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reasons advanced in paragraph 29, the results may be affirmed to be based upon the false supposition of the earth being a plane instead of a sphere. Now, as the difference between an arc on the earth’s surface and its chord amounts only to 34 feet in 69½ miles, and as the limit of error assigned for our work is considerably greater than this amount, it follows that for the purposes intended the omission is immaterial, and taking into consideration the means at command, it may also be advanced that the computations have been affected on the true assumption of the sphericity of the earth with as much propriety as if the very small necessary corrections had been strictly attended to.

Computations of Latitudes and Longitudes.

39. Hitherto the plot of the work has been entirely based on the principles of Plane Trigonometry. Sir John Herschel remarks, "The true way of conceiving the subject of a Trigonometrical Survey when the spherical form of the Earth is taken into consideration is to regard the network of triangles with which the country is covered as the bases of an assemblage of pyramids converging to the centre of the Earth." With reference to these observations instructions for the computations of the latitudes and longitudes of the stations and the convergency of the meridians from the computed sides and bearings of the triangulation, and for the graticule of the map will be hereafter issued.

Minor Triangulation.

Instructions for the Major Series generally applicable for the Minor Series.

40. As ample instructions have been given for conducting the Major Series of triangles upon principles the best suited for the attainment of a degree of accuracy to be within an assigned limit of error, and as the same principles modified are generally adaptable to all trigonometrical operations, it is only necessary to show, without repeating that which has already been described, their application to the Minor Series of triangles succeeding the first process.

Average size of the Triangles, and the class of Instrument to be used.

41. The sides of the triangles should average from 2½ to 5 miles, and the class of instruments the best adapted for the work is the 5 or 6 inch Transit and Everest Theodolites.

Triangles to be based upon the sides furnished from Major Series.

42. The base should be derived whenever practicable from the sides of the major triangles by what is technically termed "breaking down" from the latter sides.

Thus the sides AC, BC of a major series furnish suitable bases for the determination of the minor points D, E and F, and the sides deduced from such data become in turn new bases for extension of the minor series. When it is impracticable to emanate a base from the major series of triangles, recourse must be had to actual measurement, as detailed in paragraphs 12 to 15. The measured length ought not to be less than one mile, and the limit of error allowable is one link for every hundred chains.

Form of the figures for extension of the Triangles and manner of marking the Stations.

43. Extension of the triangles by net work or in longitudinal series throwing out additional triangles from the flanks where required according to circumstances that present themselves should be adopted taking care that every major point that lies within or adjacent to the scope of operations becomes also a point of the series, thus incorporating the whole of the work so as to form an harmonious combination. The stations are to be marked with the totara block and iron peg described in paragraph 17.

Angular Observations and limit of error.

44. All three angles of every triangle for extension must be measured with the same care for guarding against errors as explained in paragraphs 21 to 26. The triangular errors from experience have been proved to average less than 20'', and in any case should not exceed the limit of one minute.

Tertiary points fixed by intersection.

45. Tertiary points lying within the minor series of triangles should be determined by intersection from at least three