162 



Mr Galbraith on Trigonometrical 



employed. The fourth and fj/lh tables have already been ex- 

 plained. 



Practical Rides. 

 To illustrate the method of employing these tables in calculation, let P 

 be the north pole in this instance, E a point in the equator, B a point of 

 which the latitude and longitude are known, T another place whose 

 bearing and distance from B are given, and from these the latitude and 

 longitude of T, and the azimuth of B from T, are required. 



Also let PBE be the meridian passing through B, PTF the meridian 

 passing through T, PBT the azimuth de- 

 noted by a in the tables, or m' in the formu- 

 la, BT the distance or curvilineal arc a in 

 feet, of which the chord is k, Tx a perpen- 

 dicular from T, the required point upon 

 the meridian passing through the given 

 point B, the distance from the foot of 

 which from the equator, measured by Ex, 

 is the latitude of x ; /' the latitude of the 

 place nearest the equator, / that of the 

 more distant, and Tl the parallel of lati- 

 tude passing through T, making E / the 

 the latitude of T, or that required. 



It must likewise be observed that B x is 

 a small arc of the meridian to be added to 

 the given latitude in proceeding towards 

 the pole, or subtracted when receding 

 from it, to give the latitude of the foot of 



the perpendicular x, the argument for taking the log. P from the tables. 

 The argniment to obtain M is half the sum of the latitudes approximately 

 or 4 (/ 4- I'), to be derived from a provisory calculation, in order to get 

 the mean latitude between the given stations. The number of minutes 

 to be added to the smaller latitude l' or substracted from the greater / 

 to get i(J + 1') may be computed from the following rule. 



To the constant logarithm 5.914630, add the log. of the meridian dis- 

 tance in feet, the sum will be the log. of half the difference of latitude 

 in minutes, or I (Z — /') to be added to /', or subtracted from /, to give 

 ^ (/ 4- I') the middle latitude, sufficiently near the truth for taking 

 log. M from the tables. 



1. By a provisory calculation, such as that just given, or, by a repeti- 

 tion of the more accurate method now to be shewn, if thought necessary, 

 find the middle latitude or ^ (/ -j- l'). 



2. To the logarithm of the curvilineal distance, or arc o, add the 

 log. cosine of the azimuth, or m, and the log. M from the tables, I., IV,, or 



