An Improvised Dip Meter

5 04 2012

On 19 March this year (2012) on NavList, Alex Eremenko reported some strange results for observations made by him and a friend from the shores of Lake Michigan. Much discussion followed about abnormal refraction conditions that can cause large errors in the dip of the horizon and the possibility that clocks corrected by radio signals could occasionally be in error by a whole minute. As correcting the observations for an error of a whole minute in time then gave results that were uniformly as good as these experienced observers normally obtained, it seemed to Alex (and to me) that the clock hypothesis was the correct one. However, discussion of the matter then moved on (28 March) to how to determine whether there is abnormal dip of the horizon, a condition likely to occur when there is warm air over cool water, which is particularly common and severe in arctic regions. Uncertainty about dip swamps most other potential errors in measuring the altitudes of heavenly bodies at sea.

Figure 1: Dip with and without allowance for refraction

For those not familiar with the concept of dip, Figure 1 shows that the height, h, of the eye of an observer O affects the apparent horizontal. This is shown in dotted red. But, especially close to the horizontal, light does not travel in straight lines, because the density of the atmosphere decreases with height. Generally the light path, shown in full green, is bent or refracted so that it is convex upwards. This has the effect of making the distance to the horizon greater and the angle between the apparent and true horizontals, the dip, smaller. However, when atmospheric conditions are abnormal it can be much greater or even reversed. For a much fuller treatement of dip and its abnormalities, see

 If the angle between the horizon in front of the observer and the horizon behind him can be measured, then dip can be deduced directly, as it is half the value of that angle.This is not a new problem. In 1900, John Blish of the United States Navy applied for a patent for an attachment to add to a normal sextant. The patent can be viewed on Google Patents by searching for Patent number 714,276. Figure 2 shows one of the patent drawings.

Figure 2 : Blish prism attached to nautical sextant.

Essentially, the device is a prism that diverts light rays through 180 degrees so that the horizon directly behind the observer can be viewed at the same time as the horizon in front and the amount of dip read out directly from the sextant’s scale.

Several other inventors devised instruments or attachments to do the same thing. Among the more complex dedicated instruments was one patented by Boris Gavrisheff in 1961 (US Patent number 2,981,143). A telescope views via two prisms light coming from one horizon behind the observer at the same time as the light from the horizon in front of the observer. One of the prisms is rotatable so that the deviation from 180 degrees, i.e. the dip, can be directly read off a micrometer drum. A third prism, labelled 12 in the diagram, diverts the rays into a telescope (Figure 3).

Figure 3 : Gabrisheff’s dip meter.

It occurred to me that expensive prisms are not needed. They are not used in nautical sextants though for some reason most American bubble sextants used them. I had a box of wreckage from three Hughes and Son Mark III survey sextants that a kind friend gave me, so I set about building a dip meter as an exercise to illustrate the principle rather than as a serious sea-going device, though it could certainly be made more robust for sea-going use. An index arm extension carries a mirror that receives light from the rear horizon over the top of the observer’s head and diverts it through 45 degrees into another mirror that diverts it another 45 degrees into the telescope. The telescope receives light from the front horizon over the top of the second mirror so that, provided the mirrors are correctly aligned, both horizons can be viewed at once and the deviation from a straight line be measured using the micrometer drum. Figure 4 shows the layout of parts and Figure 5 the path of the light rays from front and back.

Figure 4 : Parts of the dip meter

Figure 5 : Ray path of dip meter.

Figure 6 shows how the dip meter is adjusted. Two autocollimators are set up facing each other and their axes adjusted so that they coincide in the vertical and horizontal planes and are parallel to the surface of the surface table. One is then “shuffled” sideways using a mirror, so that its axis is displaced from but remains parallel to the axis of the other. The plane of the sextant’s arc is set parallel to the table using a dial indicator and shims under the feet of the sextant. The sextant is set to zero and the two mirrors adjusted until the images of the crosswires of the autocollimators coincide when viewed through the telescope. The dip meter is then ready to measure the angle of dip directly.

Figure 5 : Light paths from the autocollimators

Figure 6 shows how the mirrors are adjusted, the same way that an horizon mirror in a standard sextant is adjusted, with screws bearing on the back of the mirror opposite spring clips bearing on the front.

Figure 6 : Mirror adjusting screws.

If you enjoyed reading this post, you will enjoy reading my book The Nautical Sextant, available from the joint publishers, Paradise Cay and Celestaire and via Amazon. Readers in Australia and New Zealand may Contact me, as I am able to offer them a discount on the published price.