J 82 PHILOSOPHICAL TRANSACTIONS. [aNNO I697, 



westward, as he is encroached on by b, and b's eastward neighbours encroach- 

 ing on him, and so forward and clear round. Whereas, by a due allowance for 

 the variation of the needle, all this confusion and disagreement is avoided, and 

 every thing fits right. 



What is here said, on supposition that the magnet had no variation at the 

 time of the first survey taken, and that it had 7° variation westward at the time 

 of the second survey, may easily be accommodated to any other variations at the 

 first and second surveys, mutatis mutandis ; for knowing the variations, we 

 knovir tiieir difference ; and if we know their difference, this gives us the angle 

 apq, by which we reduce them to each other. The best way therefore to make 

 maps invariable would be, for the surveyors who use magnetic instruments, to 

 make always allowance for the magnetic variation, and to protract and plot by 

 the true meridian. 



Periiaps it may be objected, that surveys may be taken without magnetic in- 

 struments, and that therefore this error, arising from the magnetic variation, 

 and change in the bearing of lines, may be avoided. To which I answer, first, 

 that granting a survey may be taken without magnetic instruments, this is 

 nothing against what we have laid down relating to surveys that are taken with 

 magnetic instruments, as the Down survey actually was, and as most surveys at 

 present actually are taken. Secondly, Though a survey may be taken truly 

 without magnetic instruments, so as to show the exact angles and lines of the 

 plot, and consequently the true contents, yet this will not give the true bear- 

 ings of the lines, or show my position in relation to my neighbours, or the other 

 parts of the country. This must be supplied by the magnet, or something 

 equivalent, as finding a true meridian line on your land by celestial observations. 

 And I doubt not but the ancient Egyptians, before the discovery of the magnet, 

 were forced to employ some such expedient in their surveys, and applotments of 

 lands, after the inundations of the Nile ; which, we are told, gave the firs-t 

 original to geometry and surveying. 



And this leads to another objection, which may be made against the instance 

 before laid down : it may be said, that certainly the surveyor which b employed 

 was very ignorant, who would choose to judge of the line pq, rather by its 

 bearing than by determining the point a, by measuring from h and g. To this 

 I answer, what if both the points h and g were vanished since the Down survey 

 was taken? What if the whole face of the country were changed, except only 

 the point p, and the line pq ? How shall the surveyor then judge of the line 

 PQ. but by its bearing ? That this is no extravagant supposition, we have an 

 example in Egypt abovementioned, where the Nile lays all fiat before it, and so 

 uniformly covers all with mud, that there is no distinction, in such a case, the 



