For full directions as to its use consult Loomis’ Practical Astronomy, a book which should be in the library of every one who has the least interest in celestial observations. Suffice it to say here that the ring micrometer is very simple in use, and the computation of the results is quite easy. In Fig. 130 F is the edge of the field, R the ring, and a b, a′b′, the paths of the stars s and s′, the former well into the field, the latter just within the ring. The necessary data comprise the time taken by each star to transverse the ring, and the radius of the ring in angular measure, whence the difference in R. A. or Dec, can be obtained.[20]
Difference of R. A. = ½ (t′-t)½ (T′-T) where (T′-T) is the time taken for transit of second star. To obtain differences of declination one declination should be known at least approximately, and the second estimated from its relative position in the ring or otherwise. Then with these tentative values proceed as follows.
Fig. 131.—Double Image Micrometer. (Courtesy of The Clarendon Press.)
Put x = angle aob and x′ = angle a′o′b′
Also let d = approximate declination of s and
d′ = approximate declination of s′
Then sin x = (15/2r) cos d (T′-T)
sin x′ = (15/2r) cos d′ (t′-t) and finally
Difference of Dec. = r (cos x′-cos x), when both arcs are on the same side of center of ring. If on opposite sides, Diff. = r (cos x′ + cos x).
There is also now and then used a square bar micrometer, consisting of an opaque square set with a diagonal in the line of diurnal motion. It is used in much the same way as the ring, and the reductions are substantially the same. It has some points of convenience but is little used, probably on account of the great difficulty of accurate construction and the requirement, for advantageous use, that the telescope should be on a well adjusted equatorial stand.[21] The ring micrometer works reasonably well on any kind of steady mount, requires no illumination of the field and is in permanent working adjustment.
Still another type of micrometer capable of use without a clock-drive is the double image instrument. In its usual form it is based on the principle that if a lens is cut in two along a diameter and the halves are slightly displaced along the cut all objects will be seen double, each half of the lens forming its own set of images.
Conversely, if one choses two objects in the united field these can be brought together by sliding the halves of the lens as before, and the extent of the movement needed measures the distance between them. Any lens in the optical system can be thus used, from the objective to the eyepiece. Fig. 131 shows a very simple double image micrometer devised by Browning many years ago. Here the lens divided is a so-called Barlow lens, a weak achromatic negative lens sometimes used like a telephoto lens to lengthen the focus and hence vary the power of a telescope.