOMBOID. 



And the manner of deducing these may be given as 

 an example of one of the methods* of analysis appli- 

 cable to these investigations. 



The general equation of a plane in relation to 

 three co-ordinate axes, is known to be 

 A#+By-f C * + D = o. 



Let the distances from the origin at which the 

 plane cuts the three axes, be represented by p, q, 

 and r. 



We shall then have the following equations of the 

 points where the axes are cut by the plane. 



For the point on the axis x we have x nz j?, 



y y </> 



To find the values of the co-efficients A B C D, in 

 function of the quantities p, q, and r, with a view to 

 substitute those quantities in the general equation 

 for the co-efficients A, B, C, and D, 



Let y o, z zz o, and x 



x zz o, s = o, . . y 



A 



--D 

 IT 

 D 



C 



Therefore ~ p, whence A =z 



A p 



~B~ ' q ' ~Y~ 



D c _ D 



C r 



* This method of determining the relations that may exist among 

 crystals, has been used in a paper published by Mr. Levy in the 

 Edinburgh Philosophical Journal, relative to another object which will 

 be referred to in a later part of this Appendix. 



3 A 



