392 LATITUDE AND LONGITUDE OF CAMPOS RODRIGUES. 



" The geodetic measurements, on this portion of the Portu- 

 guese triangulation, Hnk in the 17 points with 94 directions, so 

 that the calculation of this connection alone would comprise, as 

 is known, the resokition by the method of least squares of a 

 system of 47 equations with 94 unknown (quantities. This, how- 

 ever, would involve an excessive amount of labour, and would 

 not compensate us, seeing that great precision in the result would 

 be almost useless, as it was not necessary to determine the posi- 

 tion of the Observatory with a precision above one-tenth of a 

 second of arc, or three metres in linear extension. 



" This part of the calculations will, however, be done when 

 the compensation for the general network is to be proceeded with. 

 For the present we are quite satisfied (without prejudice to the 

 indispensable accuracy as will be seen) with a provisional com- 

 pensation which is incomparably more rapid. 



" The line from the Observatory to Ipoy is cut at Ipoy by 

 seven other different directions, three of which, Kanghekane, 

 Estatuene and M'Ponduhine, give two independent solutions 

 each. 



" Nine dift'erent values result therefore for the distance 

 Observalory-I})oy, with different weights, and depending on the 

 sine of the angles which served to arrive at the determination of 

 the crossings. The division of 1,000 (an arbitrary number) by 

 the addition of the logarithmic differences corresponding to an 

 error of one second in the original angles was acce])ted as being 

 the weight of each of the crossings mentioned. 



" We could have resorted to two methods in order to find out 

 the most probable distance between the Observatory and Ipoy : 

 the elementary analytical one. being the average with weights ; 

 the other being the graphic study of the most probable crossing, 

 for which I availed myself of the elementarv geometrical pro- 

 cesses which I have employed in rapid triangulations of colonial 

 frontiers. 



" The data for the calculations are summarised in Table I. 



" According to the analytic solution, the mean distance, with 

 weights, is : 



76,828'".6i :t 0^.25 ; 

 the geometrical solution gave a slightly different value : 



76,828"\79 

 the most probable value to acce])t being, therefore, 

 76.828'".7o-bo'".25; 



it being hardly worth while, on account of the labour involved, 

 to ascertain the probable error of the geometrical solution. 



" This value of the distance is founded on the base of Man- 

 hi(;a, which was measured about 80 kilometres North of 

 Lourenco Marcjues, and the length of which was 



1 2, 090'" .9009 i I '"-I ; 



this length being a provisional one, as the actual length depends 



