50 IMPROVED METHOD OF PROJECTING 



The radius of a circle of which the chord of any given arcli 

 shall contain just as many equal parts of the radius as the arch 

 contains degrees, is easily calculated. The one I have chosen 

 is that of a circle of which the chord ot an arch ot 25 de- 

 grees shall equal 25 parts. This radius is 57.L very nearly. 

 Now it will be found that of this circle the chord of any arch 

 under 30 degrees will never vary more than T *_ part of a unit 

 from the number of degrees in that arch. 



Hence to lay down an angle of any given number of de- 

 grees and parts you have only to take, with a pair of compasses, 

 from any line of equal parts, 571, and with this radius describ- 

 ing an arch, apply thereon, from the same line, the chord of 

 the angles required, if not exceeding 30 degrees; (calling each 

 part or equal division of the line a degree) and the two radii 

 drawn from the center to the points of application on the arch, 

 will contain the angle required. If the given angle exceeds 30 

 degrees, first apply the radius (which equals the chord of 60 de- 

 grees) and then taking from the line of equal parts the chord 

 of the difference between 60 degrees and the given angle, ap- 

 ply it on the arch from 60 either forwards or backwards ac- 

 cording as the given angle is greater or less than 60 degrees. 



The measuring of an angle being only the reverse of the for- 

 mer will consist in describing an arch round the angular point 

 as a center with a radius equal 571, and then applying the 

 chord of this arch comprehended between the two lines inclu- 

 ding the angle, if not exceeding 30 degrees, to the same line 

 of equal parts from which the radius was taken. But if the 

 angle exceeds 30 degrees you must first apply the radius, and 

 then measure the arch of excess or defect above or below 60 as 

 above. 



Though the above method of projecting and measuring an- 

 gles will never be liable to an error of more than five or six 

 minutes of a degree, which in practice may be safely neglect- 

 ed, yet even these small errors may, when thought necessary, 

 be allowed for as follows — 



From 6 decrees to 21) „ , , . (more) 



From 28— to 3o} Ca11 the an S le 5 minutes { l ess } 



than it measures and if this allowance be made the error will 

 scarce ever exceed one minute. 



