S96 SURVEY OF THE COAST 



subject of the present papers, I had reason to entertain the 

 liighest expectations. It was executed under my own in- 

 spection l)y that distinguished artist Mr, Edward Trougliton 

 of London, agreeably to our united views, and with that in- 

 terest for its success, which the great friendship with which 

 lie was pleased to favour me could alone inspire. 



The actual operations made at a station of a survey on 

 solid ground, in a proper place, with good signals, ^c. are in 

 every respect best adapted for the trial of the instruments, 

 and ibr devising a proper method of observing with them. 



From the remarks which will be found in their proper 

 place, on the method of dividing used in England, it may be 

 observed and has been observed already by Ramsden in de- 

 scribing his dividing engine, that the exact placing of the 

 axis in the centre of the division is still effected by trials and 

 indirect means, and that when obtained exact, it may even 

 lose this position by transportation or accident. It will there- 

 fore be proper to inquire whether the instrument be well 

 centred or not, and, at all events, to use the indiscriminate 

 mean of the two or more equidistant readings, which are 

 now made on every instrument, as one single reading would 

 be affected by the whole error of the eccentricity. 



The half sum of any two vertical arcs in a circle is equal 

 to the arc at the centre. Therefore the indiscriminate mean 

 of any even number of opposite readings on an instrument 

 will be equal to the angle at the centre. Also the third of 

 of three angles at the same point out of the centre of the 

 circle is equal to the angle at the centre of the circle. And 

 in general it will be seen, that the indiscriminate mean of any 

 number of equidistant readings will be equal to the angle at 

 the centre of the circle. This property is new as far as I 

 know, and may be demonstrated as follows : 



Plate V. fig. 1. — Let C be the centre of the division, C the 

 centre of motion, d the point on the limb marking the read- 

 ing of the alhidade ; C<f=the radius of the division. Then 

 C'CM is the line joining these two centres (protracted), 



