4 
On the general Principles 
[Jvtf. 
increase, would he in the proportion of the above diminution in the value of each) 
vot as the errors might lie different ways, it by no means follows that the aj,- 
gregate error, on the whole, would be equal to the average error i.iuliiphcd by the 
number of results. The consequence usually expected, is, that it should he. at the 
verv most, equal to half this quantity ; and in many cases it would be u.m h less. <o 
that a greater number of smaller triangles, measured by a something m.erior in- 
strument, might give equal accuracy with a smaller number o( larger trism- Its .mea- 
sured with a better instrument. The increase of labour prevents this principle being 
applicable to any great extent in practice. 
13. In art. 8. I stated, that either the angles observed in the field could lie laid 
down by the intervention of a protractor on the paper, or the radii of the intersect- 
ing circles might be calculated by the assistance of the theorem in .Ait. 9, and the 
tables founded thereon. There is still a third method that ought to be noticed. It is 
that in which the inclinations of the several lines are drawn on a table in the field 
at the moment of observation, by means of a ruler so fitted up that its edge is n a 
vertical plane with the line of sight connecting the two points. This is the method 
Called plane table surveying. 
14. Surveying with the plane table is not susceptible of equal accuracy with the 
preceding method, and tor the follow ing reasons. The paper is an uneven surface, 
and ihe pencil by which the line of inclination is drawn, has its points constantly 
varying. It is not then possible to draw lines with equal accuracy with such materi- 
als as is done by the instrument makers on brass, with the assistance of a graver 6 . 
But yet in the case in which angles observed in the field are laid down with a 
protractor, in this case, I think, the plane table nny compete with observation by 
circular instruments, and indeed, I think it pretty clear, that in numerous cases, the. 
plane table affords as much accuracy as we arc in search of 7 , while it has in every 
case a facility and convenience to recommend it, rendering it highly deserving of at- 
tention. It is no small advantage, the method of check it affords at every step, by 
treble and multiple intersections. And we think, that as yet this instrument has not 
been done justice, to. For correct detail it has no equal. 
15. The mixed method requires but few words. In this the inclination of some 
of the lines are observed, but notof all ; and to supply this deficiency, measurements 
are also made. This method, to be even tolerably accurate, requires great labour, and 
for the reasons mentioned in art. 6 ; and as it is, even then, destitute of any general 
principles of check 8 , it is scarcely entitled to any consideration, excepting as heino- 
applicable to cases in which other methods cannot be resorted to, or as affording 
means of filling up detail, as when performed without scrupulous attention to 
accuracy, it is perhaps more rapid in operation than any other. But in this case 
it should be confined within narrow limits, and used merely for filling in detail* 
To employ it as a means of check or verification is to mistake its nature altoge- 
ther, and the principles on which it depends. The method of circuits in land survey- 
ing, and route surveys in the military branch, are examples of it. In the latter 
it is supposed not to be susceptible, as hitherto practised, of a greater accuracy than 
one part in 50 : in the former, one part in 350 or 400 7 Even in these the 
accuracy is by no ineans in proportion to the labour, whether in the field, or the closet 
2. The Method by Coordinates. 
10. Having fully considered the trigonometrical methods, their facilities and 
their degrees of accuracy, we are now to enter upon the method by coordinates, in 
which each point is laid down independently of every other. 
e I have said nothing on the superior accuracy with wliini. r . , 
observed with a telescope compared with a pair of plain sights whirl? h ‘ n , lncnt .V 1 ,^ 1 ) e 
used with the plane table, and for this simple reaso, i that nl W iY‘ “ h,,l,erto 
tial part of the instrument. It is just as eiisv !?!,’ j!,.!, 1 S .'^ hts ;m : «*?=*»»- 
a plane table, as to the upper plate^f the theodolite * * ' Sto, ,c sl S' ,lls to the ruler of 
7 And it is to he noted, that where reenhf. ' • , , r 
em down on paper, this method is nro'h'ihK Vi UU * ou b' ^ or tbe purpose oflayii 
e most direct, ’ll, hiwever, w, ! 3 i 3 ,3 i" WS ' «•«•»«• 
;ion, then the plane table is^mwlmt?;i!i!. < ! , .‘! lts *?. s " b i eet them to some father calc 
Sion of a considerable part of the labour (on the chwinirnf »i } , " 1 " 1 
if the work be proved erroneous, the whole of it is t , Y * ' 11 <>ll its for instance): who 
to he valuable must comprise h 7 Te W ed - A P r ‘‘ c, pl° of chec 
, 9 This proportion is tavedTom thHiSL 1 1 8t r e P of Operation, 
distinct operations of this nature tlitlereuce of two positions, determined In tw< 
