Life^ Researches^ and Discoveries of F. W. Bessel 317 

 zenith sector and repeating circle, which had hitherto been used 



for that purpose. As respects the calculation of the triangles, 

 also, a general mode of treatment was now, for the first time, 

 adopted, combining the whole system of observations in all the 

 triangles, so as to lead to a single conclusion as to the final results 

 of the total work, and not (as had been the practice in all pre- 

 vious cases) to derive by several distinct combinations several 

 distinct conclusions, either as to the whole or to subordinate parts. 

 In the method pursued, each triangle is supposed affected with 

 unknown or rather indeterminate errors in all its angles. The 

 observations of the angles in each, with the application of the 

 spheroidical excess, gives a sum to which all the errors must con- 

 form as nearly as possible. In the language of modern compu- 

 tation, it affords an equation of condition which takes its place 

 and acquires its due influence as an element of a final system of 

 similar equations, whose joint solution is then accomplished by 

 the application of that powerful process, the method of least 

 squares, to which our knowledge of physical truth is so much 

 indebted. In the measurement of the base, also, much ingenious 

 contrivance and many peculiar features occur ; and the operation, 

 taken all together, will ever be regarded, apart from its adventi- 

 tious circumstances of interest, as one of the most instructive 

 geodesical measurements which has ever been performed. 



occu 



the general subject of the figure of the earth, as resulting from 

 geodesical measurements, and more especially to the best and 

 most effectual means of availing ourselves of the vast accumula- 

 tion of data obtained at such enormous cost and labor, m India, 

 in France, in Britain, and elsewhere. To grasp the whole of 

 this mass under one general and systematic process of reduction 

 and calculation appeared to him an object worthy of his powers, 

 and this design was carried out in that powerful, regular, and at 

 the same time highly artificial mode which had now become ha- 

 bitual to him, in a series of Memoirs communicated to the Astron. 

 Nachr., 333-6, 338. The first of these contains the general ex- 

 hibition of the most advantageous mode of combining the sev- 

 eral independent measures of meridian arcs, so as to obtain by 

 the method of least squares the most probable result as to the di- 

 mensions of the terrestrial spheroid, and applies that method to 

 the received values of the arcs, as given by their severa mea- 

 surers, taking for granted the correctness of their computation ot 

 their own triangles, and the latitudes of their extreme points, 

 out he did not stop here. On 





deepe 



enter upon a recomj 

 pal stations in the Briti 



frv or^tirAhr according to 



<* combination used in his own East Prussian tnangulation, the 



