4 One great series of crust waves from east to west is crossed by a ' " **Areal** and mittlere Erhebung der Landflachen sowie der Erdkruste " in Gerland's Beitriige zur Geophysik, ii.

The corresponding equations in **areal** co-ordinates are readily derived by substituting x/a, ylb, z/c for a, 1 3, y respectively in the trilinear equations.

The crystallines are confined to the portion of the belt east of the Great Valley where Paleozoic rocks are always highly metamorphosed and occur for the most part in limited patches, excepting in New England and Canada, where they assume greater **areal** importance, and are besides very generally intruded by granites.

- N / (z cot IC) =o, with centre sin A, sin B, sin C; the escribed circle opposite the angle A is - N I (- x cot ZA)+ -1 (y tan 2B) + -V (z tan 2C) =o, with centre - sin A, sin B, sin C; and the selfconjugate circle is x 2 cot A+y 2 cot B+z 2 cot C =o, with centre tan A, tan B, tan C. Since in **areal** co-ordinates the line infinity is represented by the equation x+y+z=o it is seen that every circle is of the form a 2 yz+b 2 zx+c 2 xy+(lx+my+nz)(x+y+z) = o.

The various forms in **areal** co-ordinates may be derived from the above by substituting Xa for 1, µb for m and vc for n, or directly by expressing the condition for tangency of the line x+y+z = o to the conic expressed in **areal** coordinates.

As the planet revolves around the centre, each radius vector describes a surface of which the area swept over in a unit of time measures the **areal** velocity of the planet.

We shall thus have a projected **areal** velocity, the product of which by the mass of the planet is the moment of momentum of the latter.