CHEMICAL DRAWING ZV.
Charts, Graphs, and Diagrams
EDWARD M. HOSHALL 1311 Park Avenue, Baltimore, Maryland
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HE USE of graphic methods by the chemist is rapidly increasing, as a survey of chemical literature in technical publications over the past score of years will show. Nearly everyone who uses the equipment forthesemethods does so on limited acquaiutauce with the general subject. Most chemists are familiar with only a few types of charts, but there are many forms of which they could avail themselves to their greater convenience and e5cieucy. Graphic methods owe this popularity not only to their laborsaving aspects but to their ability in many instances to achieve results impossible to older methods.
There are many important functions that may he performed by graphic charts, each of them susceptible of accomplishment by this method generally more perfectly than in any other way. It is to show the general adaptability of charts, and how best, most effectively, and with the minimum of mathematical elaboration these graphic methods may he applied to chemical problems that this article is presented.
diagrams which the chemist may use to tabulate data, solve problems, and present facts. The following paragraphs will be devoted to the various types of equipment for graphic analysis which may be of interest to the chemist. They will he discussed in some detail, examples of each will he illustrated, and their various chemical applications suggested. Rectilinear Charts.-In general, the rectilinear chart consists of a plane surface ruled off into squares or, in some cases, rectangles. The spacing between lines is arbitrary, graph paper being obtainable with rulings of 4. 6. 8, 10. 12. 16, and 20 divisions Der inch. and also with i &d 2 mi~imeterrulings. &ally every fifth or tenth line is of heavier weight to assist in reading and plotting.
In use, it is customary to make the lower left-hand corner the origin and, if necessary, to present the legend in the upper right-hand quadrant. Any conventional scale may be used with magnitudes increasing from the origin. When practicable, a scale should be so selected that the zero point will appear at the origin, in order that a clear conception of relative values may be obtained. This type of chart is widely used by the chemist, TYPES OF CHARTS chiefly for presenting data and for calculations. FigThe general term, graphic chart, may he taken to ure 1shows a typical application. A fractional crystalinclude all those charts, graphs, sectional papers, and lization scheme is effectively shown in Figure 2 by the 235
use of a rectilinear chart. Figure 3 shows an equilibrium diagram. Note in the latter how use has been made of type legends rather than those executed by hand. Rectilinear charts ruled into rectangles are used both to tabulate data as in "data sheets," and also to plot a variable against an independent quantity such as time. (Figure 4.) Recording thermometers, barometers, and other apparatus of like nature use such charts. Logarithmic Charts.-The logarithmic chart is constructed by ruling two sets of parallel lines a t right angles to each other, the spaces between lines being proportional to the logarithms of the numbers that appear on the margins and not to the numbers themselves. With the aid of logarithmic charts the operation of multiplication is reduced to the graphic addition of logarithms, and since the numbers corresponding to these logarithms appear on the margin instead of the logarithms, correct answers may be read immediately. In like manner the operations of division and extraction of roots may be readily camed out by simple means. It should be remembered, however, when interpolating between two lines, that the divisions are not uniform, and due account should be taken of that fact. Aside from their mathematical advantages, - . logarithmic charts are used for comparisons and demonstrations because of the wide range of data which may be covered. This range depends upon the number of "cycles" used. Thus Figure 5 makes use of three and a fraction cycles horizontally and two and a fraction cycles vertically. The cycles are usually numbered from one to ten, and the decimal point may he placed to give the scale range desired for the data. The applications of this type of chart to chemical problems, especially those involving mathematical analysis, are many and varied. Log paper ruled in one, two, three, or more cycles (sometimes termed "decks"), and also in fractional parts of cycles or decks, may be purchased. Semilogarithmic Charts.-This type is a composite of the rectilinear and the logarithmic chart, the rulings in one direction being those of the familiar Cartesian coordinates and in the other, logarithmic. The semilogarithmic chart has a wide usage for the plotting of comparative statistics of similar kind but dissimilar magnitude, in that the rectilinear ruling permits the uniform spacing of an independent variable, such as time, and the logarithmic ruling provides for the dependent variable. In Figure 6 the second and third cycles have vertical rectilinear rules and horizontal logarithmic rules. It will be noted that the first or lower cycle is a rectilinear chart. The chemist uses this chart extensively in reporting and displaying data covering physical or chemical variations over a period of time. Use of this chart is also made, to some extent, by various recording devices such as the automatic pH recorder, the pH being read directly over a period of t i e .
The Polar Chart.-The polar chart consists of a series of concentric circles 0.1 inch or 1.0 or 2.0 millimeters apart. The circles are divided by radial lines from the center or the origin to the outermost circle. The outer circles are divided into 360 degrees and are nnmbered clockwise or counterclockwise, or both. This chart was designed primarily for plotting curves by the use of polar coordinates. Many other uses have developed; some which may be of interest to the chemist are as light-distribution charts, heat-intensity charts, flow diagrams, or in various recording devices, where the independent variable, usually time, is represented by the divisions of the circumference. Figure 7 is an example of this chart.
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Isometric Charts.-This chart is a device especially designed for the rapid construction of isometric drawings. It has horizontal and vertical lines, and lines a t 30 or 60 degrees to the horizontal, depending upon the position in which the paper is held. Perspective drawings may he readily and conveniently made using this chart. It is seldom used by the chemist. Trilinear Charts.-By means of a "triaxial" or trilinear chart, computations of the percentage composition of a three-component system can be made graphically. The theory is based on the fact that in any equilateral triangle the sum of the perpendiculars from any point to the three sides is equal to the altitude of the triangle. Thus if the altitude represents a number (say 100 per cent.) and a point is placed a t such distances from the
parallel to each other; one line may he inclined or take the form of a curve. The number of lines depends upon the number of variables in the formula or equation to be plotted. Ravenscroft (1) explains the theory and construction of the alignment chart and its various applications to chemical problems. To use such a chart, known values of two variables are joined by a straight line, and the intersection or projection of this line upon the third axis gives the desiredvalue. Thus in Figure 9, with a known boiling point and a known solution composition, the vapor pressure can be readily ascertained by means of a line drawn as shown. The planning and construction of this type of chart is somewhat involved, but its simplicity in use is evident.
three sides that those distances represent the percentages of the three respective components contained in the body, the location of the point then will give a rigid representation of the three components considered. Thus in Figure 8, a phase diagram for lead-tin-cadmium, the eutektoid composition would by inspection seem to consist of tin, 50 per cent., cadmium, 18 per cent., and lead, 32 per cent. This form of chart lends itself admirably to the analysis of tertiary alloys, phase diagrams of threecomponent systems, and, in general, the properties of a system of three variables. Nomographic or Alignment Chart.-A simplified picture of this alignment chart is that of three or more lines
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The fact, too, that several variables can he represented by an alignment chart makes a device of especial interest to those applying mathematical equations to the solution of chemical problems. Bar Charts.-A chart of this nature is classified as a "popular chart"-ne which will be understood by diversified and non-technical readers. Popular charts are usually made so that results and facts may he presented impressionably, since they are not studied critically but are merely observed. The bar chart consists of "bars," composed of horizontal or vertical segments, crosshatched or shaded for contrast. the length of each bar being proportional to the magnitude of the quantity represented. A scale is usually supplied
in order that the numerical values represented by the bars may be ascertained. Figure 10 is an example of a vertical bar chart. This chart might mislead the casual observer, who
Figure 14, or in pairs. The chemist finds many uses of this general type of chart in presenting facts and making comparisons. Coal Sample NOH (2id2 Sulfur) Ind. Enn. Chrrn.. Anobl. E d . FIGURE
10
would be likely to acquire the impression of a 10 or 12 per cent. variation in the length of the bars on the left and a 50 per cent. variation in the pair on the right. Critically viewed, the variations are seen to be only 0.14 per cent. and 0.5 per cent., respectively. An interesting variation of a horizontal bar chart is seen in Figure 11.
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Ind. Eng. C h m . FIouns
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There are many variations of the bar type of chart, chief of which are the "staircase" chart, so called when the bars are shown touching each other, as in Figure 12, the "staircase curve," formed by a line representing the profile of tops of bars shown in Figure 13, and the "compound bar charts, combinations of two or more bar charts either superimposed on each other as in
Pie Diagrams.-Another of the popular types of chart is the "pie" diagram, in which circle sectors are used to represent percentages or parts of the total. The numerical information should appear on the circum-
Peat ference or in the secSoluble 1 -CIOz Residue tors. For clarity it is Lignin 36.8 per cent best to distinguish the 63.2 per cent 2 per eent NaOH or sectors fromeachother 4 wr cent NHaOH b y crosshatching. Humic materials I .,R;e$ This chart is mainly 85.3 used for s t a t i s t i c a l HCI Cellulosepmtective materials Water soluble information. Area and Volume Fulvic acid Precipitate Diagrams.-Pictorial 4.5 Hot almhol charts of this tvoe Soluble . are hymatomelanic acid 1 R[id~;~ynic acid used chiefly for comparisons, the shaded Cooling surfaces representing Wax melting 19' t h e a r e a s obtained precipitates out NaHC03 from the data, or in E I 10 " I some cases representResin acids ing volumes. This latter application may be misleading, since volumes vary as the cubes and not the squares of linear dimensions. preciplW 4 t hH~ Figure 15 is an example of an area diagram, the horiSoluble, apparently fulvic Precipitate zontally shaded area representing work of extension and the crosshatched shaded area work of retraction. F'yridini soluble The Route Charl.-The route chart is a device for I Pyridine iwluble showing the various steps in a process-a type of outI e d . E m . Chcm., Annlyt. Ed. line. The chemist uses such outlines in fractional FIGURE 16 crystallization and in separation procedures. Figure 16 is a typical example. ) Classificatwn Chert.-This type of chart is designed interrelationship of the parts with each other. Figure to show the relationship of a part to the whole, and the 17 shows a relationship chart of this nature.
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DRAFTING
The Joint Committee on Standards for Graphic Presentation has recommended a number of rules which may assist those contemplating chart construction and aid those interpreting charts. They are:
Standards for Graphic Presentations The general arrangement of a diagram should proceed from left to right. Where possible, represent quantities by linear magnitude, as areas and volumes are more likely to be misinterpreted. For a WNe, the vertical scale. whenever practicable, should be so selected that the zero line will appear in the diagram. If the zero line of the vertical scale will not normally appear in the curve diagram the zero line should be shown by the use of a horizontal break in the diagram. The zero lines of the scales for a curve should be sharply distinguished from the other coardinate lines. For cunres having a scale representing percentages, it is usually desirable to emphasize in some distinctive way the 100% line or other line used as a basis of comparison. When the scale of the diagram refers to dates, and the period represented is not a complete unit, it is better not to emphasize the f i s t and last ordinates, since such a diagram does not represent the beginning and end of time. When curves are d r a m on logarithmic coardinates, the limiting lines of the diagram should each be at some power of 10 on the logarithmic scale. It is advisable not to show any more coardinate tines than necessary to guide the eye in reading the diagram. The curve lines of a diagram should be sharply distinguished from the ruling. In n w e s representinga seriesof observations, it isadvisable, whenever possible, to indicate clearly on the diagram all the points representing the separate observations. The horizontal scale for curves should usually read from left to right and the vertical scale from bottom to top. Figures for the scale of a diagram should be placed a t the left and a t the bottom or along the respective axes. I t is often desirable to include in the diagram the numerical data or formula reoresented. ' 15 If numerical dataare not included in the diagram it is desirable to give the data in tabular form accompanying the diagram. 16. All lettering and all figurer in a diagram should be placed so as to be easily read from the base as the bottom, or from the right-hand edge of the diagram as the bottom. 17. The title of a diagram should be made as clear and as comolete as oossible. Sub-titles or desniotions should be added if necessary, to insure clearness.
In addition to the above standards, there are some special considerations which must be applied to charts or diagrams intended for reproduction by means of the "zinc etching" or other photo-lithographic processes. These considerations are as follows: 1. Charts or diagrams for reproduction should be pcncilcd to two or three times the size of the required cut. 2. When mardinate paper is used it should be printed in blue only.
3. The important cv5rdinate lines should be ruled over in 4.
5. 6.
7.
black; the black-ruledsquare being, in general, not less than ten millimeters on a side. The lines of the curve should he the heaviest on the chart with the exception of the border lines. Points on the curve should be indicated by true circles, crosses or dots being used only when additional symbols are necessary. All lines, legends, numbers, and letters which canndt be set in type at the margin of the cut but must constitute a portion of the cut are to be so proportioned that they will be clearly legible in the cut. The numbering of the coardiite axes, the number of the figure, and any necessary explanations of the figure should be written in pencil in the margin of the sheet, as they are usually set up in type rather than reproduced from the drawing. GENERAL ORDER OF DRAWING CHARTS
Bearing in mind the standards for graphic presentation and the special considerations which must be observed on those charts intended for reproduction, a logical order of drawing is suggested as follows: 1. Assemble all data. 2. Determine type of chart. 3. Determine size of chart, and ascertain whether or not the type selected is available in ruled sheets of the required size. 4. Determine the scales for the abscissas and ordinates from the data limits. 5. If line coijrdinates are used, determine the scales of the ~
variables. .--.--. . . .
Lay off the variables on their respective axes Plot the points obtained from the data. Pencil the curves and lettering. .Ink the chart (follow the "order of inking" as given in Part 1). 10. Compose and letter legends, titles, numerals. 6. 7. 8. 9.
The use of graphic methods is an important tool in the hands of those familiar with the subject and this r & u d of charts, graphs, and diagrams is intended to assist the chemist, and especially the student, in the compilation of his results for publication.
Acknowledgment is gratefully made to those who have given permission to reproduce cuts from their articles. SELECTED REFERENCES
(1)
RAvENsmoaT. E. A., "Line -dinate
charts for representing chemical engineering data." Ind. Eng. Chem., 21,120310 (Dec., 1929). (2) PEDOLE.J. B.,"The construction of graphic charts," McGraw-Hill Book Co.. New York City. 1919, 158 pp. (3) HASKELL, A. C.. "HOW to make and use graphic charts." Codex Book Company, Inc.. New York City. 1920, 539 PP.
