138 



Remarks on the use of 



[July 



artificial horizon, and, consequently, no altitude can be taken with it 

 above 60°— unless the instrument is made with a second index glass at 

 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 port- 

 able zenith sector. Let A (PI. 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 



= -1(180— LC) 

 O' , Z D = 90 - \ C. 



In using the circle, Mr. Galbraith says that Captain Kater has ob- 

 served the latitude by a single observation of the pole star, with only 

 a maximum error of — 28''. 



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. 



1st mean of 12 altitudes. r= 18° 19' 32" N. 



2d do. 13 do. = 18 19 34 



3d do. 8 do. , =18 1*9 55 



4th do. 9 do. = 18 19 9 



5th by a watch without a second, wanting for the seconds. 

 Mean of 6 altitudes. ~ 18° 20' 17" 



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 er- 

 ror of 1' in the latitude, if the hour angle is 20 minutes, as may be 

 found by differencing the formula for reduction. 



2 2 



~sin i" sin § P. cos. dect. cos. lat. cosec Z D 



^ . t t~. , -r> cos. lat. cos dec. n •> i „ . a 



Error = sin I P. cos. \ P. . — =- . 2 x when x" is the 



sin Z. D. 



