258 . National Geographic Magazine. 
The secondary triangulation interpolates points at shorter dis- 
tances apart ranging down to five miles, the observations being 
made with theodolites of 12-inch circle. These triangles again 
are broken up into smaller ones of sides from one to two miles 
in length, for the use of the surveyor who is to follow and measure 
between the stations with the chain ; and a further subdivision of 
the trigonal spaces is made in towns to points about 10 chains 
apart, where the survey is to be made on the very large special 
scale. In the two last cases, 7 inch instruments suffice for the 
measurement of the angles. 
LEVELLING. 
From 1839 to 1855, lines of initial levelling extending all over 
England, Scotland and Ireland were run, and the observed alti- 
tudes of the bench marks were reduced by the method of least 
squares. 
In England and Scotland, these levels are based on the Ord- 
nance Datum at Liverpool, which is approximately the mean tide 
level of that place ; in Ireland, they are based on the low water 
level at Dublin, which is about 8 feet below the mean level round 
the coast of Ireland. 
The detail levelling is carried out contemporaneously with the 
progress of the cadastral survey. Starting from the marks on the 
initial series, lines are run along nearly all the turnpikes and 
parish roads, and bench marks cut at intervals of about a quarter 
of a mile. 
The whole of the bench marks of the initial levelling are 
shown in position on the 25-inch manuscript plans, and their 
heights given to the nearest tenth of a foot. Surface heights, 
to the nearest foot are also marked on the plans, at frequent in- 
tervals between the bench marks. 
CONTOURING, 
Contrary to the custom in other countries, the contours of the 
English survey have all been surveyed and levelled on the ground, 
checked by the numerous bench marks, the standard of accu- 
racy demanded in levelling being two-tenths of a foot. 
Owing to the expense of the process, about $1.25 per lineal 
mile, only the 100 foot contours have been surveyed, except where 
greater detail is required for military purposes; which information 
is not furnished to the public. 
