120 



HYDROGRAPHICAL SURVEYING [chap, v. 



Table of 

 Chords 



Calculat- 

 ing 

 Chords. 



A table of chords for a radius of 10 inches is given in Ap- 

 pendix,* which saves mucli time and chance of errors, as the 

 cliord to the angle required can be taken from the table, and 

 multiplied by the radius with which it is meant to lay off the 

 angle, divided by ten ; but in case this is not at hand, we must 

 calculate our own chords. 



Tables of natural sines are not included in Inman's, the 



tables generally in use at sea, and logarithms of sines are in 



that work only given for every fifteen seconds, and we may 



want to take the angles out exactly. Moreover, by using the 



logsine, three logarithms will have to be taken out, and the 



process is somewhat longer. It is simpler, therefore, to use 



the table of natural versines, which are given in Inman to 



seconds. 



ft ft 



As sin - = versine (90+ )-l, our required cliord will be 



n 



2 radius (vers. (90 + ) - 1). 



Versines are given for a radius of 1,000,000, so we have to 

 divide the versine taken out by that number. This reduces 

 the rule in practice to this. 



Look out the natuial versine of 90° + half the required 

 angle, leaving out the left-hand figure 1, and putting a decimal 



Example. 



Fig. 21. 



point before the remaining six figures. Multiply this number 

 by twice the radius, and the result will be the chord required. 



Let us take now an example in practice. 



At A, Fig. 21, the angle between B and C is 35° 14' 30". 

 The hne A L from A passing through B is already drawn. 

 We want to lay off this angle, and requiring accuracy, we 

 take a long radius, i.e., 45 inches. 



* Appendix J. 



