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Stonehenge and Other British Stone Monuments Astronomically Considered, by Norman Lockyer, [1906], at

p. 329


IT will probably be found useful if I give here a few hints as to the precautions which must be taken in making the field observations and an example of their reduction to an astronomical. basis.

For the azimuths of the sight-lines the investigator of these-monuments cannot do better than use the 25-inch, or 6-inch, maps published by the Ordnance Survey. Their accuracy is of a very high order and is not likely to be exceeded, even if approached, by any casual observer having to make his own special arrangements for correct time before he can begin his surveying work.

In some eases, however, it may be found that the Survey has not included every outstanding stone which may be found by an investigator on making a careful search many of the stones are covered by gorse, &c., and are not, therefore, easily found.

In such cases the azimuth of some object that is marked on the map should be taken as a reference line and the difference of azimuth between that and the unmarked objects determined. By this means the azimuths of all the sight-lines may be obtained. When using the 25-inch maps for determining azimuths it must be borne in mind that the side=lines are not, necessarily, due north and south. The Director-General of the Ordnance Survey, Southampton, will probably on application state the Correction to be applied to the azimuths on this account, and this should be-applied, of course, to each of the values obtained.

If for any reason it is found necessary or desirable to make observations of the azimuths independently of the Ordnance Survey, full instructions as to the method of procedure may be found in an inexpensive instruction book 1 issued by the Board of Education: The instructions given on p. 49, § 3, are most

p. 330

generally applicable, and the form on p. 76 will be found very handy for recording and reducing the observations.

In making observations of the angular elevation of the horizon a good theodolite is essential. Both verniers should be read, the mean taken, and then the telescope should be reversed in its Ys, reset, and both readings taken again. One setting and reading are of little use.

The Ordnance Survey maps may also be employed in a preliminary reconnaissance to obtain approximate values of the horizon elevations. This may be done by measuring the distances and contour-lines shown on the one-inch maps. This method, however, is only very roughly approximate owing to the fact that sharp but very local elevations close to the monuments may not appear on these maps and yet be of sufficient magnitude to cause large errors in the results.

Where trees, houses, &c., top the horizon, they should, of course; be neglected and the elevation of the ground level, at that spot, taken. Should the top of the azimuth mark (stone, &c.) show above the actual horizon, its elevation should be recorded and not that of the horizon.

Having measured the angular elevation of the horizon along the sight-line, it is necessary to convert this into actual zenith distance and to apply the refraction correction before the computations of declination can be made.

The process of doing this and of calculating the declination will be gathered from the examples given below:—


Monument:—E. circle Tregeseal, lat. 50° 8″ N. i.e. colat = 39° 52´.

Alignment. Centre of circle to Longstone.

Az. (from 25″ Ordnance Map). N. 66° 38´ E.

Elevation of horizon (measured) 2° 10.´

Reference to the May-Sun-curve, given on p. 263, indicates that this is probably an alignment to the sunrise on May morning. Therefore, in determining the zenith distance, the correction for the sun's semi-diameter (16´) must be taken into account, allowing that 2´ of the sun's disc was above the horizon when the observation was made.

p. 331

Zenith Distance:

Bessel's tables show that refraction, at altitude 2° 10´, raises sun 17´. If 2´ of sun's limb is above horizon, sun's centre is 14´ below.

∴ True zenith distance of sun's centre=87° 50´ + 17´ + 14´ =88° 21´.


Having obtained the zenith distance, and the azimuth, the latitude being known, the N.P.D. (North Polar Distance) of the sun may be found by the following equations:—


tan θ = tan z. cos A,

where θ is the subsidiary angle which must be determined for the purpose of computation, z is the true zenith distance, and A is the distance from the North point.



where Δ is the N.P.D. of the celestial object, and c is the colatitude (90° - lat.) of the place of observation.

In the example taken this gives us—

Reference to the Nautical Almanac shows that this is the sun's declination on May 5 and August 9. We may therefore conclude that the Long-stone was erected to mark the May sunrise, as seen from the Tregeseal Circle.

Had we been dealing with a star, instead of the sun, the only modification necessary in the process  of calculating the declination would have been . to omit the semi-diameter correction of 14´.

Having obtained a declination, we must refer to the curves given on pp. 115-6 in order to see if, there is any star which, fits it, and to find the date.

p. 332

Take, for example, the case of the apex of Cam Kenidjack, as seen from the Tregeseal circle—

Az. = N. 12° 8´ E.; hill=4° 0.´ lat.=50° 8´.

This gives us a declination of 42° 33´ N., and a reference to the stellar-declination curves (p. 115-6) shows that Arcturus had that declination in 2330 B.C. From the table given on p. 117, we see that at that epoch Arcturus acted as warning-star for the August sun.

In cases where the elevation of the horizon is 30´, or in preliminary examinations, where it may be assumed as 30´, the refraction exactly counterbalances the hill, and therefore the true zenith distance at the moment of star-rise is 90°. Hence the N.P.D. of the star may be found from the following simple equation


cos Δ = cos A cos λ

where Δ and A have the same significance as before and λ is the latitude of the place of observation.


329:1 Demonstrations and Practical Work in Astronomical Physics at the Royal: College of Science, South Kensington. Wyman and Sons, 1s.

331:1 cos (c - θ) = cos - (c - θ).

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