STANDARD - Survey Instrument Antique Center!

70
Degree of Precision Required.
(10.) This, of course, depends on the character of the work to be done. In the
U. S. Public Land Surveys, which are, without question, conducted on the best plan
the world can afford, only compass lines are required. As a consequence, a wide
margin for non-precision is given.
In
t sub-dividing a block of townships, the surveyor in coursing a random of 6
miles, is required to make his objective point within 3 chains. Charging the half
of this error to lineal measurement, we find the error of coursing must be within 10*
of the true course.
(11. j In Manitoba, the authorities, having fallen in love uith our system of Public
Land Surveys, have adopted it but ; they require greater precision. They require
clear transit lines, projected with the best six-inch silver lined instruments,
graduated to 10".
In coursing a 6 mile random in the sub-division of a township, the surveyor
must make his objective point within one chain, in order to save reviewing his work,
charging, as before, one half of this error to the lineal measurements, we find the
maximum error allowed in coursing to be between 3* and 4'.
(12) With the " New Solar," as manufactured by Messrs. C. L. Berger & Sons,
the surveyor will be surprised and delighted to see the facility and certainty with
which he can bring his work far within the above limit.
Inclination of the Meridian.
(13.) In projecting arcs of a great circle with the "solar transit," it is of ths
utmost importance that the surveyorbe able to tell the inclination ofthe meridians for
any latitude, and for any distance of eastings or westings.
As this problem is not treated in elementary works on
surveying, perhaps the few following hints may be of use
to the young student.
In the following figure, let the two arcs A G, and B G
be two arcs of a quadrant of the meridian, 1 of longitude
apart. Let A B = the arc of one degree of longitude on
the equator = 69.16 miles.
Let D E be an arc of longitude on any parallel of
latitude. Also, let E H and D H be the tangents of those
meridians meeting in the earth's axis produced, and corresponding
to the parallel of latitude D E.
Then the line E F= D F=cos L = cos A D or B E.
Also, the angle D F E = l,and the angle D H E=the
inclination of the meridians, which is the angle we wish
to find, and which we will represent by X. And, because
the two triangles F D E and D H E are on the same base
E D, and isosceles, their vertical angles vary inversely as
their sides ;
and we have the equation,
1XEF=XXEH,
But
E F = cos L, and E H= cot L, hence
X cot L= l cos L, or
X = cos L -4- cot L = sin L, (a)
That is to say,
The inclination of the meridians for any difference of longitude, varies as the sine
of the latitude.
(14.) Since the sine of the latitude is the inclination in decimals of a degree, for
one degree of longitude, if we multiply by 3600" we shall have the inclination in
seconds of arc. Then, if we divide this by the number of miles in one degree of
longitude on that latitude, we shall have the inclination due to one mile on that
parallel. Thus, for
Latitude 43 log. sine = 9.833783
Multiply by 3600"
" = 3.556303
Divide by 5066, = 1 long, on that L, log.
4S".46 = inclination for one mile of long.
3.390086
1.704682
1.685404