86 Mr. Nixon on the Measurement by Trigonometry of the 



would, without doubt, have materially increased their accuracy 

 to have repeated them (circumstances permitting) with the 

 telescope reversed in position ; but such was the inconvenient 

 situation of the tangent screw of the upper circle, as to render 

 the method impracticable*. To make a second set of obser- 

 vations with the telescope in its original position was the only 

 alternative. 



As data for the reduction of the observations to the centre 

 of the base of the signal, the telescope was pointed so as to 

 bisect the latter, and the reading of the verniers in addition 

 to the distance of the centre of the circles to that of the signal 

 registered in the usual manner. In order to comprehend the 

 nature of the reduction, let S in the annexed figure represent 



. o 



the centre of the signal, T that of the divided circle, U the 

 prolongation of the straight line passing through S and T, and 

 O the object observed. Make TO' parallel to SO ; then, as 

 the angle USO equals that of UTO', the angle USO must 

 exceed the observed angle UTO by the angle OTO', equal 

 to SOT. It is -also clear that the observed angle, whether 

 acute or obtuse, to the left or right of the line UST, will al- 

 ways be in defect. To calculate the angle SOT we have 

 given the angle STO, the side ST, and (approximative^) that 

 of SO. Then, as the graduations of the circle are numbered 

 from left to right, the angle at T between U (or S) and an 

 object O to the right, will be equal to the reading of O minus 

 that of U ; and we must add the angle of correction SOT to 

 O, in order to make the registered readings coincide with those 

 of another theodolite placed over S, the reading for U being 

 alike by the two instruments. When the object (P) is to 

 the left of the line UST, it will form with it at T an angle 

 * I have since discovered that, by unfixing the clamp on the upper pa- 

 rallel plate, the circles might have been moved half-round in azimuth. 



equal 



