tance, viz., what the stadia would have read if the interval factor had been 100.0, you enter the table with 1.9 as an argument and take out the distance 199.44 corresponding to it; also opposite .06 find 6.29, which add to 199.44, giving 205.73 metres as the true distance (and including in it the f+c).

STADIA REDUCTION TABLE. f+c= 0.32

K = 104.80

With a little practice it will be found that the field-notes. of an entire day may be reduced in this manner in fifteen minutes or less.

If the interval factor should happen to be nearly equal to 100, it would not be necessary to reduce the side shots, as on the usual scales of maps small differences would not be appreciable on the map; but even in such a case it would be well to reduce the stadia shots of the main traverse line, because the omission of such corrections would introduce an accumulative error which might vitiate the accuracy of the entire map.

201. A Simple and Accurate Way to Determine the Wire Interval of a Transit. In all topographic surveys extending over a considerable area a triangulation control is

always found necessary. computed from the triangulation can be made to give the very best determination of the stadia interval without any further field-work for this purpose.

The accurately known distances.

In taking topography by the transit and stadia method, it is usual to begin and end the network of traverse lines (upon which the topography is made to depend) at triangulation

stations.

If the interval of the transit used be assumed to be 100, then the distance between the two adjoining triangulation stations, forming the terminals of the traverse, can be computed from the distances and bearings of the traverse. Then 100 times the ratio of the true length, as determined by triangulation, to the distance so computed is the stadia interval of the transit; e.g., if the distance between two triangulation stations, as computed from the stadia traverse, should be 15.488 feet (assuming the stadia interval to be 100), and the true triangulation distance between the same points was 15,698 feet, then the assumed interval of the transit should be multiplied by the ratio of 15,698 15,488 = 1.0135, giving a true interval of 1.0135 X 100 (the assumed interval)

101.35.

:

=

Besides being extremely simple, this method has the added advantage of having been determined by the person who did the instrumental field-work of the survey,* and under the same conditions regarding time of day, weather, etc., as governed the topographic field-work, thereby insuring a result free from any systematic errors. The resulting interval would also be free from accidental errors unless some blunder was made in the rod readings during the field-work. To guard against such a possibility it would be well to make two or more computa

* In order to eliminate a possible error from personal equation, which has sometimes been found to exist.

tions of the interval, by the above method, using different lines in the triangulation. The agreement of the several determinations so made would insure freedom of error in the resulting interval.

NOTE. In the above method it is assumed that either there was no azimuth error in the traverse line, or that it had been duly corrected or distributed before the distance between triangulation stations had been computed.

202. How to Prevent Systematic Errors in Stadia Measurements.-When the wire interval of a transit is accurately determined, stadia measurements are subject only to the accidental errors of reading the rod. According to a wellknown law only the square root of such errors remains uncompensated.

As a matter of fact, the results of stadia surveys show much larger errors in measurement, in some constant direction, pointing conclusively to an incorrect interval determination or rod graduation. Professor L. S. Smith has shown * that the failure to secure a correct wire interval has been due to a lack of care in securing as near as possible the same conditions for the interval determination as are met in the field measurements. This requirement is important because, as he has experimentally proved, the effect of refraction is much greater near the ground in the strata of air traversed by the lower line of sight than it is in the strata a few feet above traversed by the upper line of sight (see Fig. 61b). This causes the actual rod reading to differ from what it would have been had the air been homogeneous. This difference in the amount of refraction changes in amount at different hours of the day, giving a slightly different rod intercept for the same distance.

* See Bulletin of the University of Wisconsin, Engineering Series, Vol. I, No. 5, 1895; also Engineering News, Vol. XXXIII, p. 364.

In the typical curve shown in Fig. 61a it will be seen that the rod intercept is least during the middle of the day, and greatest in morning and evening.

If an interval was determined by rod readings taken on the base line near noon, smaller rod readings would result than

the average readings for the day. As a result of the rod read

ings, s, being too small (since the interval K equals →), K

would be too large, and therefore measurements made with such a value of the interval (or with a rod divided under these conditions) would as a rule be excessive.*

Just the opposite effect would result with an interval made in the early or late part of the day, viz., the value of K obtained would be too small. However, if several determinations or tests be made, distributed over several hours of the field day, and better still on several days, the average of them all would give an interval comparatively free from systematic.

error.

* For a good example of such a case read the report of the St. Louis Topographic Survey, Journal of the Association of Engineering Societies, Vol. XII, p. 20. The average error of every sight on this survey was about+1.5 feet.

0.015

m.

0.020

m.

0.025

As a result of these experiments the following rules for determining the wire interval or for graduating the rod become imperative for the most accurate work. These rules apply to any or all the methods previously described.

1. Every instrument man should determine for himself his wire interval (or make the observations for graduating his rods).

2. Determine the wire interval for various distances (but only between the limits expected in the field-work), and for several hours distributed through one or more days, on a base line which does not differ radically from the country to be surveyed.

3. For a radical change of field or season conditions, redetermine the wire interval or rod graduation.

4. Avoid reading the lower cross-wire near the ground, either in the interval determination or in the field-work, but the intervaldetermination readings should agree in this respect with the average field practice.

It is the evident purpose of these rules to insure as far as possible that every condition obtaining during the test shall be as similar as possible to the conditions expected or planned for the field-work. The experiments described in this article have unquestionably proved that if these rules be followed the accuracy obtainable will be very considerably increased and the stadia method thereby made even more valuable than it has been in the past.

203. Adaptation of Formulæ to Inclined Sights.-The discussion given in Art. 200 is applicable to horizontal sights only.

If the rod be held on the top of a hill, and the telescope pointed towards it, the reading on the rod will give the linear distance from instrument to rod, provided the rod be held perpendicular to the line of sight. As it would be inconvenient to do this, let the rod be held vertical in all cases. When the line of sight is inclined to the rod, the space intercepted is increased in the ratio of 1 to the cos of the angle with the horizon.