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been found essential to success. In the first place the squads of men are limited to two. There are never more than two men at one instrument, even the plane table. The great advantage of that is that each student has abundant opportunity to become familiar with the instruments. Where squads of five or six men are together, one man out of the six will do most of the work, and the chances for each man getting at the instrument are only one-sixth of the total time, and the probability is that one or two students will absorb the greater part of the time, and the others will permit it. Again, with large squads it is much more difficult to maintain discipline. Not more than two students can be kept busy at once. A student who is unfamiliar with an instrument cannot keep more than one assistant busy. With squads of two men they are kept very busy, and they have abundant use of the instrument. So far as practice is concerned, it may be said that a day where there are only two men on the squad is equivalent to a week where there are six men on the squad.
The next point is that everything is done to insure economy of the students' time. At Columbia there is a large force of assistants, and the work is so subdivided that each assistant has charge of a few squads only, and can visit these squads at frequent intervals. While the student is made responsible for the work and the accuracy of it, he need not lose time because of any uncertainty as to the best methods of carrying on the work, because the assistant is always near to give advice. Where accuracy is required, of course there is the danger that the students will resort to dishonest practices in order to obtain the desired accuracy without doing the work. This of course is fully appreciated and has been guarded against very carefully, the principle being to make it a little more difficult to do the work in a dishonest way than to do it properly, and to remove as far as possible all temptation from the student to do work of this character. For example, the line of levels laid out over which all the squads have to run is a mile in length with stations every one hundred feet, and with bench marks every five hundred feet. At each station where there are bench marks there are placed some six or seven benches, the levels of which are known accurately, and at each station there are six, seven or eight plugs driven in the ground, the elevations of which are known but which are changed from time to time. It is evident that by starting squads from different benches, giving them the same datum, but really a different elevation, and by obliging them to check
different benches along the line, and to use different stakes, the permutations and combinations of this single line of levels are almost infinite and the trouble of computing a theoretical line of levels along the route given is so great as to deter the pupils from doing it. Even if this were attempted it would be an easy matter to detect it. It has been found by careful determination of the result that there is a certain law of error, so to speak, that is that errors, unless gross mistakes are made, tend to increase or decrease pretty regularly, and by simply finding
out what are the errors as determined from the average of the levels given, by determining the errors you can tell by inspection very quickly whether the work has been honestly done or whether it has been done by some dishonest method. A similar plan is followed for the traverses. There are on this farm some one hundred or more stone monuments which are placed about two hundred, two hundred and fifty, or three hundred feet apart, on the corners of a series of quadrilaterals, making a large number of quadrilaterals covering about half the area of the farm. These stones are placed in the earth. In the center of each monument is a copper bolt and the center of this bolt is marked by a small center punch. At the cost of a great deal of labor all the distances between these monuments (and there are a great many hundreds of them on the sides and diagonals of the quadrilaterals) have been measured with a steel tape, so that the distance between these stations is known probably to less than one-hundredth of a foot even in a three or four hundred foot course. The angles also between the different lines at the intersections of the quadrilaterals have been determined very carefully, so that the angles are known to a probable error of about four or five seconds. Each year these measurements are repeated so as to tell whether the monuments have shifted, and the shifting monument again is a deterrent to an accumlation of data for dishonest purposes, so that each year we know just what the distance is between these monuments.
Again, the lengths of the tapes which are used by the student are determined. The measurements are made with tapes three hundred feet long, by a method introduced by Mr. Cox, of Pennsylvania. The error of each one of the tapes given out to the students is known. The students do not know these errors, consequently if they should use some other tape or the measurements obtained from some other tape, they would obtain results which would not agree with the results which ought to be expected from that tape.
Again, the limits of error in the students' determinations are accurately known, for these can easily be determined from the measurements of the same distance by different squads, and if there has been any collusion by the errors being abnormally small, or the distances before being corrected being the same, and after correction very different, the fraud can be detected.
The great advantage of this system which has been followed is that the students are checked, not on finished work, but on every measurement that is taken, on every reading of the level rod, on every measurement of length, on every measurement of angles.
The student is required to make preliminary reports on the work that he has done during the day, and if it is found that there are two or three measurements that are wrong, he is required to repeat double that number. If as many as half the measurements on a traverse are wrong, he is required to repeat the whole traverse. Before they have gone too far with inaccurate or improper methods, the instructor is enabled to correct their methods of work, and to insure that they shall adopt, the next day, proper methods.
Again, the students are not permitted to repeat a measurement of any kind more than three times. The first time that an incorrect measurement is reported, he is required to have an assistant present when he repeats the measurement once, to make sure that the proper method has been adopted the second time. If an incorrect measurement is reported a second time, the professor himself generally tries to be there when the third measurement is made. After that, the student is not permitted to repeat it again. This avoids wasting the student's time, for it may be, of course, that the error may be due to the instrument, may be due to the rod or the tape, or it may be an error in the original determination of an elevation or distance or angle, as the case may be.
Now as to the course adopted in surveying. The course begins with a pacing survey. The student is practiced in determining the length of his pace. The natural
is first determined on level ground, then on sloping ground, up and down hill, and from the results of this determined natural pace an artificial pace is assigned him, slightly shorter than the natural pace, and with this artificial pace he makes his measurements. It has been said that it is desirable that students should always use their natural pace in surveying. This, however, is impractical because the natural pace varies so. In going up or down hill some people lengthen and some shorten their pace, but even