e 



K D. Pretton— Measurement of the Penman Arc 7 



It then appears that, the temperature factor alone would give 

 to uncertainties far greater than the difference between the 



two results. i-i i 



The angles of the triangulation were measured with quad« 

 rants whose radii varied from two to three feet. Two tele- 

 scopes were provided, a fixed and movable one, the whole 

 instrument being universally mounted by means of two right- 

 angled cylindrical elbows. Micrometers were here applied to 

 instruments of this kind for the first time, and it is believed 

 , that Bonguer was the first who called attention to errors of 



C eccentricity. As the limb of the instrument only included 

 ninety degrees these errors could not be studied by the method 



^ now 'emploved of comparing diametric readings throughout 



the entire circle. Independent measures of two known angles 



- gave two equations, in which the known quantities were the 



S errors, and a function of the angle itself, and the unknown 



^ quantities were the rectangular coordinates of the center of 

 rotation, referred to the center of graduation as the origin. 

 These coordinates being known from the solution of the equa- 

 tions, corrections applicable to any part of the limb could be 

 calculated. Besides this, six or seven angles, which together 

 closed the horizon, were measured. These were corrected for 

 inclination and their sum compared with 360°. The error of 

 closing was on the average about two minutes. Measures of 

 equilateral triangles gave an additive correction of 20" for an 

 angle of 60°. Other combinations showed a correction of 40" for 

 90°. The separate spaces of five degrees were examined by 

 comparing with a known angle of this magnitude. A month 

 was devoted to the study of the errors of the instrument. 



With instruments capable of this degree of accuracy we can- 

 not expect a close agreement between the measured and calcu- 

 lated base. They differ by about two feet. The triangulation 

 is two hundred miles long and contains thirty-two principal 

 triangles. But the result of the side computations from this 

 principal network was twice modified. Once at the eighth 

 triangle where some auxiliary figures gave a result different 

 by two and one-half toises from the regular work, and again at 

 the sixteenth, where results having a range of seven-tenths^ of 

 a toise were obtained, from three different methods of deriving 

 the same line. In both these cases the auxiliary work was 

 combined with the regular triangulation, and the resulting line 

 upon which the succeeding work depended, was changed by 

 one and one-tenth toises in the first instance, and by three- 

 tenths- of a toise in the second ; so that we should not be sur- 

 prised at a much greater discrepancy between calculation and 

 observation at the end of the chain of triangles. Bouguer 

 shows that admitting an error of 15" in each angle the accn- 



