account of their thickness and stiffness, and when rolled for the sake of portability they acquire the rolling habit and object to lying flat ever after. (6) The use of a scale of 10 ft. 1 in. for plotting cross-sections is not satisfactory, since the eye does not accurately interpolate between

Bridge 3

=

the 10-in. lines; consequently the plotting is actually accurate to the nearest 100-in., ordinarily representing 10 of a foot. The same degree of accuracy in plotting can be accomplished on a paper ruled to about half this scale.

In the case of profile paper we found that for most purposes there were the following objections: (1) It cannot be blueprinted unless tissue papers are used, and these are easily destroyed by careless handling, or even by heavy gusts of wind when they are not properly tacked down to

the drawing paper. (2) It does not take erasure well. (3) The horizontal spacing of the heavy lines (4 in.) is inconveniently great for the plotting of 100 ft. stations, and the 10-in. space is a little too small for the same purpose where two or more pluses must be entered between two 100ft. stations. The approximate location of the pluses cannot be marked

closer than to the nearest 10 or 15 ft. except with the use of a scale, which involves a serious waste of time. (4) The vertical spacing is usually not convenient, the heavy lines indicating feet or 10 ft., etc., and the light ones feet, or % ft. To obtain greater precision than o ft., a scale of 1 ft. per in. must be used, involving a value for the smallest space of 25 ft., which is neither necessary nor convenient. (5) The profiles when rolled up are most inconvenient to carry about, and they occupy a very large space in the files, due largely to their shape. (6) In making use of them much time is lost, rolling them back from end to end to find the point wanted where the profiles cover a considerable length of line.

The inconveniences mentioned before came to mind with such monotonous regularity that after a number of years it was decided to experiment with sheets of paper 81⁄2 in. wide by 11 in. long-the size of a standard letter head-punched in the left-hand margin for filing in a loose-leaf book, and ruled to 20-in. with every fifth line heavy and every tenth line extra heavy.

In making detail sketches dimensions are furnished by the lines on the paper instead of by drawing lines and marking out points with a scale. as when sketching on blank sheets. Sketches can be made in this manner very much more rapidly, and with the same degree of accuracy, as in the old way.

The

The record thus made on a durable grade of paper is as nearly permanent as anything of this sort can be. It will probably be as fresh and clear and legible fifty years hence as the day after it was made. sheets may be filed in a standard letter file with the papers belonging to their particular piece of work, or they may be filed in loose-leaf books or bound in permanent form with special binders. All these methods have been used interchangeably.

For use as cross-section paper these sheets, containing an area of 30,000 sq. ft. on a 20th scale, are sufficiently accurate for most purposes, and can be plotted to the nearest 0.2 ft.

For surveys involving a very large number of sections it has been suggested that blueprints from these sheets on thick paper be used, determining the areas by cutting out the sections and weighing each on a chemical balance. Cross-section paper is sometimes objected to for plotting sections which are to be planimetered, as its shrinkage necessitates a planimeter setting that is difficult to determine. Where the weighing method is employed shrinkage is of no importance as the section is to be compared by weight to a unit section which has shrunk uniformly.

For use as profile paper these plates have been entirely satisfactory, each sheet running for 20 stations horizontally and for 150 vertically to an accuracy of 0.2 ft. or 15 ft. vertically with an accuracy of 0.02 ft. When so used it has the advantage that mass diagrams and cross-sections can be placed on the same sheet, together with the tabular data accompanying the latter.

This paper has been used a great deal for progress diagrams, for which a 31-day month may be listed the short way of the paper, reading vertically when these sheets are filed in a loose-leaf book, and allowing a range for plotting of from 0 to 20 or any multiple thereof.

The original purpose for which the paper was designed was the plot

ting of curves, and for this the 20-in. ruling has turned out to be very well adapted, since across the paper it runs from 0 to 150 and lengthwise from 0 to 200, thus giving a range sufficiently great for almost any kind of work.

One of the most convenient uses of the paper, and perhaps the last one which ordinarily would suggest itself, is for stress diagrams and equilibrium polygons in graphical statics. It would appear that small diagrams on this paper could not be made to sufficiently great precision to give a satisfactory check, but experience with it has shown that this is not the case. If the points are set with care, and the parallel lines ruled with a pair of small but accurate triangles and a wedge-pointed pencil, the resultant precision of the work is remarkable. It is entirely possible to obtain results within 15 of 1%, which is satisfactory for most purposes. Very long lines on tracing cloth will be found not to be as accurate as they appear.

A convenient size of the equilibrium polygon is half the length of the paper or 1,000 divisions. Working to one-fifth of one division for half of this length gives an average error of one in five thousand. This is very much smaller than the error in the setting of the rolls for the manufacture of structural steel shapes, and therefore any greater degree of refinement than this is a bit ridiculous.

The paper is used very largely in computing and tabulating figures, as will be noted by reference to Figs. 4, 5 and 6 which have been taken more or less at random from the files of this office. It is often convenient to typewrite titles and notes on this paper rather than taking the trouble to letter them on freehand. When this is done, a piece of carbon paper placed underneath the section paper with the carbon side up will so strengthen the imprint of the type that most excellent blueprints are obtained.

A curious feature of this paper is that it can be used as a protractor, and is more accurate than the ordinary paper protractors on the market. Use of Rectilinear Chart in Mechanical Drawing. What follows is from an article by Clarence E. Howell, published in Industrial Arts Magazine, May, 1919.

In mechanical drawing it is possible for a student to make a most excellent and commendable drawing, so far as the finished product is concerned, without really knowing very much about what he has accomplished or how he has done it.

It is, therefore, essential that we should know whether the student is really securing a definite, usable understanding of the problems presented, or whether he is merely becoming an expert copyist. Many a student seems perfectly clear on the points presented at the time of the demonstration, and can go through the entire problem with facility, but a few days or a few weeks later when he meets the same problem in class work or in a test, he falls down completely on it. Such lapses in essential knowledge, occurring habitually and among a wide diversity of students, can constitute nothing less than a severe criticism of our teaching methods. Often the things forgotten are the very ones the student should know above all others, indeed must know, if he is to carry away a usable knowledge from his school work.

The only plausible reason for these apparently complete lapses in

memory is either that the pupil never really understood the problem in the first place, or else that he was not drilled upon it sufficiently to impress it indelibly upon his mind.

The ordinary method of school drawing does not provide either a quick and economical way for testing the ground-knowledge of theory beneath the delineation, or a convenient and easy scheme for drill in this theory.

The following plan, worked out to meet this situation, has been used successfully in actual classroom practice. This plan contemplates a series of short, rapid repetitions of essential problems connected with the regular drawing work, and is based upon the supposition that, in this instance, accuracy and appearance may be made secondary to speed and results.

Problems, Figs. 7 and 8, such as these should be introduced into odd moments of the regular class periods, to be worked out by the students with pencil, triangles, scale and compass, on 8 in. x 11 in. sheets of cheap grade %-in. cross-section paper, without the aid of the tee square. The paper should not be tacked to the drawing board, and the section lines of