3. The two micrometer screws (X and Y, fig. 17), which actuate the movable slides, have heads divided into 100 parts, one revolution =0·5 mm.; so that ten revolutions are =5 mm., or = the interval between two adjacent réseau-lines, or = the interval between the sides of the “fixed square.”
4. Two other screws, o, p, the heads of which are not graduated, give motions to the whole micrometer box through ±1 mm. in directions parallel to the axes of the two micrometer screws.
5. Each of the two micrometer screws X and Y moves a system of six parallel webs, placed 4″ of arc apart from each other. These webs serve not only for pointing on stars to determine their coordinates (in manner afterwards described), but also for estimating the diameters of the star-images in terms of these 4″ intervals.
6. All the essential parts of the micrometer, including the slides, micrometer box, tube, &c., are of steel or cast-iron, so that changes of temperature do not affect the adjustments.
Fig. 17.
The necessary adjustments are the following:—
1. The webs of each set of movable webs shall, inter se, be strictly parallel, and the two sets shall be strictly at right angles to each other.
2. The double webs composing the sides of the fixed square shall be strictly parallel, and shall form a true square of exactly ten revolutions of the screw on the side.
3. The two micrometer screws shall be without sensible periodic or other error, and exactly alike in pitch.
4. The micrometer readings for coincidence of the movable webs with the webs of the fixed square shall, be exactly 0·000R and 10·000R.
5. The image of a normal réseau-square, as viewed in the microscope, shall exactly coincide with the square formed by the fixed webs—that is to say, the image of the sides of a normal réseau-square shall measure exactly 10 screw-revolutions.
Assuming that these conditions can be rigidly realized, we have the following very simple modus operandi:—
1. By means of the quick rack motions A and B move the plate so as to bring the réseau-square into the centre of the field of the micrometer; then, by means of the screw heads o, p, perfect the coincidence of the “fixed square” of webs, with the image of the réseau-square.
2. By means of one of the micrometer screws X place the star’s image in the middle of the six parallel webs which are moved by X.
3. Similarly, place the star’s image in the middle of the webs moved by Y.
4. Estimate the diameter of the star’s image in terms of the 4″ intervals of the movable webs.
By employing both hands, operation (1) can be made as quickly as a single pointing with the ordinary spider-line micrometer, and operations (2) and (3) can be similarly performed in the time required for a single pointing. The reading (2) is then the required co-ordinate in x and that of (3) is the required co-ordinate in y; or, if the plate is reversed, 180°, these readings have to be subtracted from 10·000R. A general idea of the construction of the machine can be gathered from fig. 17 above, but the reader will find a detailed account of it, and of the manner in which the requisite adjustments are made, in the paper already quoted.
The apparatus has been used with complete success at the Royal Observatory, Cape of Good Hope, and at Melbourne, Sydney and Cordoba.
Effects of Wear on the Micrometer Screws.—The accuracy of this apparatus has been frequently criticized on the ground that errors are produced in the screws by the effect of wear. One reply to this is that it is not difficult to determine from time to time the errors of the screws and to apply the necessary corrections to the observations. But a little consideration will show that when the plate is reversed 180° the effects of errors of the screws produced by. wear are practically eliminated.
In discussing the effect of wear upon a screw, it will be convenient to imagine the thread unrolled and forming a wedge, of which we can represent the unworn bearing-side by a straight line AB (fig. 18),
Fig. 18.
on which rubs the block CD, which represents the female screw or bush, and moves between the points E and F, sometimes towards E, sometimes towards F, but having as often to measure short distances as long distances from the middle point of this range, and these as often towards E as towards F. Now, if CD is pressed by its weight or by a spring on the surface AB, the effect of wear will be to produce a symmetrical grinding away of both surfaces, which may be represented thus, fig. 19.
Fig. 19.
That is to say, the screw-errors will be identical for revolution n and for 10−n, and thus will disappear in their effect in the mean of observations made in reversed positions of the plate. At the Cape of Good Hope, after more than 200,000 pointings had been made, the screw-errors were redetermined; the results proved the truth of the above conclusions, viz. the absolute freedom of the derived co-ordinates from the effects of wear of the screws in the mean of measures made in reversed positions of the plate.
Hinks’s Measuring Machine.—A very refined modification of the Cape machine is described by A. Hinks (Monthly Notices, R.A.S., vol. 61, p. 444), and the instrument contains many elegant mechanical and optical details due to Horace Darwin and Messrs Zeiss respectively.
Its fundamental principle is that, by a combination of glass scales with a micrometer screw, “the chief part of the distance to be measured is read off on the scale; the fractional part of the scale space is not estimated but measured by the screw.” Hinks claims that thus never more than one- or two-tenths of a revolution of the screw need be used in making the measure, and little time is lost in running the screw backwards and forwards. All this is true, but three readings instead of one for each pointing, much more figure-work in computation (especially if corrections have to be applied to the scale readings to reduce them to exact normal screw readings), are factors which involve a far greater expenditure of time than making a few additional turns of a screw in the process of measurement. Hinks’s further claim that, in consequence of the small motion of the screw, less error is produced in the screw by wear is not true; for, although large movements of the screw produce a large amount of wear, that wear is spread over longer parts of the screw but remains the same for any particular part of the screw; the resulting errors are exaggerated towards the extremity of the range of screw employed (see Monthly Notices, R.A.S., vol. 45, p. 83), and are therefore more likely to produce errors which are not eliminated on reversal of the plate in cases where the screw range is not strictly limited, and the wear therefore not strictly symmetrical.
The excellent manner in which the scales and micrometers are mounted, the employment of a compound microscope for viewing the scales, with its ingeniously arranged and admirably efficient reversing prism, and the perfection of its slow motions for focusing and reading, combine to render this a most accurate and convenient instrument for very refined measures, although too slow for work in which the measures must depend on single pointings in each of two reversed positions of the plate, and where speed of working is essential.
Apparatus for Measuring Star-Spectra, &c.—These machines may be divided into three classes, viz. A, in which the motion of the slide which carries the photographic plate is measured entirely by a screw; B, in which that motion is measured by combination of a scale and screw; and C, in which the
