Page:Madras Journal of Literature and Science, series 1, volume 6 (1837).djvu/160

138 artificial horizon, and, consequently, no altitude can be taken with it above 60°—unless the instrument is made with a second index glass it right angles to the first, and has dark glasses fitted to the second eye hole, when it may be used to measure the sun's altitude when in the zenith with the meridional horizon, and in fact becomes a sort of portable zenith sector. Let A (Pl. 4, fig. 2) be the sun's place near the zenith, B the artificial horizon, and C the place of the eye, and the angle measured by the sextant, then will the sun's zenith distance be equal to half the angle A B C or

$$\begin{align} & = \tfrac{1}{2} (180-\text{L C}) \\ \Theta', \text{Z D} & = 90 - \tfrac{1}{2} \text{C} \text{.} \end{align}$$

In using the circle, Mr. Galbraith says that Captain Kater has observed the latitude by a single observation of the pole star, with only a maximum error of —26″.

No doubt in the hands of so scientific an officer as Captain Kater, the instrument would be made to give more exact results than when used by other persons, but, without attempting to arrive at so much nicety, the instrument from rough observations, such as are likely to be made by travellers, can give results practically very useful, without wasting any more time that would be required with larger instruments.

The following observations for the latitude of Calingapatam were made by reducing the altitude of the sun's lower limb to the meridian by a common watch, the error of which was found by equal altitudes a quarter of an hour before and after the meridian passage.

The three latter observations were made very roughly to ascertain the maximum error possible to take place. In these observations all the work was concluded in 30 minutes, including the observations for equal altitudes.

Had a pocket chronometer been used, the results would doubtlessly have been much more exact, for an error of 8″. in the time, gives an error of 1′ in the latitude, if the hour angle is 20 minutes, as may be found by differencing the formula for reduction.

$$= \frac{2}{\sin l''}\sin^{-2}\tfrac{1}{2} \text{P. cos. deet. cos. lat. cosec Z D}$$

Error $\sin \tfrac{1}{2} \text{P. cos.} \tfrac{1}{2} \text{P.} \frac{\text{cos. lat. cos dec.}}{\sin \text{Z. D.}} \times 2x$ when $x$  is the