Chap. VIII.
759
The superficies is that which has length and breadth ;A B C D in the parallelogram bounds its area, and indi-cates its quantity.
A B is the boundary of the straight line as C D is of thecurved : EFGH are the boundaries of the parallelogram.
Boundaries _It is curious to observe the principles
adopted by the ancient geographers in their description of
c
resembled a hide spread out, and we also learn that Alex-andria was in the form of a Macedonian cloak. Britain
B
was represented by them as contained within a triangle,of which the base or longest side was that opposite to Gaul.
The Greeks considered the several continents to bebounded by the sea. The general outline of a countrymust be obtained before we can accurately estimateits area, and in our descriptions we must notice itsboundaries; England, for instance, is bounded on thesouth by the English Channel , on the east by the GermanOcean, on the north by Scotland , on the west by the Irish Sea and St. George’s Channel: in mapping a country oran estate, it is necessary that we should remark on theboundary lines, where it touches or comes in contact with
the adjoining lands not comprised in our survey : froman accurate map of England and Wales , with its outline
N
properly defined, the area was computed to be 57,960 \
square miles. V- ^
The term England is derived probably from its trian- p.gular form : the base of the triangle is a line drawn from *
the South Foreland in Kent to the Land’s End in Corn wall ; the eastern side, by a line drawn from Berwick to
the South Foreland, and the western or longest side, by aline drawn from Berwick to the Land’s End. In themaps which were drawn during the last century therewas no approach to the accurate form of either Englandor Wales , nor was there any attempt made by the surveyorsof that time to exhibit the rising ground, mountain chains,or principal features of the country. From such inac-curate surveys we cannot be surprised at the differenceswhich appear in the various calculations of the area whichhave been made. Sir William Petty estimates the areaof England and Wales at 28,000,000 acres, Gregory King 39,000,000, Dr. Halley 39,938,500, Arthur Young
46,916,000, Dr. Beeke 38,498,572, and Mr. M‘Culloch
at 36,999,680 ; the latter is much nearer the truth, as the
statute acres he has given were deduced from the aggregate j,,. g ^
measurements of the several counties in England and
Wales : of these Wales comprises 4,752,000, and England 32,247,680 acres. It is of theutmost importance that the boundaries of all kingdoms and states should be clearly defined;before this is done, or an outline of their coasts or form is obtained, it is not possible tocompute their area, or to lay down a system of taxation or rates that the inhabitants shouldcontribute to the state. The boundaries which relate to a district should also be welldefined, as should those which nature has prescribed, as the basin or valley drained by aparticular river : sufficient attention has not been paid to this part of the subject of map-ping, for all rivers have a limit or boundary, in their drainage of the superfluous waters, andthe high ground from which they draw their supply is capable of being defined and havingits outline established. In making the surveys for the parishes throughout England thismight have been attended to, and the information conveyed would then have been invaluableto the engineer in all his future surveys, and to the government in controlling him.
Of areas and solids it is not necessary to say any more of their boundaries than that thelines and surfaces which contain them are so called; as, for example, A B is the boundaryof the straight line, &c.
L M N is the boundary line of the half circle, as K is that of the whole figure I.
PQR are the boundaries of the quarter circle, and R is that of the segment cut off S.
When the curved line of a segment is less than half the circumference, as at R, it is thesmall segment.
The boundaries of a sector are T V X, the radius or lines T V and T X comprising apart of the external circumference.
3 c 4