8G2 MR HENRY BRIGGS ON 



that such a result as that just obtained {viz., L = 23 feet) can only be a very rough one 

 even under the stated conditions, and must by no means be taken as being generally 

 correct. In this instance it is the method illustrated which possesses value, and not the 

 result derived. There are so many factors to be taken into account that it is not 

 possible to discuss the general case completely. In the above example we have, if any- 

 thing, favoured the theodolite in assuming (3\ the error in bearing of the first line of the 

 traverse as being zero. Were a value to be taken for fi\, equation (8) would need to 

 be applied to include its effect, Wfi\ being written instead of x v and the " total 

 error" from (20) instead of x 2 . Now, it is evidently quite impossible to give any 

 specific value to ^\ such as would serve, even approximately, as a general average ; the 

 magnitude of ft\ depends on things at present outside our knowledge— namely, on what 

 occurred prior to the commencement of the traverse under discussion. Questions such 

 as the following immediately arise in reference to this initial error : Does the theodolite 

 traverse commence from a triangulation station and become oriented by means of a pre- 

 liminary sight over a triangulation line ? If so, may it be assumed that the triangulation 

 was conducted with such a degree of accuracy that the assumption fi\ = is sufficiently 

 near the truth for our purpose ? Or, was the traverse oriented by taking the magnetic 

 bearing of the first line using, say, the trough compass ? — in which case ft\ can by no 

 means be neglected. These, among other possible cases, will serve to show the difficulty 

 of dealing with the problem in a general way ; yet, in making a comparison of the 

 compass and theodolite under any actually existing set of conditions, all questions such 

 as the above are quickly answered. 



When the comparison is made between a theodolite traverse referred to the true 

 meridian and a compass traverse referred to the magnetic meridian, another factor of 

 the first importance enters, namely, the accuracy by which the magnetic meridian 

 has been determined. In the case where the compass can be sighted over a line — such 

 as a triangulation line — whose true bearing has been carefully computed, the declination 

 may be taken as being determined with an average error of u ; the average total error 

 in the compass traverse must then be adjusted by means of (8), x x being Wu, and x 2 

 the value given by (19). 



In short, while it is a matter of the greatest difficulty to make any serviceable 

 general comparison between the accuracy of compass and theodolite traversing, it is 

 not at all so difficult to make a comparison to suit any set of conditions which may 

 arise in practice. 



Section V. The Propagation of Errors in Minor Triangulation. 



To solve any triangle of a triangulation scheme it is necessary to know the angles 

 of the triangle and the length of one side. In the first triangle of the scheme the 

 length of one side is actually measured, and this line is termed the base of the scheme. 

 Every angle in every main triangle is measured by the theodolite ; it is only in 



