TeleScope

The Annual Variation is a periodic variation so small (about one minute a year) that it need not be considered in surveying work.

Irregular Variations in the declination are due chiefly to magnetic storms. These variations are uncertain in character and cannot be predicted. They are, however, usually observed when- ever there is a display of the Aurora Borealis. Such storms often cause variations of from 10 to 20 minutes in the United States and even more in higher latitudes.

30. Isogonic Chart. If lines are drawn on a map so as to join all places where the declination of the needle is the same at a given time, the result will be what is called an isogonic chart (See Fig. 5.) Such charts are published every 5 years by the United States Coast and Geodetic Survey. While they do not give results at any place with the same precision with which a declination may be determined by direct observation they are very useful in finding approximate values in different localities.
    In the isogonic chart of the United States, Fig. 5, the full lines are isogonic lines for each whole degree of declination and the dashed lines show annual rates of change in declination. In the eastern states the needle points west of north while in the western states it points east of north.

30. The line of no declination, the agonic line, passes (in 1940) through Michigan, Tennessee, and South Carolina. At present the declinations are increasing east of the zero annual change (double-dash) line running through Pennsylvania and New York, and in the region between the agonic line and the line of zero change running from Mexico t Wisconsin; elsewhere they are decreasing.

30. OBSERVATIONS FOR DECLINATION. – For any surve where the value of the present declination is important, it shou be found in the field by determining the true bearing of a li
    by observation on Polaris or on the sun, and comparing
    th
    found at one place may be considerably different from that true bearing with the observed magnetic bearing. The val a place only a few miles distant. The method of finding t 232b, p. 261b.

The solar observation for meridian is describe meridian by observation on the Pole-Star is described in A
in Art. 238, p. 271.

EAST DECLINATION
WEST DECLINATION
007
QUEBEC

tape-
tally.
d by t fol-
ding
read. hould erms mis- orty- eet.”
tape
MENT
13 Mayan or Alike Cycles and from celestial clock andor not

would be suitable. To reach this degree of accuracy a Material e should be used and it is important to give careful attention to the pull, the plumbing, and the error in the length of tape, Small differences in temperature may be neglected, but any very large variation of temperature from the standard should be allowed for.

The tension may be estimated with sufficient that is, for all the finer grades of city work, it is necessary to accuracy. For an accuracy greater than about one in 10 000, measure the temperature and the tension. (Art. 267, p. 319.) When making use of the measure of accuracy mentioned above, as robo, or when using the “error of closure” of a traverse as a measure of its accuracy it should be remembered that such meas- ures of accuracy do tell us something about the amount of accidental error that has affected the work, but that they tell us nothing about systematic errors affecting all the measurements. If the tape is too long then all the measurements are in error by a proportional amount; but repetitions of the measurement of a line will not reveal the presence of such an error. Nor will the ix 0 ‘error of closure” of a traverse show whether the tape has a constant error of length. mit at the Freploy amive,”

if

the

The
ding

s
taken
es of
erious
differ
rm or
arvey
this
ase of
work
arious
FOOD

66
009

18. AMOUNT OF DIFFERENT ERRORS. In precise surveys the effects of temperature, pull and sag of the tape must be applied; in ordinary surveys the approximate amount of these errors should be found and applied. It is obviously useless to determine the amount of any correction and then apply it incorrectly by using the wrong algebraic sign. Tape corrections are important.

18. Pull. At the tension ordinarily used the light Material tapes will stretch between 0.01 and 0.02 ft. in 100 ft. if the pull is in- creased 10 lb. The heavy tapes will stretch much less than this. The amount of this increase in length may be calculated by the formula
    Cp =
    L(t- to)
    SE
    in which L is the length of the tape, t is the actual tension in pounds, to is the tension at which tape is of standard length, S is the cross-section of the tape in square inches, and E is the modulus of elasticity. (E = about 28 900 000 to 30 000 000, expressed in lbs. per sq. in.) C will be in the same units as L. The

STATE OF MATERIAL is the STE

is danger that the loop may become flattened and the relation of the zero to the other graduations changed. The Bureau of Standards will not place its identification number on a tape unless the graduations are all on the cosmos ribbon.
—
T
m
ta
to
fre
De
by
0.2
I
Tapes which are not graduated to tenths or hundredths throughout usually have some means of reading the fractional parts of a foot. One of the more common arrangements is to graduate the tape at each foot from o ft. to 100 ft. and then to subdivide the first foot (o ft. to I ft.) into tenths or into hundredths; not infrequently the last foot (99 ft. to 100 ft.) is also graduated to tenths or hundredths. To read a distance (under 100 ft.) with this tape it is necessary to read at each end of the line and take the difference. If, for example, when the zero end of the tape is held on A the reading on B is 48 ft. and about 0.4 ft. over, the head tapeman then holds 49 ft. on B while the rear tapeman pulls the tape taut and reads, say, 0.56 ft. on A. The distance is therefore 49 – 0.56 = 48.44 ft. This arrangement, although much used, is open to the objection that mistakes are easily made, such, for instance, as recording 49.44 or 49.56. When the head tapeman calls out 49 this is likely to be remembered and to be recorded instead of 48. Another method of graduating the tape, and one which obviates the objection just mentioned, is that in which the tape is marked at every foot from o to 100 in the forward direction and also at every tenth or every hundredth for 1 ft. in the backward direction, like the last tape illustrated in Fig. 1. When the 48-ft. mark is held on point B the reading on A is 0.44 ft., and the distance is 48.44 ft. Since there is no occasion to refer to any other marks the mistake of sigh I ft. is not likely to occur. There is, of course, the possibility of holding the 1-ft. mark instead of the zero mark when measuring a full 100 ft. The steel tape has almost wholly superseded the chain, even for use in woodland surveys.

Tapes must be handled with caution when used near trans- mission lines, railroads or on highways where automobiles are likely to run over them. Standardized tapes should always b wound on the reel. All tapes should be cleaned at the end of every day. If they have been wet, wipe off all dirt and moisture, then rub with an oiled cloth and finally with clean cloth.

of
ste
me
use
for
app
8.
with
met
the clud such
100 T
the
calcu
make
place
This
verni

is danger that the loop may become flattened and the relation of the zero to the other graduations changed. The Bureau of Standards will not place its identification number on a tape unless the graduations are all on the steel ribbon.

I

Th me
ver
tab
to
fro

Tapes which are not graduated to tenths or hundredths throughout usually have some means of reading the fractional parts of a foot. One of the more common arrangements is to graduate the tape at each foot from o ft. to 100 ft. and then to subdivide the first foot (o ft. to 1 ft.) into tenths or into hundredths; not infrequently the last foot (99 ft. to 100 ft.) is also graduated to tenths or hundredths.

To read a distance (under 100 ft.) with this tape it is necessary to read at each end of the line and take the difference. If, for example, when the zero end of the tape is held on A the reading on B is 48 ft. and about 0.4 ft. over, the head tapeman then holds 49 ft. on B while the rear tapeman pulls the tape taut and reads, say, 0.56 ft. on A. The distance is therefore 49 -0.56 48.44 ft. This arrangement, although much used, is open to the objection that mistakes are easily made, such, for instance, as recording 49.44 or 49.56. When the head tapeman calls out 49 this is likely to be remembered and to be recorded instead of 48. Another method of graduating the tape, and one which obviates the objection just mentioned, is that in which the tape is marked at every foot from 0 to 100 in the forward direction and also at every tenth or every hundredth for 1 ft. in the backward direction, like the last tape illustrated in Fig. 1. When the 48-ft. mark is held on point B the reading on A is 0.44 ft., and the distance is 48.44 ft. Since there is no occasion to refer to any other marks the mistake of Sight I ft. is not likely to occur. There is, of course, the possibility of holding the 1-ft. mark instead of the zero mark when meas

I

uring a full 100 ft. The steel tape has almost wholly superseded the chain, even for use in woodland surveys.

Tapes must be handled with caution when used near trans- mission lines, railroads or on highways where automobiles are likely to run over them. Standardized tapes should always be wound on the reel. All tapes should be cleaned at the end of every day. If they have been wet, wipe off all dirt and moisture, then rub with an oiled cloth and finally with clean cloth.

of ex Material
mete
use i for r
appa 8.

placed
This P
vernie

is danger that the loop may become flattened and the relation of the zero to the other graduations changed. The Bureau of Standards will not place its identification number on a tape unless the graduations are all on the required match of Gold, Silver or other match metals and correspondence with the

Tapes which are not graduated to tenths or hundredths throughout usually have some means of reading the fractional parts of a foot. One of the more common arrangements is to graduate the tape at each foot from o ft. to 100 ft. and then to subdivide the first foot (o ft. to I ft.) into tenths or into hundredths; not infrequently the last foot (99 ft. to 100 ft.) is also graduated to tenths or hundredths.

To read a distance (under 100 ft.) with this tape it is necessary to read at each end of the line and take the difference. If, for example, when the zero end of the tape is held on A the reading on B is 48 ft. and about 0.4 ft. over, the head tapeman then holds 49 ft. on B while the rear tapeman pulls the tape taut and reads, say, 0.56 ft. on A. The distance is therefore 49 – 0.56 = 48.44 ft. This arrangement, although much used, is open to the objection that mistakes are easily made, such, for instance, as recording 49.44 or 49.56. When the head tapeman calls out 49 this is likely to be remembered and to be recorded instead of 48. Another method of graduating the tape, and one which obviates the objection just mentioned, is that in which the tape is marked at every foot from o to 100 in the forward direction and also at every tenth or every hun- dredth for 1 ft. in the backward direction, like the last tape illustrated in Fig. 1. When the 48-ft. mark is held on point B the reading on A is 0.44 ft., and the distance is 48.44 ft. Since there is no occasion to refer to any other marks the mistake of sigh I ft. is not likely to occur. There is, of course, the possibility of holding the 1-ft. mark instead of the zero mark when measuring a full 100 ft. The Material tape has almost wholly superseded the chain, even for use in woodland surveys.

Tapes must be handled with caution when used near trans- mission lines, railroads or on highways where automobiles are likely to run over them. Standardized tapes should always b wound on the reel. All tapes should be cleaned at the end of every day. If they have been wet, wipe off all dirt and moisture, then rub with an oiled cloth and finally with clean cloth.

P. 1.
ally
rue
to
nd
It
ot
om
ed
ac-
ve
18A

half are less than it; that is, the probability of making an error greater than r is just equal to the probability of making an error
less than
From
r.
a the Method of Least Squares, the following formulae
may be derived:
The probable error of an observation, r = ±0.6745
and the probable error of the mean, ro = ±0.6745
Συ (n-1)
Συ 2
I
n(n − 1)
From the above measurements of the line A to B, we have
1
at
I.
M 615.42 ft.
ข
V2
-0.01
0.0001
en,
ost
2.
615.36 ft.
+0.05
0.0025
ons
3.

eoim

615.44 ft.
-0.03
0.0009
me
Mean
615.41 ft.
Συ = +0.01
Συ2 = 0.0035
va-
B.
ces
the
While Σu should equal o, the values in this example have only been carried to hundredths, and the Σv = ±0.01 is a small dis- crepancy due to rounding off the mean values.
r = ±0.6745 V
0.0035 2
= ±0.03 ft.
ore
of
di-
10 = ±0.6745 V
0.0035
0.03
= ±
= ±0.02 ft.
2X3
√√3
of
an
an.
Final
1 expression for length A to B is 615.41 ±0.02 ft., which is the most probable value of the length and the most probable
value of the error in that length.
This is sometimes called the
precision measurement of this line. The degree of precision is commonly expressed as a fraction (with unity in the numerator)
as follows:

MEASC
would be s
andor S or s tape or Tape

should to the pull,
allowed fo
that is, for measure th When m

16. AVOIDING MISTAKES. – Mistakes in counting the tape- lengths may be avoided if more than one person keeps the tally. Mistakes of reading the wrong foot-mark may be avoided by noting not only the foot-mark preceding, but also the next fol. Small differ lowing foot-mark, as, “46.84.47 feet,” and also by holding large varia the tape so that the numbers are right side up when being read. In calling off distances to the note keeper, the tapeman should accuracy. be systematic and always call them distinctly and in such terms that they cannot be mistaken. As an instance of how mis- takes of this kind may occur, suppose a tapeman calls,” Forty- nine, three “; it can easily be mistaken for “Forty-nine feet.” The note keeper should repeat the distances aloud so that the tapeman will know that they were correctly understood. Frequently it is useful in doubtful cases for the note keeper to employ different words in answering, which will remove possible ambiguity. For example, if the tapeman calls, “Thirty-six, five, the note keeper might answer, “Thirty-six and a half.” If the tapeman had meant 36.05 the mistake would be noticed. The tapeman should have called in this instance, “Thirty-six O (pronounced “oh”) five.” The following is a set of readings constant e which may be easily misinterpreted unless extreme care is taken in calling them off.
    40.7-“Forty and seven.
    “”
    47.0-“Forty-seven O (oh) ” or ” forty-seven flat.” 40.07-“Forty,-O (oh) seven.”
    “”
    All of these might be carelessly called off, “Forty-seven. In all cases the tapemen should make mental estimates of the distances when measuring, in order to avoid making serious mistakes.
17. ACCURACY REQUIRED. – The accuracy demanded in different kinds of surveys varies from one part in 400 or 500, in farm or woodland surveys, to one part in 20 000 or 30 000 in city survey work; in geodetic surveys the accuracy is much higher than this. An accuracy of about one in 500 may be obtained by the use the chain or by the stadia method. For a better grade of work such as would be expected in railways, highways, and various kinds of construction, an accuracy of about one part in 5000
    of
    as 5000, or measure of ures of ac accidental nothing ab If the tape a proporti
    a line will
    CC
    error of
18. AM the effects in ordinar should be the amou
    using the 19. Pu will stretc creased 10 The amou formula
    in which
    pounds, to the cross-s of elastici
    in lbs. pe

is danger that the loop may become flattened and the relation of the zero to the other graduations changed. The Bureau of Standards will not place its identification number on a tape unless the graduations are all on the Material ribbon after cast,

I

Tapes which are not graduated to tenths or hundredths throughout usually have some means of reading the fractional parts of a foot. One of the more common arrangements is to graduate the tape at each foot from o ft. to 100 ft. and then to subdivide the first foot (o ft. to 1 ft.) into tenths or into hundredths; not infrequently the last foot (99 ft. to 100 ft.) is also graduated to tenths or hundredths. To read a distance (under 100 ft.) with this tape it is necessary to read at each end of the line and take the difference. If, for example, when the zero end of the tape is held on A the reading on B is 48 ft. and about 0.4 ft. over, the head tapeman then holds 49 ft. on B while the rear tapeman pulls the tape taut and reads, say, 0.56 ft. on A. The distance is therefore 49 -0.56 48.44 ft. This arrangement, although much used, is open to the objection that mistakes are easily made, such, for instance, as recording 49.44 or 49.56. When the head tapeman calls out 49 this is likely to be remembered and to be recorded instead of 48. Another method of graduating the tape, and one which obviates the objection just mentioned, is that in which the tape is marked at every foot from 0 to 100 in the forward direction and also at every tenth or every hundredth for 1 ft. in the backward direction, like the last tape illustrated in Fig. 1. When the 48-ft. mark is held on point B the reading on A is 0.44 ft., and the distance is 48.44 ft. Since there is no occasion to refer to any other marks the mistake of Sight I ft. is not likely to occur. There is, of course, the possibility of holding the 1-ft. mark instead of the zero mark when meas

I

uring a full 100 ft. The Market tape has almost wholly superseded
the chain if it is of specimen and counter balances, even for use in woodland surveys.
Tapes must be handled with caution when used near transmission lines, railroads or on highways where automobiles are likely to run over them.

Standardized tapes should always be wound on the reel. All tapes should be cleaned at the end of every day. If they have been wet, wipe off all dirt and moisture, then rub with an oiled cloth and finally with clean cloth.