propofed trigonometrical Operation * 2 r <y 
As far as we are enabled to judge at prefent, from the exa- 
mination of the divifions of Mr. Ramsden’s inftrument, 
there is every reafon to believe, that in taking angles around 
the horizon, the mean of feveral repetitions of the fame angle, 
as referred to different parts of the circumference of the circle, 
will differ verv little from the truth, fo little indeed, that in 
many cafes the error will totally vanifh. But in elevating the 
telefcope towards the pole, let us fuppofe that an error of 5 
feconds on each of the contained angles at ‘Tatter lees has been 
committed ; and further, that even an error of 5 feconds of 
latitude, equal to about 84! fathoms on the meridian, may 
have been fallen into, in effimating the co-latitude (which 
never can happen, but is only here admitted, to place the 
example in themoftdifadvantageouscircumftances pofftble); then 
whoever will give themfelves the trouble to recompute the two 
triangles with thefe new data , will find the refult in longitude 
not to be varied thereby, in the firff cafe above -Jth part of a 
fecond, or r x T th part °f a ^ ec °ud in time ; and in the laff not 
quite 1 fecond, or -Arth part of a fecond in time. Hence I 
conclude, that the beft mode of determining the differences of 
longitude will be by the inftrument itfelf, applied in this way, 
in taking the angles between the pole ftar and very remote 
Rations, diftinguifhable at night by the help of the Indian 
lights, and whofe diftance is accurately known. This method 
will, it is true, be liable, as well as aftronomical obfervations, 
to the imperfections of the inftrument, particularly thofe of 
the telefcope, and the unavoidable error in its application ; but, 
on the other hand, it will be entirely free from the irregula- 
rities of clocks, and the imperfections of vifion in marking 
the inftantaneous explolion of light. When both methods 
have, been repeated a fufficient number of times, with all 
F f 2 imaginable 
