582 



BEPOET — 1893. 



consists in producing the chord of the arc to a point, half its own length 

 distant, and with this point as centre, and with a radius equal to J of 

 the chord, drawing an arc to meet the tangent at that extremity of the arc 

 which is nearer the centre. The length of the tangent so intercepted 

 differs from the actual length of the arc by a distance. 



,^(arc)5 (arc)' 



10807-4 ^54432r« ' * ' 



Culmanu states that ' the only practical method of setting off an arc 

 along a tangent is to plot a chord the same number of times both along 

 the arc and along the tangent, and to add the final remainder ' (this 



Fig. 6. 



operation being indicated in fig. 6), and remarks that this raises the 

 question as to how great an arc must be chosen in order that the error 

 should not be greater than d when an arc a is measured by the plotting 

 of the chord I along it. The difference between an arc and its chord is 



4.6.r2 4. 6. 8. 10. r* 



+ 



this being obtained by expanding from 2r sin ^ and subtracting from the 



2r 



I 



arc a (r denoting the radius of the arc). The error d therefore is — times 

 this difference, since the arc a has been plotted times along I. We have 



therefore 



d= 



I 



aH 



a 24?-2 24r2 



the arc a being chosen so small that the second member of the difference 

 may be neglected with regard to the first ; in which case 



'24d 



/24c 



