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. 1914 Excerpt: ...x is varied, Z will move around the circle aZb and will make one complete revolution for each increase of T units in x. In the case represented, tan (1 +i1) = 0.2718 + i 1.084 = 1.118/7s.q16. From Fig. 23 it is evident that the angle AeO is equal to x, and angle eAO is thus the complement of x. Hence half the angle ...
Read More
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. 1914 Excerpt: ...x is varied, Z will move around the circle aZb and will make one complete revolution for each increase of T units in x. In the case represented, tan (1 +i1) = 0.2718 + i 1.084 = 1.118/7s.q16. From Fig. 23 it is evident that the angle AeO is equal to x, and angle eAO is thus the complement of x. Hence half the angle between rx and rt is the complement of x. Moreover y = loge yjrt/n. Therefore, if OZ = u + iv, Constructions For tanh (x t'y) And tanh.1 (- ro) In Fig. 24 mark off on the axis of reals xOX two points T and X such that the former is distant by tanh x and the latter by coth x from the origin O. Find the point C midway between T and X. Incidentally, this point will be distant coth 2x from O. With F1g. 24.--C0nstructi0ns f0r tanh Gr_ i) and tanh-1 (.I. I'p) center C and radius CF = CX = cosech 2x, draw the circle TXZ. Mark off on the axis of imaginaries yOY, two points / and y such that the former is distant by tan y and the latter by cot y from the origin O. Find the point c midway between them. Incidentally, this point will be distant cot 2y from O. With center c and radius ct = cy = cosec 2y, draw the circle By At. This circle will cut the axis of reals at two points A and B distant each one unit from O. It will also intersect the circle TXZ perpendicularly at Z. Connect OZ. This vector OZ is the required hyperbolic tangent of the complex angle (x + iy) radians. DEGREE OF PRECISION OF TABLES Introduction If a numerical quantity, freed from decimals, is correctly expressed to within say 1 part in 1000; i.e., 1 part in 1o3, then this degree of precision may conveniently be described as precision of the third order. In general, therefore, if a numerical quantity be correctly expressed to within 1 part in 10," where n is any re...
Read Less