Dun Echt Observatory Publications Volume 2 (Paperback)

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. 1877 Excerpt: ...changing the angle between the spider webs and the axis of rotation of the screw, and producing an error at the middle point of the web depending on the sine of the indication of the head and the square of the number of revolutions from the point of maximum bend.1 As all these errors are small, we can suppose them to be capable of expression by cos u + b1 sin u + a2 cos 2U + b.2 sin 2u + nx r + nt + &c, when nx and -2 are coefficients to be determined, and r, the number of revolutions reckoned from o. The following table is the result of the last of several series made for determining the errors of the screw. In the earlier series only one revolution was examined at a time; these series, therefore, only permit examination of periodic error. It was supposed at first that in so short a portion of a screw as four revolutions it would not be necessary to take the terms r and n2 r1 into account, but the considerations previously quoted, as well as internal evidence of former series, seemed to point to the necessity for a simultaneous investigation of all four revolutions. Two of the wires separated almost exactly or-4 were used. A black speck on Scale A was first bisected by one of these wires, and then by the other, the head reading approximately or-0 and or,4 for the two bisections. The micrometer was now set at o-l, and the scale moved by the slow-motion handle till the speck was again bisected by the first web; then the micrometer screw was put back about half a turn, and the first web brought up carefully to correct bisection of the speck, and then the speck was bisected by the second web. These readings will be approximately or-x and or-5. In this way the distance between the webs is measured by forty symmetrically disposed different parts of the ...