428 Lord Kelvin on the Elasticity 



§ 32. Hence we see the following simple way of drawing 

 a special tetrahedron. Choose as data three sides of one face 

 and the length perpendicular to it from the opposite angle. 

 The planes through this perpendicular, and the angles of the 

 triangle, contain the perpendiculars from these angles to the 

 opposite sides of the tetrahedron, and therefore cut the 

 opposite sides of the triangle perpendicularly. (Thus, par- 

 enthetically, we have a proof of the known theorem of ele- 

 mentary geometry that the perpendiculars from the three 

 angles of a triangle to the opposite sides intersect in one point.) 

 Let ABC be the chosen triangle and S the point in which it 



is cut by the perpendicular from 0, the opposite corner of the 

 tetrahedron. AS, BS, CS, produced through S, cut the 

 opposite sides perpendicularly, and therefore we find the point 

 S by drawing two of these perpendiculars and taking their 

 point of intersection. The tetrahedron is then found by 

 drawing through S a line SO of the given length perpendicular 

 to the plane of ABC. (We have, again parenthetically, an 

 interesting geometrical theorem. The perpendiculars from 

 A, B, C to the planes of OBC, OCA, OAB cut OS in the 

 same point ; SO being of any arbitrarily chosen length.) 



§ 33. I wish now to show how an incompressible homo- 

 geneous solid of wholly oblique crystalline configuration can 

 be constructed without going beyond Boscovich for material. 

 Consider, in any scalene assemblage, the plane of the line 

 A'OA through any point and its nearest neighbours, and 

 the line B'OB through the same point and its next-nearest 

 neighbours. To fix the ideas, and avoid circumlocutions, we 

 shall suppose this plane to be horizontal. Consider the two 

 parallel planes of points nearest to the plane above it and 

 below it. The corner C of the acute-angled tetrahedron 

 OABC, which we have been considering, is one of the points 

 in one of the two nearest parallel planes, that above AOB we 



