108 HYDROGRAPHICAL SURVEYINCx [ciiAr. iv. 



The true difference of longitude can also be calculated from 

 the tables of lengths of a minute of latitude and longitude in 

 the Appendix M as follows : 



No. of feet in minute of Lat. 



True diff. long. = dep. ^^ — --7- — : — 7 — t^ — ~~ 



No. of feet m minute 01 Long. 



Working out the above example this way, we have : 



Dep 1-973128 



6053 3-781971 



5-755099 

 6722 3-757548 



2V«ed. long .. 1-997551 99-44' 



or 1° 39' 26-4" 



which gives the same result as the other method. 

 Calcuia- When calculating the true bearing between two points whose 

 T^^^ Bear- astronomical positions are known, it is necessary in the first 

 ing be- place to calculate the spheroidal correction, and add the cor- 

 Astrouo^° rection to the true (or chronometric) longitude to obtain the 

 micai spherical diff. long. 



lositions. ^Yiti^ the spherical diff. long, and diff. lat. the mercatorial 



bearing and distance is found by middle latitude sailing, which 



is an equally correct but shorter method than that by spherical 



trigonometry, and may be safely used when dealing with 



distances not exceeding 120 miles. 



Correct- In the example of triangulation we have given we have 



ing Tri- supposed ourselves to be working from a measured base. If 



tion for the survey is extensive, the ultimate scale of the chart will 



Error of (depend upon the astronomical positions. It is very unlikely 



rary Base that when these are obtained, the distance between the extreme 



and Bear- pQJj^^g depending upon them will agree exactly with that 



deduced from the short side, and therefore all the sides will 



want correction in probably both bearing and distance. 



The readiest way of doing this is to get a proportion between 

 the two total distances, as found by the triangulation and by 

 the astronomical positions respectively, in the shape of a 

 logarithm, and multiply each side found by it, which will give 

 the true value as dependent on observations. The bearing 



