VOL. XIX.] PHILOSOPHICAL TRANSACTIONS. 181 



the meridian shown by a needle, agree but in very few places of the world; and 

 this too, but for a little time together. The difference between the true and 

 the magnetic meridians perpetually varying, and changing in all places, and at 

 all times ; sometimes to the eastward, and sometimes to the westward. 



On which account it is impossible to compare two surveys of the same place, 

 taken at distant times, by magnetic instruments, (such as the circumferentor, by 

 which the Down survey, or Sir William Petty 's Survey of Ireland was taken,) 

 without due allowance be made for this variation. But this is not to be under- 

 stood, as if a map of the same place, taken by magnetic instruments at never 

 so distant times, should not at one time give the same figure and contents as at 

 another time. This certainly it will do most exactly, the variation of the needle 

 having nothing to do either in the shape or contents of the survey. All that 

 is affected by it, is, the bearings of the lines run by the chain, and the boun- 

 daries between neighbours. And how this may cause a considerable error, 

 unless due allowance be made for it, is fully proved thus. 



Let AB, fig. 3, pi. 4, represent the survey of two lands, one in the possession 

 of A, and the other in the possession of b, taken for instance, An. (657, when 

 there was no variation. Let the line ns, running through the point p, be the 

 true meridian, and consequently the magnetic meridian also at that time ; and 

 let this line ns be also the boundary between the two lands a and b. In 1695, 

 when the variation is supposed to be 7° from the north to the westward, b 

 having a map of the former survey, and suspecting that his neighbour a had in- 

 croached on him, by a ditch pa, employs a surveyor to enquire into the matter : 

 the surveyor finds by his map, that the boundary between B and his neighbour 

 A ran from the point p through a meadow directly according to the magnetic 

 meridian spn ; but observing the ditch pa cast up much to the eastward of the 

 present magnetic meridian, he concludes that a has encroached on b, and that 

 the ditch ought to have been cast up along the line pq, the angle apq being an 

 angle of 7°, that is the present variation of the needle ; and the line pq the pre- 

 sent magnetic meridian : for which variation, not making any allowance, he 

 positively determines that b has all the land in the triangle opq, more than he 

 ought to have ; and that his ditch ought to run along the line pq. 



It is true indeed, if the surveyor go the whole round of the lands a and b, 

 he will find their figure and contents exactly agreeable to the map. But then 

 the bearings of the lines are all 7° different from the bearings in the map, and 

 they will run in and out upon the adjacent neighbouring lands, and cause end- 

 less disputes between their possessors ; as is manifest from the figure, wherein 

 the pricked lines represent the disagreement in the bearings of the lines, pro- 

 tracted from the point p : and we see a encroaching on his neigiibours on the 



