64 
So that the longitude of the stations in the county of Longford 
may be considered as certain within a furlong. I have connected 
the triangulation through Roscommon with some of the stations 
made use of by Mr. Bald in his excellent map of Mayo. 
Even with the slight data, that I can now give, the differ- 
ence of latitude and longitude of the east and west coast of 
this island is known within a few seconds of time. The principal 
angles in Roscommon I took in the year 1814, with a six inch 
theodolite made by Troughton. 
~ But Iam now in possession of a repeating circle of eighteen 
inches diameter of his make ; and a repeating theodolite of Reich- 
enback, which, from the trials that Major Colby and Captain Kater 
kindly encouraged me to make of this instrument, at some of the 
trigonometrical stations in England, in comparison with the cele- 
brated theodolite of Ramsden, I think I could be as certain of an 
angle to two seconds, as formerly I was to twenty seconds. 
So that it would be well worth while to employ this repeating 
theodolite to correct, by a few well chosen triangles, Galway and 
Sligo with Dublin, and to determine exactly the distance on the 
meridian between Dublin and Armagh Observatories. A few more 
triangles would connect Armagh with the stations on the coast of 
Ireland, which have been intersected by Major Colby. 
If I were to give a diagram of all the triangles that I determined 
in Roscommon, you would find a station nearly in every square mile, 
as my object was to secure the accuracy of the map. 
The manner in which | laid down the triangles on paper may 
be found useful to those few who are employed in similar labors. 
After having carefully drawn mile squares of four inches asunder, 
and laid down a long base, I made use of a nine inch protractor 
of Troughton’s, with extending conical points. Over one of these 
