W. Harkness — Magnitude of the Solar System. 247 



to tlie effect upon adjacent triangles. Consequently the adjust- 

 ment of the errors was imperfect, and in computing the interval 

 between any two distant points the result would vary some- 

 what with the triangles used in the computation — that is, if 

 one computation was made through a chain of triangles run- 

 ning around on the right hand side, another through a chain 

 of triangles running straight between the two points, and a 

 third through a chain of triangles running around on the left 

 hand side, the results were usually all different. At that time 

 things were less highly specialized than now, and all geodetic 

 operations were yet in the hands of first-rate astronomers who 

 soon devised processes for overcoming the difficulty. They 

 imagined every observed angle to be subject to a small correc- 

 tion, and as these corrections were all entangled with each 

 other through the geometrical conditions of the net, by a most 

 ingenious application of the method of least squares they deter- 

 mined them all simultaneously in such a way as to satisfy the 

 whole of the geometrical conditions. Thus the best possible 

 adjustment was obtained, and no matter what triangles were 

 used in passing from one point to another, the result was 

 always the same. That method is now applied to every impor- 

 tant triangulation, and its omission would be regarded as proof 

 of incompetency on the part of those in charge of the work. 



Now let us compare the conditions existing respectively in 

 a triangulation net and in the group of quantities for the deter- 

 mination of the solar parallax. In the net every angle is sub- 

 ject to a small correction, and the whole system of corrections 

 must be so determined as to make the sum of their weighted 

 squares a minimum, and at the same time satisfy all the geo- 

 metrical conditions of the net. Like the triangles, the quanti- 

 ties composing the group from which the solar parallax must 

 be determined are all subject to error, and therefore we must 

 regard each of them as requiring a small correction, and all 

 these corrections must be so determined as to make the sum of 

 their weighted squares a minimum, and at the same time satisfy 

 every one of the equations expressing the relations between 

 the various components of the group. 



Thus it appears that the method required for adjusting the 

 solar . parallax and its related constants is in all respects the 

 same as that which has so long been used for adjusting systems 

 of triangulation, and as the latter method was invented by 

 astronomers, it is natural to inquire why they have not applied 

 it to the fundamental problem of their own science % The 

 reasons are various, but they may all be classed under two 

 heads. First, an inveterate habit of over-estimating the accu- 

 racy of our own work as compared with that of others ; and 

 second, the unfortunate effect of too much specialization. 



