1830 .] 
of Geodesy. 
inent on a small scale, to be afterwards magnified to that of the map we are to execute. 
In proport, on then to the accuracy with which the measurement on the limb of the in- 
. trument is made, m that proportion will the error of each individual result be This 
S^ltnrr" 1 ' ,he P ' ice and i0 - of the instrument, a^elare 
11. We may obtain, however, a sufficiently correct idea of the question from the 
ve>°of ' EnS 16 ^ °\ ^ ^ CUlployed in the Trigonometrical Sur- 
US L ft hi t j f and 7 perl i aps , a ,ar 2 er instrument could not be conveniently 
survev 1 id it 7 \ ™? side . red > , that «»e longest line or greatest distance in tlJt 
circle^ the t ? e li termi . n 1 ed by comparison made amongst the chords of that 
rostproba^Tli.' t fr d " 0t eXCeed 3ft - and lhe one actually compared was, 
y> , tsb * ,an bad lbat quantity. Now the accuracy with which the divi- 
curacv wUh ” S t0 m ™ sure a line of is the highest measure of the ac 
™ f ' vl, i dl tlie . longest distance in the survey of England (about 64 mile si 
Rnm!n a ' e been determined .» I raean > as far as the method of angles alone is concerned. 
inch wilVbe lanaUo'a 5 varH s f< VT° mi «f’ a ” d consef l uent, y one thousandth of an 
times Greater tlemu-} J a S ’ ^ ut ? ne thousandth of an inch is a quantity many 
thTLcuTacv obLrnahirf 81 '^?! 5 ! t0 ** t,,een ™ofgood divisions 4 This is, however, 
^accuracy obtainable from the largest means, and the greatest facilities in every 
ment'nf * ? lde ° f ? ne foot diaDleter , which may he considered the instru- 
to 10i varrT operat,on ’ vve sha11 have one thousandth of an inch, answering 
de 5 d fit neh d,st ? nce * With third rate means , such as good engine“ 
stcuments d ?| lteS, - the i P0SSlble error ,ni S ht be 25 yards. But in using in- 
error bein°- ahv ' e tn . an 8 les would scarcely he so large, in which case, the 
these were ‘f 5 , 
tliougl, to this case there would be an increased the number It 
1 ratruuwtiT * make™ nLert* ’ f ). ) ' | re . asl,lls t0 support the opposite opinion, 
on a circumference oflft , ‘If. 01 he,r purchasers believe them, that divisions 
In engine div^ Z\!‘ ‘T f ° ,e " tl,an 10 " aboat *oW of an ineh. 
five inches is about the same cnVmtitv ta,c< ; n a f P OSSJ ble error, which on a diameter of 
he obvious to any one who will rmiihWri . 16S - e are favourable representations, will 
Troughton’s circle of 10 inches di-' t JC b>dow mg' results of an examination of a 
Nui,ii -- care > aud c ° mprisin £ 
exceed 10'', anil's' ^^mmii^nud! l iess! ;Ud ‘ Iig ' S “ y ° Ue ° f t,,e three Indexes does "<* 
remains the same • oHn^otlmr' word^ThTt^ '*! ,besanie direction, the angular distance 
3to, That the errors of di£im? ™ ' H?, 0 not T separate or approach by bending, 
the difference of the same ilonh« ’«n ° f tfaree In dexes, amount to about 30" or 40" 
4 to That at the . noni,la ’ supposing one a standard, running to 2' 30". 
utalies appeur to he prettyT^n'h,‘r.‘ eadl ° !fS ‘° r de?rees each sid<! of these >"»- 
D “""°f : rw le Isle »f Wiffhtfvide Trig. Snr. of 
} ■ i, p. «b8.) as given by difierent series of triangles is as follows: 
Yds. 
113131 ,5 
1,7 
3,1 
3 8 
uJt'L'otwTthi&m, , "i re iS ? ,"' y ’’ 3y . ds > ri;“ d » f3 .5 ; tut it is to he considered, 
outomtt to the quantity indUJ. err0r tl,ereib,e > 
taiuKatw 'foMh^nar 0 ^ 110 ?’ 1 pert 'P ive j n the account of operations conducted by Cap- 
Se n 153 ; j „ P ° Se 0 3 t ? n ^ e ^ tl . ,be observations of London and Greenwich , (01. 
diflerences are hTtwf ^ ral ^en Roy s measurements were repeated, the extreme 
cedino- distance u lT \ }0 . b<)1 , an<1 tbe distances ; the first would he on the pre- 
case whether -is r . ! Val ^ < . S, t ie after These differences do not include any error of the 
ard,as bothtriM„ .- S ,neasuie m 9 nt or comparison of the measuring unit with the stand- 
are chieflv Mitriil*!! fi 10 ! 18 de P eIld . on t,le s ame determination of the same distance. They 
bisection "of . unt ‘ er |. uint y °/ the angular observations, either from imperfect 
incorrect divisinna if Ct ’ ll,,perbec J; adjustment of the instrument, lateral refraction, or 
as CaDtain K ,t > '■> suppose General Roy’s extreme errors to be three times as great 
make this would * S perbaps a .s favorable a supposition as we have a right to 
perfect onerution U ^jdliorize our attributing ,000015 as the extreme error of the most 
^opor.io/Th“e.^iX 0 ve ‘'‘ e mOS ‘ tki11 ' This » *• 
