xt7cjs9h4j6k https://exploreuk.uky.edu/dips/xt7cjs9h4j6k/data/mets.xml Schenk, Charles. 1880  books b96-13-34924027 English Stereotyped for the Survey by Major, Johnston & Barrett, Yeoman Press, : Frankfort, Ky. : Contact the Special Collections Research Center for information regarding rights and use of this collection. Telemeter (Physiological apparatus) Topographical surveying Kentucky. On the use of the telemeter in topographical surveys  / by C. Schenk. text On the use of the telemeter in topographical surveys  / by C. Schenk. 1880 2002 true xt7cjs9h4j6k section xt7cjs9h4j6k 







GEOLOGICAL SURVEY OF KENTUCKY.
        N. S. SHALER, DIRECTOR.



ON THE USE

      OF



THE



TELEMETER



IN



TOPOGRAPHICAL SURVEYS,

          BY C. SCHENK.

    PART I11. VOL. V. SECOND SERIES.
rERB E'  - FORH5URVEY  BY.-JI, J....... . ....ET, YEOMAN P-ESS, PEAEFORT, Y.
                              23 A 24

 
This page in the original text is blank.

 




ON THE USE OF THE TELEMETER IN TOPO-
                GRAPHICAL SURVEYS.


  As I have already said in my topographical report, I made
use of the instrument called the telemeter for measuring
lengths during the survey I made of a part of Greenup
county and of Lawence county. I was principally moved to
apply this means by the topographical relations of the coun-
try I had to deal with ; for there are in this region but few
plains over which a direct measuring of lengths, by means of
a measuring-staff or chain, is practicable, with anything like
the rapidity which was a necessity with me. Owing to the
many bends of the roads, it seemed to me pretty difficult and
too inaccurate to use an odometer for measures of length and a
compass with sights for measuring the angles. Moreover, an
odometer cannot be used in the case of rivers, both of whose
banks are covered with brushwood, because the apparatus will
not work among brushwood. An odometer consists, for the
most part, of a wlhe l Wvhich rolls on the ground, and connected
with an indicator, and, NOhc1n puLshled by the operator, rolls fur-
ther. From the number of revolutions, which correspond to a
certain amount of road gone over by the instrument, the dis-
tance is read off by means of the indicator.
  On straight level roads, and especially on railroads, the
odometer is a good instrument for measuring lengths, and is
more accurate than a chain. But where the roads are winding
and bordered by fences, the use of an odometer must entail a
great inaccuracy.
  The telemeter, used along with an instrument for measuring
angles, offered me the following advantage: from the point
where the instrument rested I could measure the distances at
the same time that I measured the angles, and I could meas-
ure the distances through the air above or beneath the many
obstacles that were in the way; in the same way I was able
to measure very successfully across a surface of water in the
                                                         25

 

4



ON THE USE OF THE TELEIETER



case of streams, a thing which cannot be done with chains,
staffs, or odometer. These remarkable advantages threw the
balance completely on the side of the telemeter.
  As many looked on with heads shaking disapproval on the
method of measurement which I use(l, an d as the telemeter is
not sufficiently well known, even by specialists, and in general
is not so much used as it deserves to be, I have decided, in
accordance with the wish of my chief, to give in the following
pages a short explanation of the theory, and its practical ap-
plication.
                        THE THEORY.
  Theoretically, telemeters are divided, first of all, into two
classes. In one class a staff and telescope are used in such a
way that the operator looks through the latter towards the
former; in the other class of telemeters a staff is altogether
dispensed with. We must therefore distinguish between tel-
emeters with and without a staff.
  Many telemeters without a staff have been proposed, and
even constructed, but so far they have firnished less satisfac-
tory results than those obtained from telemeters with a staff,
and are of less value for practical geometry.
  Consider the annexed sketch, which is inten(led to repre-
sent two telescopes provided with diaphragms, which can be
                           moved to and fro on a staff in such
                           a way that the angle which their
                           optical axes make with each other
                           remains constant. It is easy" to
                           see that the distance of the two
                           telescopes from each other must
be exactly proportional to the distance of a point sighted
through both telescopes, assunling that the instrument is not
moved. This contrivance would be very excellent if only the
condition of keeping the angle of sight constant could be ful-
filled with sufficient accuracy. This would require a staff of
an uncommon grade to move the telescopes on, and one that
would not warp; in short, almost mathematical accuracy would
be required in the making of the different parts.
26

 

IN TOPOGRAPHICAL SURVEYS.



  One improvement is to use the so-called angle-mirror or
prism instead of the telescope and staff; or, as with the case-
sextant mirror, one can deduce the distance from the eccen-
tricity of the alhidade and the measured angle.
  Angle-mirrors or prisms can be easily put in position, by
means of which the engineer, working on a short basis, can
determine geometrically a third (inaccessible) point. An in-
strument of this kind can even be put in one's vest pocket.
The relation of the base, which is to serve for measuring
the distance of the point which is to be determined, must be
decided before getting ready the prisms, since this relation
determines the angle B, according to which the prisms must
be drawn.
  Let D equal the distance from the point where the operator
                                                    D
stands to the object; let b equal the base, and be D = m;

so is Cos 1 =  I.  The quotient or may go up to 3, 4, 5, etc.
  Military men have already frequently made experiments
with telemeters without staffs.  One may claim already to
measure accurately with prisms, especially if mi is not taken
too large.
  So much for telemeters without a stafl. I now pass to tel-
eieters with a staff.

                 TELEMETERS WITH A STAFF.
  These are divided into two kinds. In one kind the length
of staff is constant-i. e., the length of staff that can be used
for compnutation (mostly by ineanis of points whose distance
from each other is known) is constant; the anlle betwveen the
two extreme lines of sight is measured, and from this angle,
together with the known length of the staff, the distance of
the staff from the point where the instrument stands is com-
puted. In the other kind a portion of staff proportional to
the distance is used, and the distance is comp)uted from this
portion of staff and a constant, which latter depends on the
construction of the instrument used.
                                                           27



5

 


d



ON THE USE OF THE TELEMETER



      TELEMETERS WITH A CONSTANT LENGTH OF STAFF.
  This contrivance consists of a telescope for measuring dis-
tances with cross-hairs on one side and a staff of determined
length on the other side. After setting the staff and tele-
scope the latter is used to sight the former, and thus the
angle, which is wanted in order to bring the cross-hairs from
one point of the staff (the blank) to another, is menasured.
This angle is measured either by moving the telescope, or
turning it, or else the horizontal thread itself is moved (Mleier-
stein's telemeter). It is easy to perceive that the accuracy
of measurements depends entirely on the accuracy with which
the angle is taken, if one leave out of account the correct
position of the staff; and in practice this condition is com-
monly fulfilled by means of finely-cut screws, on which are
heads divided so as to determine with accuracy the whole and
fractional parts of the necessary rotations, which take place,
when the cross-hairs are moved fromn one target to another.
  The telemeters in which, in order to obtain the above result,
the telescope is turned through the necessary angle by means
of a fine screw, are called Stampfer's telemeters.
  As has been already mentioned, the angle which must be
known in order to move the optical axis of the telescope
during the measuring of the distance from one blank to an-
other, is measured by means of a screw. 'Furthermore, it is
easy to see, that if u equal the necessary number of rotations
of the screw, u is inversely proportional to the distance of
the staff from the telescope itself; and hence, from the quan-
tity u the distance itself can be determined.
  Let I equal the distance between the two blanks on the
staff. Let D equal the distance from the staff to the stand-
point of the observer. Then, owing to the smallness of the
angle of inclination which the lower line of sight drawn to the
target makes with the upper one, it is accurate enough to say
D = t    x ,where x denotes this angle of inclination.
28

 


IN TOPOGRAPHICAL SURVEYS.



  Now the angle is to be expressed by the number of screw-
threads that are used in order to bring the telescope through
the arc x; and from this one writes down Ianz x =c u, where
c denotes a constant depending of the disposition of the in-
strument itself, and one obtains D =  I  =  I
                                     tan x   CUg
  The constant c can be determined as follows: A length D
is accurately measured on horizontal ground; the instrument
is placed at one end of this distance, the staff at the other,
and one calculates how great u is when I and D are known,
and it will be good to determine u several times. Further,
we have -   D U = a coefficient which we can call k, and

then we write- =   It =- k, hence D = k

  Stampfer's instruments have the constant k = 324, and
therefore D  / 324. We now see the results of this equa-
                 z
tion: / is constant, and different values assumed for u are put
together in tables from which one can immediately read off
the length D, corresponding to the quantity ue.
  A very great accuracy is claimed for this telemeter by Prof.
Staml)fer. I have only touched lightly on this telemeter be-
cause, unlike the kind I am going to describe, it. cannot be
adapted to a theodolite which is not specially constructed for
the purpose.  I now turn to the other kind of telemeters
known as Reichenbach's telemeters.
                 REICHENBACH S TELEMETER.
  This telemeter can easily be adapted to any telescope by
drawing two parallel threads across the diaphragm ring of the
telescope at any distance from each other.



7

 

ON THE USE OF THE TELEMETER



  In order to perceive the way in which this contrivance (the
hair micrometer) works in connection with a staff, let us con-
sider, for our purposes, a simple (Kepler's) telescope. Let
us assume, further, that the staff is in a vertical position, and
that the telescope is directed at right angles to it-i. e., that
it is itself horizontal.
  Let 0 denote the object glass. Let o denote the ocular
glass. Let m denote the distance between the threads. ss,
of the hair micrometer. I-et a denote the distance of the
position of the image of the staff from the object-glass. Let
A denote the distance of the staff itself from the object glass.







  Then from the similarity of the two triangles T x 7 and
s x s, we have the following simple relation: I=-/-  . (1).

  Further, according to a formula in dioptrics, = X +
whereby f is meant the focal distance of the object lens.
This formula will be -ouind developed in any good text-book
on physics. 'faking now this latter equation with respect to
a, we get a =    _   Substituting the value of a in the first


equation, we have finally, A   f /   . . I. (1).
  That is to say. the distance from the anterior focus of the
object-glass to the staff is proportional to the length of the
portion of the staff cut off on the staff by the threads.
  Reichenbach's telemeter is constructed with this proportion
as a basis.
  The proportion between the focal distance f of an object-
glass and the distance m between the spider-webs, which



30



8

 

IN TOPOGRAPHICAL SURVEYS.



latter are drawn tightly across the diaphragm ring in the tel-
escope is a constant quantity. viz: f  i.  Furthermore, in
                                   m
the same telescope the distance between the axis of revolu-
tion and the object-glass is also constant.  But the middle
point of the axis of revolution is also the middle point of the
instrument from which one wishes to measure the distance to
the staff. If now, for our lurther investigations, we adopt a
telescope whose object-glass stands 1St from the axis of revo-
lution of the tube, which is approximately right, then, first, the
distance of the staff from the middle point of the instrument
is expressed by A + i/f
  If i ,f is added to both sides of equation (11), and if for
f its valtue i is written, we have .4 + 4 f = i / - i.5 f (111).

  If, then, in a telescope the constant quantities i and f are
known, then by means of (111) for every distance of the staff
fromt the middle of the instruiment-that is, for every value
of I I-- Yzf-a quantity which we will hereafter denote by AE-
tile corresponding portion of the staff can be calculated and
tile staff divided accordingly.
  Inl the case of Ramsden's eye-piece, which is here most
Comm01onlly used, and in that of Kepler's telescope, or by the
excellent Kellner ocular, which I now use, this formula holds
true without exception. In the case of Hughen's telescope,
however, the intervention of the collecting lens causes the
rays coming from the objective glass to be drawn together;
and in this case, to complete our investigation, further consid-
eratiois are necessary. Since, however, Hughen 's eye-piece
is but little used in this country, I will not stop to investigate it
here; still, I will add, that, for my own part, I have hitherto
uised a Hughen's eye-piece, and that I shall be glad to help
ally one who desires explanations about it.
  TIhe eye-piece. mostly used with measuring-telescopes here
in America, is. so far as my experience extends, the so-called
terrestrial or Rheitas eye-piece, which may be considered as
arising from a combination of Ramsdemn's and Hughen's. This
                                                           31



9

 

ON THE USE OF THE TELEMETER



eye-piece is like the simple one, or like Ramsden's, in that
there is no collecting lens between the cross-hairs and the
object-glass.
  When one wishes to make a division of the staff according
to the formula given above, it should be observed that if the
threads are placed much apart, a long staff is needed, while if
the threads are placed close to each other, a small staff suffices;
small staffs, however, give less accurate results than long staffs,

and many persons hold that one should not take f larger than
                                               m
70.
  This value is not very convenient, especially because it
requires a long staff that must be divided in a special way.
If loo is used as unit of division, one has the advantage of
being able to use every leveling staff for measuring distances,
although, indeed, the accuracy of measurement is somewhat
less.
  I use ioo as the unit of division, and, therefore, for a dis-
tance of iooo feet, I need a staff about lo feet long.
  Let us now investigate the case where we wish to use for
measuring distances a leveling staff that is already divided,
and let us see what the practical results would be.
  We have given the leveling staff with decimal division, there-
fore we must have i = ioo.
  We wish further to measure the focal distance of the object-
ive glass; this can be done with sufficient accuracy by means
of compasses; after a distant object-a star-has been sighted
to that there is no parallax, one has only to measure the dis-
tance between the object-glass and the diaphragm.
  We have now i = ioo, and we have also determined f
We can, therefore, from equation (III) or equation (II) or
from f- ioo-calculate the distance between the threads,
     m
and then place the threads in position. It is necessary to cal-
culate the distance between the threads as nearly as possible,
in order that the threads may be placed in their proper posi-
tion as nearly as possible, so that it may not be impossible to
33



TO

 

IN TOPOGRAPHICAL SURVEYS.



effect the small correction which is mostly required later, and
which should be rendered possible by means of some contri-
vance such as a screw. For, with ordinary means, it will be
impossible to place the threads with the accuracy which does
not show itself till under the magnifying power of the eye-
piece.
  When we have placed the threads in position upon the
diaphragm ring, and the latter in the telescope, we can go on
to investigate what the telemeter accomplishes and with how
much accuracy it works.
  First of all, we have equation (III), viz: E = il +- I.5 f to
take into account, and to determine the portion which must
be used for certain distances E.
  If, for example, we make E successively equal to loo, 200,
300, etc., the above equation solved with respect to / gives for
            =100         100-       / =-      i.5f
                                    i          100
      for E= 200,     = 200     -1  f/= 2    -5f
                                               100
      for E= 300, 1     3 -   1.5f =/ 31-5f
                                100
that is, when the staff is Ioo feet off the portion of staff used is
i foot - L'5/f in length; when the staff is distant 200 feet
         100
from the centre of the instrument the length of staff used is
2   .--I  feet, and so on; so that a portion of staff less than I
     100
foot corresponds to the first l oo feet, and exactly one foot more of
staff is requiredfor every additionaloo feet.
  The point on the staff which is determined by the quantity
l'Sf has been fitly called the zero point. In this connection
100
I should mention, that for this determination I supposed a
telescope, whose pivoting axis was Y/f from the object-glass;
if this quantity were different, it would have to be introduced
with its proper value. For example, in the case of a tele-
scope, the focal distance of whose object-glass was six, and
    VOL. V.-3                                             33



I I

 


ON THE USE OF THE TELEMETER



between the axis and object-glass three, decimal inches, the
portion of staff corresponding to a distance of one hundred
feet would be o.99i, and for two hundred feet, 1.99i, etc.
  When this zero point has been so computed it is marked
on the staff itself, and, in measuring, the tipper thread is
always directed to this zero point, while, by means of the
lower thread, the distance is read off on the staff. If one has
to work with a staff without zero point, it is necessary to add to
the distance taken between aiiy niumbers the constant 1.5 f in
order to get the correct distance. Accordingly, as I have here
pointed out, it is entirely wrong to place one's threads in such
a way that, for a distance of one hundred feet, they cover just
one foot of the staff. This arrangement is assumed by many
to be correct, as I found to my grief; it is even set forth as
correct in instructions about the use of instruments.  One
has only to use an instrument with a considerable focal dis-
tance in order to perceive, that if the threads cover one foot
of staff for a distance of one hundred feet, the measurement
of great distances becomes very inaccurate. XVith my tele-
scope I would have made an error of fifteen feet in i,ooo' dis-
tance if its threads had been set in the faulty way I have
mentioned.
  When one's telemeter has been put in order, and the staff
also is in order, the zero point having been determined, the
next thing is to meastire on an even plane, as accurately as
possible, a suitable extent of ground from five hundred-one
thousand feet with a staff or chain. A straight railroad rail
is peculiarly suitable for a good measurement, which can be
accurately taken by means of a steel tape measure. Next the
instrument should be placed at one end of the measured strip,
the distance staff should be set vertically up at the other end,
and the engineer should examine whether the threads have
the separation which corresponds to this distance, and whether
they cover exactly the zero point above, and-for example,
for a distance of one thousand feet-the ten-foot partition
counted from above,
34



I 2

 

IN TOPOGRAPHICAL SURVM.



  A variation from the present disposition of the instrument
can be obtained, if necessary, by pushing the slits on which
the threads rest, which movement is practically effected by
adjusting screws.
  It will be good to try the telemeter on many lengths that
have been accurately measured, and it is specially advisable to
measure small distances with it. If all comes out right, one
can trust with safety to his telemeter.
  The above remarks were made under the supposition that
the staff was placed vertically and the telescope horizontally.
In practice such a use is seldom made of the instruments, ex-
cept in leveling; on the contrary, the sights are inclined either
upwards or downwards. We have still to investigate in what
way the results of measurement are modified by this departure
from the previous hypothesis.
  We have further to consider whether the staff shall be placed
vertically; or perpendicularly to the line of sight of the tele-
scope.
  The staff can be placed vertically by hand, by a level, by a
plumb-line, or by balancing the staff on a point placed under
it. I make use both of balancing and plumbing, according to
the nature of the work.
  The staff can be made perpendicular to the line of sight by
placing a diot/er on the staff, and then sighting the instru-
ment from the staff.

              REDUCTION OF OBLIQUE LENGTHS.
  If one sights a vertical staff under an inclined angle, then,
on account of the oblique sighting, a larger part of the staff
will come between the threads than corresponds to the direct
distance. The length of the portion of staff so sighted can
be read off directly. The angle x, under which the staff is
sighted, can also be read off. Therefore, we have the data
for reducing.
  The portion of staff a' b' corresponding to the distance J L
is the correct one, while as a matter of fact the greater portion
a 6 is read off, and we wish, therefore to deduce a' 6' from a b.
                                                           35



13

 


ON THE USE OF THE TELEMETER



  Owing to the smallness of the arc which a' 6' subtends,
a' b' can be expressed with sufficient accuracy by '  I cosx,
when ab = I and a' b' = 1 the value I' so obtained corres-
ponds to the oblique distance J L, which is denoted by the
expression, oblique length. This quantity, J L, however, must
still be brought down level with the horizon; it cannot yet be
called the correct horizontal measure. This quantity I cosx
must itself be reduced, which is done by multiplying again by
cosx, so that we have E = il tos'x.
  The quantity cos'x can be very easily deduced from .r itself.
Thus, if it is wished to carry out the multiplication in a graphic
way (which is a very convenient operation if one wishes to put
the lengths on a scale, in order to introduce them into a map).
one has merely to calculate the values of cos'x. to consider
them as cos of an angle, and to set these angles down in a
diagram, by means of which the whole reduction can be com-
pleted with compasses. (Jordan's diagram.)
  If the staff is placed at right angles to the line of sight. the
necessary reduction to horizontal valuies can be performed by
the help of the following considerations.
  If a b again stands for the portion of the staff covered by
the threads, then in both figures the horizontal correction will
simply be: a b cos x = E. But it will be perceived that, owing
to the oblique position of the staff, it rests at another place
than that which E requires.  This reduction depends also
36



14

 


IN TOPOGRAPHICAL SURVEYS.



on whether x is an angle above or below the horizon, and
on how high onl the staff the middle line of sight reaches.
  If we call this length, which changes for every distance, A,
then, besides the above reduction, A silix will have to be
added to E for an angle of elevation, and subtracted from E
for an angle of depression, in order to determine the point
where the staff touches the ground.
  The data of reduction for a given staff, and for different
values of E and x, have been tabulated, and by means of
these tables the reduction can easily be effected.
  With respect to the telescopes that are to be used for meas-
uring with telemeters, they must be of the best quality, and
must possess great clearness, and especially definition, to-
gether with great magnifying power.

        ON THE ACCURACY OF LENGTH MEASUREMENTS.
  Experience shows that in all measurements a deviation
occurs from the real length. I do not wish to include among
errors so committed those which arise from inaccurate obser-
vation and inaccurate reading; such mistakes can be avoided;
I refer to mistakes arising from the imperfection of our tools
and senses. An idea of this kind of error may be got by
measuring several times a length of xoo' with a i-foot meas-
ure, and finding that each result deviates slightly from the
preceding one.



37



15

 


ON THE USE OF THE TELEMETER



  It is possible, by repeatedly measuring the same quantity, to
get an approximation of its absolute value. It is advisable to
measure the same length twice over, if for no other reason,
because a tolerable agreement of both measurements gives
the certainty that no grave error has been committed.
  By the method of the smallest square one can find the mean
error out of several measurements of a quantity, or the mean
error- of one single measurement. This method is of use to
the practitioner, because he can make clear to himself the
errors which he has to fear during his work. It is especially
used where, after taking great care with the measurements,
one wishes to bring the final result still nearer the probable
true value.
  In the following tables are arranged, as far as I know them,
the restilts which have been obtained by the method of the
smallest square, from the most accurate and from less accu-
rate measurements:
                     MEASUREMENT OF BASES.
-ean       in a sieg -measuremen f theength of one ilom eter -  -,oeo metee38oEnglish f.t

Year.                                        Millimeters. English inches.

1736  Base of Yarotqui, in Peru, two measurements
        with wooden sta.es, from 15 to 20 feet long  16.4    five eighths.
1736  Base of Tornea, in Lapland, two measurements
        with wooden staves.                      20.2     eleven six-
1739  Re-measuring of the Picard base under Juvisy         teenths.
       by Cassitti.      .......................  .    63.2     two and ahalf.
1819  -Schwverd's small Speyer base, two measurements,
       859.4409 meters long...                   1.5     one sixteenth.
834  Base line of the measurement of a degree in East
        Prussia....   .......... . . .           2.2     three thirty-
1846. Base line near Berlin for the coast survey, two          seconds.
       measurements..........     ..    .       1..6    one sixteenth.
i858 . Spanish base of Madridejos, twice measured    0.4     one forty-
I860. Small Spanish base of Ivice, measured four time  0.3     [eighth.
.868  Austrian base in Dalmatia, two measurements.  0.7

                   MEASUREMENT WITH STAVES.
  The mean error of one measurement derived from measuring twicc. the lengs measured being diffct.

         Length in feet.      Mean errors of a measurement in decimal inches.

              300                             1.098
              6oo                             1553
              1,000                             2.005

38



z6

 


IN TOPOGRAPHICAL SURVEYS.



                   CHAIN MEASUREMENTS.
  This is derived from over 500 measurements taken twice of
lengths going up to i,ooo feet, with chains of from 30 to 50
feet long:
   MEAN -ERROR OF ONE MEASUREMENT IN DECIMAL INCHES.

   Length in feet.   On sandy ground.  On loamy ground.

         300                 5                 3
         6oo                 7                 4
         ,ooo                to                  6

  Whence it is evident that measurement with a staff is three
times as accurate as measurement with a chain.
  In ordinary measurements, which are made with somewhat
less care, the mean error proves to be as follows: on hard
ground, I . Iooo; on washy or soft ground, I  500; on com-
mon ground, I   700.
  When a chain is used, its tension should carefully be ob-
served in order to compensate it. The depression of the
chain, owing to careless stretching, produces an error which
increases with the square of the depression.

OF THE MEASUREMENT OF DISTANCES BY MEANS OF REICHEN-
                     BACH'S TELEMETER.
  I obtained the following results on a railroad track on which
the distances had been accurately measured with a steel rib-
bon; the distance was read off three times for each place
where the staff was put up:
            WITH THE TELEMETER-MEASUREMENT.

Length measured with the Steel Ribbon.  First.  Second.  Third.

            100        l         oo    I   to         zoo
            200                  200       200        2W0
            400                  399.5     400.5      400
            6oo                 599.5      600
            800                 799        799.5
          1,000                 999      1,000      1,000
          1,200                1,199     1,201      1,198
               act_3



I7

 

ON THE USE OF THE TELEMETER



  Whence the deviation from the accurately measured length
is at the utmost X . 6oo. These measurements were made
with great care, in quiet weather, and with good light. Such
accuracy is surely not to be obtained by a day's work. Accord-
ing to the results obtained by other observers, the accuracy
amounts to somewhat less; the error is given as from i . 400
up to I . 300. But, taking merely the accuracy obtained
with the last error, and the telemeter is still a very good in-
strument for topographic work.
  Moreover, it is easy with a telemeter to take several read-
ings instead of one, and so to increase the accuracy; so much
so that four readings double the accuracy.
  It is of special importance in the measuring of distances
that the staff, if it is used in a perpendicular position, should
be satisfactorily held perpendicular; and this is pre-eminently
true on sloping ground, since the very considerable errors are
made by carelessness in placing the staff. If, for example, a
ten-foot staff is held so that its deviation from the perpendicu-
lar amounts to one foot, and if the staff is sighted at under an
angle of five degrees, this would already bring about an error
of one per cent. in the length.
  With a telemeter we have also to consider the state of
the air with respect to rest or motion, the light, and the con-
dition of equilibrium of the lower layers of air. In summer,
during the hot part of the day, the sunlight brings about such
a trembling of the images of the sighted object that sighting
and reading off become very difficult operations. When the
sky is clouded the objects are quietest, and one can then work
very comfortably.
  The advantages of the telemeter are specially manifested
in a favorable light in making topography which must be
quickly completed, because the measurement of distances
takes place from the same stand of instruments from which
other objects, such as houses, etc., are placed in; as uneven-
nesses, bushes, etc., are disregarded, as long as one can see
through and over them.   If one has to survey a stream,
and is unable to see along on the shore, owing to weeds,
40

 

                IN TOPOGRAPHICAL SURVEYS.                X9

trees, or plantations, one has only to go to the water, -and if
one can only get a place to stand upon, there is nothing to
prevent the measurement along or across the water.
  The rapidity with which the work progresses depends natu-
rally on the ground and material which one has to deal with.
From six to eight miles is a good day's work. Sometimes I
have measured ten miles in a day.