H. D. Oldham — Notes on a Graphic Table of Dips. 413 



series of quadrants are to be drawn. The intervals cut off by this 

 series of perpendiculars along the base 00 form a scale of cotan- 

 gents of the angles made by their respective radii with the base OC, 

 or of tangents of the angles made with the side OA ; for convenience 

 then we may graduate the base 00 as a scale of cotangents, and 

 the side OA as a scale of tangents, and graduating the radii according 

 to the angles, they make with 00 the graticule is complete. 



In describing the use of this device, I shall refer to the point as 

 the point of origin, to the line 00 as the axis, to the lines diverging 

 from as radii, and to the perpendiculars to OC as normals to the 

 axis. Its use is as follows : — 



(1) Given the direction and amount of the true dip, to find the 

 apparent dip in any other given direction. 



(a) When the dip does not exceed 45°. Take the point on the 

 radius corresponding to the angular divergence of direction between 

 the given and required dips, which represents the angle of dip ac- 

 cording to the scale of tangents (as graduated along OA), and follow 

 the normal till it cuts the axis ; the point of intersection gives the 

 required angle of dip, using the scale of tangents as before. 



Example. — A bed dips 30° to N. 50° E. ; required its apparent 

 dip to E. 10° S. The angular divergence being 50°, take the point 

 where the 30° quadrant cuts the 50° radius, and follow the normal 

 to the axis which it cuts at the intersection of the 20° quadrant ; the 

 dip required is therefore 20°. 



{h) When the dip exceeds 45°. Take the point on the axis repre- 

 senting the given dip (using the scale of cotangents along 00), and 

 follow the normal till it intersects the radius corresponding to the 

 angular divergence between the direction of the given and required 

 dips ; and the point of intersection will give the required angle of dip. 



Example. — A bed dips 70° to N. 10° W. ; required its dip to N. 

 40° E. The angle of divergence being 50°, take the point repre- 

 senting 70° on the axis and follow the normal till it cuts the radius 

 of 50° at the intersection with the 60° circle ; 60° is consequently 

 the required dip. 



Should the intersection of the normal and radius not fall within 

 the square, a different pi'ocedure must be adopted. In this case 

 the normal from the point where the radius corresponding to the 

 divergence cuts the outer quadrant (that of 45°) must be followed 

 to the axis, and the distance between the intersections with the axis 

 and the radius corresponding to the true dip if laid off from C alono- 

 CB will give the required angle of dip ; or a line may be drawn 

 parallel to the axis through the point of intersection with the radius 

 representing the dip, and the point where it cuts the scale on OB 

 will give the required dip. For the ready application of this 

 method it would be advisable to have a series of lines parallel to 

 00, which, to prevent confusion, I have not inserted in the diagram. 



Example. — A bed dips 50° to N.E. ; required its dip to N. 10" W, 

 The angle of divergence being 55°, take the point where the 55° 

 radius cuts the 45° quadrant, and follow the normal till it cuts the 

 50° radius, and from that point follow a line parallel to the axis 



