866 



MR HENRY BRIGGS ON 



purposes does not depend merely on its shape, but also on the relative accuracy of the 

 base and angles. 



Now, since the lines of a triangulation become affected with a greater average error 

 the further one proceeds from the base (see equation (30)), and as each of these lines 

 virtually serves as base for the triangle depending on it, it follows that it is permissible 

 in practice to use triangles towards the end of a scheme departing more from the perfect 

 shape than those near the beginning. We can also conclude, that, whenever circum- 



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10 10 30 40 50 60 70 80 90 100 110 110 130 140 ISO ISO 170 ISO DCCRECS 



VALUE OF APICAL ANCLE 'C 1 



Fig. 5. 



stances are such as to preclude accurate base-measurement, the best aim in laying out 

 the scheme is not to arrange the triangles as nearly equilateral as possible, but purposely 

 to elongate them so as to cover the area with a,s few triangles as possible. 



Referring again to curve B, it is seen that even when the base is measured with an 

 accuracy commensurate with that of the angles, too great a stress may be laid in practice 

 on striving after the equilateral shape, for isosceles triangles in which the apical angles 

 lie anywhere between 50° and 90° are all almost equally well-conditioned. This fact 

 simplifies the subsequent work, for we can now proceed to consider schemes built of 

 equilateral triangles, knowing that the results attained will be of almost equal practical 

 value for triangles departing considerably from that shape. 



