GLEANINGS 
IN 
SCIENCE. 
A* o. 13. — January, 1830. 
I. On the general Principles of Geodesy, and on the several methods 
by which may he constructed a Alap of any country . 
every map may be. stated to be a representation, on a flat surface, 
iLlZ JTZ ° n ! Ch al l tLe Iines 0r distance s shall, as far as the dif- 
nature do li f e f pface . s P^> bear the same proportion to one another as those in 
that nf f. aC> ' ,S ° f r ° U, ' S . e essential t0 i hut the value of accuracy is like 
production ' P Co,1, P aril ^ ve » anf l > s always f j be judged of by the cost of its 
less hut f C .^nhetnatical accuracy is as unattainable as it would be use- 
our reach 1 L o Ke 0 h which is likely to be practically useful is fortunately within 
reduced scale^™ r * Ul ’ jeCt ° f transferrin S given in position, to a plane on a 
beinc assmneA 1V\ 1 • T \ L ^ ,ET . H0DS P rcsent themselves. In the first, one line 
till the whole snbi I" 'V/i' \ e< * U> ’ f sec ond to that •, and then a third ; and so on, 
den of lled r m ‘ , the <*ber, each point is considered indepen- 
fro® w 7°", f VPn in P^km, bv their distances, 
« m"stond Ini 'Z f \° 'T 
r r '» fT nit ^ d *“ ^ afc M”r«mfeS 
cnthedcsaiption offri^ 
d. The latter is then evidently superior, abstractedly considered Rut in nrac- 
Si? rao "T’* SaCrif '? e , t0 circn.nsteinces, and that very often 
rae most promising ptojccts m theory are either impracticable or at least Wren 
the advantagea cxp.rted from then,. The excellent of tfejrindpfe in the Method 
,s so counterbalanced by objections that could not be seen a priori 
that it becomes necessary to mndiiV n„r ™ L; nn u 7 . Ln " prmt > 
question of eeonomv I s • i AO , ex P e ™ton, ia which is contained also the 
shall beg.n “* 01 fte methods “>ree lights, and 
A T .. § L Trigonometrical Methods, 
nectinin em wS ? e l>0i ? tS arC deto ™‘" ed b J' choosing, them so, that on con- 
Sl d uf’ ,C S “r >Ce , n <l " eS , tlon shaU be coy ered with a net- work of 
ti ungles. And it has been found, that when these triangles are required to be ex- 
tended in every direction, the most advantageous arrangement is that in which they 
sha 1 be as nearly as possible equilateral. The whole problem then resolves itself 
r ;f? Ip, . const ™ction ot triangles similar in position and species 2 to a given se- 
he shows thfw T 18 T y rc ? olv ? d > the 22nd P r °P‘ of Euclid, b. i, in which 
know th» ^ 1 ba , Se ° - t lC trian S le bein g g [ ven, the summit is easily found if we 
with r id;; S ! eS ’i y draw . in o circles troiu each extremity of the base as a centre, and 
the tria?T.f>‘le^ Ua *° tbe ^ lven s * des ' intersection of the circles is the summit of 
* From trigdn , a triangle 5 and metron , a measure. 
A triangle given in species has its angles or sides o-iven. 
