108 ON THE MAGNITUDE OF THE SOLAR SYSTEM. 



When a country is covered with a net of triangles it is always found 

 that the observed angles are subject to a certain amount of error, aud 

 a century ago it was the habit to correct the angles in each triangle 

 without much regard to the effect upon adjacent triangles. Conse- 

 quently the adjustment 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 tlie computation — that is, if one compu- 

 tation was made through a chain of triangles running 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 run- 

 ning around on the left-hand side, the results were usually all different. 

 At that time things were less highly specialized than now, and all geo- 

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

 soon devised processes for overcoming the difiBculty. They imagined 

 every observed angle to be subject to a small correction, 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 determined them all simultaneously in such a way as 

 to satisfy the whole of the geometrical conditions. Thus the best possi- 

 ble 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 important triangulation, and its 

 omission would be regarded as proof of incompetency on the iiart of 

 those in charge of the work. 



Now let us compare the conditions existing respectively in a trian- 

 gulation net and in the group of quantities for the determination of the 

 solar parallax. In the net every angle is subject 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 geometrical conditions of the net. Like the triangles, 

 the quantities 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 determaied 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 tlie various (•om])onents of the group. 



Thus it appears that the method required for adjusting the solar par- 

 allax 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 incjuire 

 Why have they 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 overestimating the accuracy 

 of our own work as comx^ared with that of others; and second, the 

 unfortunate effect of too much specialization. 



