Azimuth; A treatise on this subject, with a study of the astronomical triangle and of the effect of errors in the data. Illustrated by loci of maximum and minimum errors

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1887 Excerpt: ...is a part of the locus. There remains y + 4y + 5y + 2'-2/-2y +/ + 2 = o..... (277) Infinite branches are imaginary and form at origin imaginary. If y = o, ' = o, (278) and =V--1, imaginary. (279) If x = o, y = O (280) and y--1) = o, y = ± 1, double point at N. and S.. (281) Moving origin to N., putting y =y-f-1, the form is given by x'+y = o; (282).-. imaginary branch at N. point, the same at S. point; N. and S. are isolated points. Arranging (277) as a cubic in x, we have 2'+ 5/' + (4/-2/ + 2)+/(/-2/+I) = 0..... (283) These coefficients are all positive, therefore x can have no positive root, and therefore x can have no real root. The locus is therefore imaginary, excepting the line y =0 (that is X, the prime-vertical which is the equator), and the peculiar points at zenith and N. and S. (k) For limiting form L = 900. Put A = 00 in (254) and we have y(y + 2xy + «), or y(x + yy = o-, (284).. y = o, giving X, the prime-vertical; (285) + yy = o, giving origin, zenith, a double conjugate point.... (286) (/) Not considering detached points, it is seen from (i) and (k) that starting with Lat. = O, the axis of X is the locus; and ending with Lat. = 900, again the axis of X is the locus; while between these limiting latitudes there is always one branch passing through the origin and E. and W., and always having an asymptote y =--A. On the sphere it is a continuous branch through zenith, E., nadir, W., to zenith. The question arises: How does the curve change its shape with the change of latitude, so that it shall return to its original form? note.--For the following elucidation and the determination of the envelope, the writer is much indebted to Lieutenant Rittenhouse and Professor Hendrickson. The equation (254) to the curve contains A and A'. Arrangin...