262 



Sir W. Thomson on the Determination of a [Jan. 19, 



to these values of b are to be taken as approximate declination, hour-angle, 

 altitude, and azimuth. 



(4) Either in the same or in a contiguous vertical column find similarly 

 another set of four approximate values, the two sets being such that one of 

 the declinations is a little less and the other a little greater than the true 

 declination. 



(5) On the assumed parallel of latitude mark off the points for which 

 the actual hour-angles at the time of observation were exactly equal to the 

 approximate hour-angles thus taken from the Table. With these points as 

 centres, and with radii equal (miles for minutes) to the differences of the 

 approximate altitude from the observed altitude, describe circles. By aid 

 of a parallel ruler and protractor *, draw tangents to these circles, inclined to 

 the parallel of latitude, at angles equal to the approximate azimuths taken 

 from the Table. These angles, if taken on the side of the parallel away 

 from the sun, must be measured from the easterly direction, or the westerly 

 direction, according as the observation was made before or after noon. The 

 tangent must be taken on the side of the circle towards the sun, or from 

 the sun, according as the observed altitude was greater or less than the ap- 

 proximate altitude taken from the Tables in each case. The two tangents 

 thus drawn will be found very nearly parallel. Draw a line dividing the 

 space between them into parts proportional to the differences of the true 

 declination, from the two approximate values taken from the Tables. The 

 ship's place at the time of the observation was somewhere on the line thus 

 found. 



To facilitate the execution of clause (2) of the rule, a narrow slip of card 

 should be prepared with numbers to 90 printed or written upon it at 

 equal intervals, in a vertical column, equal to the intervals in the vertical 

 column of the Table, being at the top and 90 at the bottom of the column 

 as in the Table. Place number 90 of the card abreast of a value of co-hy- 

 potenuse in the Table approximately equal to the declination, and look for 

 the other co-hypotenuse abreast of the number on the card equal to the 

 assumed latitude. Shift the card from column to column according to 

 this condition until the co-hypotenuse abreast of the number on the card 

 equal to the assumed latitude is found to agree approximately enough 

 with the observed altitude. 



When the declination and latitude are of contrary names and the 

 azimuth less than 90°, or when they are of the same names, but the 

 declination greater than the latitude, the sum, instead of the difference, of 

 the legs b of the two triangles will be equal to the complement of the 

 assumed latitude ; and clause (2) of the rule must be altered accordingly. 

 The slip of card in this case cannot be used ; but the following scarcely 

 less easy process is to be practised. Put one point of a pair of compasses 

 on a position in one of the vertical columns of the hypotenuse abreast of 



* A circle divided to degrees, and having its centre at the centre of the chart, ought 

 to be printed on every chart. This, rendering in all cases the use of a separate pro- 

 tractor unnecessary, would be useful for many purposes. 



