The dummy variable was chosen because no real direction cosine would ever be greater than 1, and the variable number of data inputs precludes a loop of fixed length. The minimum for each derivative, of course, occurs when the derivative is zero. B. The following routine will do the job. We could have solved for the third direction cosine, C, when we derived the least-squares fit, but then we would have had a messy job of solving three simultaneous equations. This approach is a lot simpler.
Many folds are conical rather than cylindrical.
Shatter cones, or fracture surfaces probably produced by shock waves during meteor impacts, have surface striations which define the surface of a cone. Conical distributions, when plotted on a stereonet, lie on a small circle. Assume the cone axis has direction cosines A1, A2, and A3 and a given line we wish to fit to the cone has direction cosines C1, C2, and C3. As before, the formula will generally not be exactly equal to zero but will have a small value E, and we find the best fit by reducing the sum of the squares of all E to a minimum. The routine we used in the previous section will work just as well here, but with modifications because we need additional sums.