Adams. — On Triangulation by Least Squares. 201 



(6.) The foot is naturally cold or artificially cooled. 



These are, I think, the reasons for the facility with which 

 the magicians perform their " fire-walk," and I must say that 

 it is a smart piece of jugglery or "savage magic," and not 

 by any means an inexplicable mystery. 



Eeferences. 



(a.) Chnstchurch Press, 16th July, 1902. 



(b.) New Zealand Graphic, 10th July, 1902. 



(c.) Auckland Weekly News, 17th July, 1902. 



(d.) Trans. N.Z. Inst., vol. xxxi., p. 667. 



(e.) " Camping among Cannibals," by Alfred St. Hill 

 Johnston. Macmillans ; 1886. 



(/.) Nature, 22nd August, 1901. 



(g.) New Zealand Graphic, 10th July, 1902, p. 106. 



(h.) "Journal of the Polynesian Society," vols. ii. and iii. 



(t.) " Journal of the Polynesian Society," vol. ii. 



(;.) Christchurch Press, 16th July, 1902, p. 6. 



(k.) Ibid., p. 55. 



(I.) "Naturalists' Vovage round the World," Darwin, 

 p. 491. 



(m.) Encycl. Britt., vol. x., pp. 260 and 262. 



(n.) Ibid., p. 248. 



Art. XIV.— The Adjustment of Triangulation by Least 



Squares. 



By C. E. Adams, B.Sc. (Honours), A. I. A., late Engineering 

 Entrance Scholar and Engineering Exhibitioner, Canter- 

 bury College ; late Senior Scholar in Physical Science, 

 N.Z. University. 



(Read before the Wellington Philosophical Society, 18th November, 1902.] 



It is proposed in the following paper to select examples of 

 the ordinary methods of adjusting triangulation as practised 

 in New Zealand and to apply to them the least-square adjust- 

 ment, so as to compare the relative results obtained, and to 

 show by actual examples that this method of adjustment alters 

 the observed angles less than any other method. It will also 

 be shown that the least-square adjustment can be simply and 

 readily applied to most cases that occur in practice. 



It is hoped that this treatment of the subject will be of use 

 to the practical computer, and that it will enable him to see 

 the advantages of the least-square adjustment by comparing 

 its results with those usually obtained. 



To make the treatment as simple as possible it will be 

 assumed that all the angles are equally well observed. 



