the graph paper should be used as guide lines whenever possible. By these methods a good deal may be accomplished in a very few minutes, provided the pupil really knows what he is about. If he does not, this type of work will soon show it, and his case can then be given the individual coaching which it demands. Assurance that practically every member of the class knows the theory, its use, and its application under varying conditions, may be obtained by repeating different applications of the same problem for successive days. The pupils may work on their

own desks without in any way disturbing their regular drawings. They can resume the latter the minute they have finished the special problem without waiting for the teacher to reach them. Thus those who solve the problem easily can go on without waiting for the slow ones.

Excellent training will result from the placing and determining of various views with reference to the size of the paper, and to the H and the V Planes. It will be well, therefore, to emphasize this by leaving the locations and the sizes optional in as many cases as possible.

Several semesters' trial showed that a much more usable type of instruction was being created than under the old system where the stress

was put on absolutely accurate, finished work to the exclusion of the fundamentals of theory.

Mapping. The use of Polar Charts for military mapping is described by Major E. F. Robinson on page 265 of his book, "Military Preparedness and the Engineer," as follows:

Machine gun companies and troops are now equipped with a self-contained range finder, consisting of a tube about 3 ft. long and 4 in. in diam., mounted at its center upon a light tripod. In one side, near the ends, are two windows, containing prisms. These refract the fields of view to the center, where they are seen superimposed through an eyepiece in the center of one side, opposite the objective windows. An ad

justing roller controls the angle of the end prisms, and consequently the position of the images in front of the eye-piece. A sliding scale is actuated by the same roller. When the two images, one from each end prism, appear in conjunction, the range may be read upon the scale. An accuracy of 0.5% may be attained with this three-foot base up to 1,500 yds.

or more.

The use of this instrument for topographical work was first suggested to the writer by an infantry officer of the regular service. Upon investigating, it was found to be feasible for very rapid work in a level coun

try. The observer takes his post upon a building or other elevated point, reads distances by the range finder and directions by a prismatic compass. It is simply the stadia method without the rodman. The use of polar co-ordinate paper, as shown in Fig. 9, is a great aid to rapid plotting.

Plotting Stadia Notes. Chas. R. Thomas is author of the following, published in Engineering News-Record, June 28, 1917:

By plotting stadia notes on separate sheets such as are shown in Fig. 10 and tracing the finished map from these sheets, the cost of plotting stadia notes has been materially reduced and the speed almost doubled. Plotting topography by this method becomes independent of drafting-room equipments, a lead pencil being the only tool required.

The method of procedure is to sketch the topography in heavy pencil. lines and either paste the sheets together for the draftsman or send them to him separately. The sheets are placed under the tracing cloth, and the finished tracing is made directly from them. The paper used for ordinary work is 81⁄2 x 11 in. in size. Using a scale of 100 ft. to the inch, a length of 1,000 ft. and a width of 600 ft. of topography may be plotted on each sheet. Topography may be plotted by surveyors on rainy days, either in the field or in the office, several men working independently on separate parts of the notes. It is remarkable how much the use of a graduated paper speeds up the interpolation of contours and increases the accuracy of scaling.

Reconnaissance Mapping. Fig. 11 and the following short quotation from an article in Engineering and Contracting, April 29, 1914, show how admirably decimal rectilinear charts may be adapted to preliminary survey work.

In mapping the reconnaissance work the drawings were made to conform as nearly as possible to the working plans for the finished road. By doing this they showed the more essential features, such as profile, alignment and drainage of the road, and were more easily handled by the officials to whom they were submitted.

A fair sample of this portion of the work is shown in Figure 11-a portion of the reconnaissance made in Clare county. The small sketch shows the routes followed. In this county there were several different roads which could be taken and used as a portion of the trunk line highway. The heavy line shows the one in preference. These maps were drawn to such a scale (1,000 ft. to an inch) that ten miles of road could be conveniently placed on a sheet 20 x 36 ins. in size. The width of the road was exaggerated in order that such things as cuts, fills, ditches, etc., occurring within the limits of the road could be shown clearly. All information gathered was placed on, or adjacent to, the plan of the road except the profile, which was shown below.

Zones. Polar charts are especially useful for mapping of zones, such as fare zones with respect to a central point, residence zones, population density zones, etc. An example is shown in Fig. 12, taken from Electric Railway Journal, which gives the rush hour passenger traffic outbound from the one-mile zone, the width of the black lines showing relative number of passengers carried.

Chart of Angles. Fig. 13 by H. Hodgkinson, printed in American Machinist, January 16, 1919, shows a use for polar paper which would