WILS GOVU Y 3.AT 7:22/ORNL-3394 OAK NATIONAL RIDGE ATOMIC ENERGY LABORATOR NL-3394 COMMISSION CASPER: A GENERALIZED PROGRAM FOR PLOTTING AND SCALING DATA UNIVERSITY ORNL-3394 UC-32 - Mathematics and Computers TID-4500 (18th ed.) M. P. Lietzke R. E. Smith SITY OF MINNESOTA 25 FEB 1963 LIBRARY OAK RIDGE NATIONAL LABORATORY operated by UNION CARBIDE CORPORATION for the U.S. ATOMIC ENERGY COMMISSION Printed in USA. Price: $0.75 Available from the Office of Technical Services U. S. Department of Commerce Washington 25, D. C. LEGAL NOTICE This report was prepared as an account of Government sponsored work. Neither the United States, nor the Commission, nor any person acting on behalf of the Commission: A. Makes any warranty or representation, expressed or implied, with respect to the accuracy, completeness, or usefulness of the information contained in this report, or that the use of any information, apparatus, method, or process disclosed in this report may not infringe privately owned rights; or B. Assumes any liabilities with respect to the use of, or for damages resulting from the use of any information, apparatus, method, or process disclosed in this report. As used in the above, "person acting on behalf of the Commission" includes any employee or contractor of the Commission, or employee of such contractor, to the extent that such employee contractor of the Commission, or employee of such contractor prepares, disseminates, or provides access to, any information pursuant to his employment or contract with the Commission, or his employment with such contractor. . Contract No. W-7405-eng.-26 ORNL-3394 Mathematics Division CASPER: A GENERALIZED PROGRAM FOR PLOTTING M. P. Lietzke AND SCALING DATA DATE ISSUED R. E. Smith JAN 3 0 1963 OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee operated by UNION CARBIDE CORPORATION for the U.S. ATOMIC ENERGY COMMISSION -ii- ABSTRACT A Fortran subroutine has been written to scale floating point data and generate a magnetic tape to plot it on the Calcomp 570 digital plotter. The routine permits a great deal of flexibility, and may be used with any type of FORTRAN or FAP calling program. A simple calling program has also been written to permit the user to read in data from cards and plot it without any additional pro- gramming. Both the Fortran and binary decks are available from Marjorie Lietzke, Mathematics Division. 1 -1- 10G CASPER: 2) M. P. Lietzke A GENERALIZED PROGRAM FOR PLOTTING AND SCALING DATA R. E. Smith INTRODUCTION CASPER (Calcomp Automatic Scaling, Plotting, Editing Routine) is a general Fortran subroutine written for use with Fortran or assembly language programs to produce scaled plots of floating point data on the Calcomp 570 plotter. A calling program is available to read and plot data if no computation is desired. CASPER offers the following options: 1) x and y maximum and minimum values may be specified or found by the subroutine; scaling and plotting may be done for blank paper (maximum sensitivity scaling with a complete grid or indicated intervals drawn) or lined graph paper (intervals are set at the inch or half-inch lines); 3) graph size may be varied (8" ≤ x axis ≤ 120", 5" ≤ y axis ≤ 9"); 4) a line connecting points or 16 different point-centered symbols (available in two sizes) may be used for plotting data; 5) title and labels for axes may be indicated for each graph; 6) CASPER will plot as many separate graphs as can be written on one magnetic tape, with a limit of 50 curves (a curve being a set of points connected by a continuous line or plotted with one symbol) and 65,535 total points per graph. Space will be left between graphs for cutting and binding. -2- 1 These options are described in more detail in the section on "Use of Subroutine CASPER". The range is computed as maximum minus minimum for each axis and an interval size is established. The maximum and minimum values are then R X set to the nearest integral multiple of the interval size encompassing the range. If the plot is to be on lined rather than blank paper, the number of intervals is adjusted so that the size of the interval will be either one or one-half inch, and the maximum x and y values are changed accordingly. The procedure is as follows: 왔 ​= X Ax = n2 x q' max X XMax Ax X MATHEMATICAL DISCUSSION If fractions exist: - Allian min Ax 10p-1 X min #1 n₁ x 10²(.1 ≤ n₁ < 1) ny ոլ where n2 = .1 if n₁ = .2 n₂ = .25 if .2 < n₁ < .5 q' na || Integer + (fraction) X .5 if n ≥ .5 = Integer + (fraction) for positive numbers q, = Integer + 1 = Integer for negative numbers q = Integer X q'x = Integer Integer - 1 -3- If there is no fraction q, or q' is used unchanged. X xx = qx XM Xm < length of x axis in inches (Sizex): XM - = ((2 × Sizex) - 9p₁x) Ax + XM XM X₁₂, = (Sizex qp 'x) AX + XM 9R'X = Sizex Xm from Max and Ymin' In both cases, R'X is then recomputed: Y = R'Y m Mo Mainten AR'Y -4- option. If 9R X Sizex, no changes are made. Υ. Similar formulae are used to recompute YM, Ry, and R'Y for this The interval sizes in both cases are set as follows: x interval size y interval size X Y m The plotting area is then outlined, the intervals indicated or a full grid drawn, and the title, YM, Ay, y label, Ym, X x label, Ax, and XM printed around the plotting area. All output numbers on the graph are of the form n x (10)P where 1 ≤ n ≤ 10: e.g., 40 would be written as 4.000 + 1. C Finally, the x and y values are normalized and plotted as follows: m -R 'X m -R 'Y X Ꭹ Sizex qRX Sizey AR "Y x Sizex = XN GAMA x Sizey YN Į USE OF SUBROUTINE CASPER CASPER makes use of a number of FAP subroutines written for the IBM-7090. These FAP codes must be rewritten before CASPER can be used on another machine. A list of these routines and their length is given in Table 4. The subroutine also calls Fortran subroutine SQUASH to set up -5- array of BCD output numbers in scientific notation and LEGEND to put out arrays of BCD information. These subroutines are all included in the binary deck of CASPER and need not be called directly by the programmer. No other subroutines in the user's program may be given these names. CASPER'S arguments are in the form of arrays. for each point (x, y) which is to be plotted, and the order in which points are given to CASPER is also the order of plotting. CASPER is called 1. Options In the following description of options available in the use of CASPER a curve is defined as a set of points to be plotted sequentially with a continuous connecting line or with a single symbol repeated for each point. A plot or graph is a complete picture including grid indi- cators, title, labels, and containing one to fifty curves. reduce curves in a plot. - 1.1 RANGE SETTING CASPER will search data for x and/or y maxima and minima or accept specified values as arguments. In the latter case points outside the specified x or y range are rejected and a message written on the output tape. The plotting pen will not be lifted for rejected points; thus, if the curve is a line plot a line will be drawn to the next acceptable point of the curve. If it is desired to "blank out" some part of a curve, each segment must be indicated as a separate curve. The x or y range for a plot cannot be zero; if the user wishes to plot a single vertical or horizontal line, he must specify some range (maximum minimum) for the other axis. Specified maxima and minima may also be used to center or -6- 1.2 SCALING Scaling and plotting may be done with maximum sensitivity, so max that the entire graph area is covered by the ranges x X min' 'max-min' For this option, either a complete grid or one-quarter inch grid indicators will be drawn perpendicular to each axis by the plotter. Blank paper should be used. the axes. If lined graph paper is to be used, CASPER sets the intervals at the inch or half-inch accented lines and merely indicates them along In this case the plotted points may cover less than the entire (Maximum reduction of the graph is 13/24 of the axis in each graph area. direction. See Fig. 3.) 1.3 GRAPH SIZE The graph size may be changed by the programmer within certain limits (8" ≤ x axis ≤ 120"; 5" ≤ y axis ≤9"). The standard plotting area is 9 x 12 with a one-inch margin for labels and binding. If the axes are shortened in either direction, titles and labels will be truncated and should be adjusted accordingly. 1.4 PLOTTING Points in a curve may be plotted with a continuous line connecting them (a polygonal plot) or with one of 16 different point- centered symbols, which are available in two sizes. Curves may also be distinguished by plotting a set of points once with a continuous line, then plotting a few of the points again with a symbol. Thus each curve on a single graph can be indicated uniquely. 1.5 TITLING AND LABELING A title and x and y labels may be written for each graph; if no labels are specified, the axes will be labeled 'abscissa' and 'ordinate'. -7- - Limit on the number of characters in the title of a graph is 48; on the x and y labels, 36 each. If the x axis is shortened, the number of permissable characters in the title is 4 x (new length of x axis). If the x axis is shortened by more than 1.25", the x label limit is [8.3(x axis - 6.5)]. 6.5)]. If the y axis is shortened by more than .75", the permissible number of characters in the y label is [8.3(y axis - 4.0)]. CASPER will automatically truncate the title or the x or y labels if they exceed the above limits. The subroutine will also print the x and y maximum and minimum values, delta x and delta y on the graph. 2. CALLING CASPER The subroutine may be used in Fortran programs by placing the necessary arguments in arrays and then calling CASPER with the array names. The following statements are necessary in the calling program: DIMENSION A(129), I(4), BUFFER (optional) CALL CASPER (A,I, BUFFER) BUFFER is the name of a floating point array dimensioned by the user to provide CASPER with storage space for the x and y coordinates which are accumulated and counted until an end of picture call. If the number of x - y coordinates is greater than the number of buffer cells, the buffer is written on logical tape 27 as many times as is necessary to handle all the points (2≤ no. of points ≥ 65,535). It is not necessary that all of CASPER'S arguments be set on every call; many are checked only once and ignored the rest of the time. CASPER does not destroy its arguments; they will remain set until changed by the calling program. Arguments such as title and labels, therefore, -8- may be set on a first call, although the subroutine will not use them until the end of picture call. 3. CASPER'S ARGUMENTS A description of the arguments grouped according to necessary calls follows. See Table 1 for complete information. 3.1 ALL ENTRIES: There are only two arguments which must be set on every call of CASPER: A(1) and A(2), the x and y values, respectively, of the point to be plotted. 3.2 FIRST ENTRIES: On the first call of CASPER for each separate plot the following additional arguments must be set: A(3), A(4), A(5), A(6), A(7), A(8): 1(1), I(2), I(4). A(3) and A(4) must be set to Xmax and x respectively if the user wishes to specify the x range; min if he wished CASPER to search for the range, he must set them to 0. The same holds true for Y and Ymin' A(5) and A(6) respectively. max ax min’ A(7) and A(8) are the length of the x and y plotting axes and may be left 0 if the user wishes a standard plotting area (9 x 12). Other- wise he must set them to the length desired (8" ≤ x axis ≤ 120", 5" ≤ y axis ≤9"). I(1) must be set to a -2 on the very first call of CASPER for the first or only graph and -1 on the first call for each additional graph. It must not be negative at any other time. I(2) must be set to 1 or 2 to indicate a maximum sensitivity graph (blank paper) or to 0 for adjusted intervals (lined paper). I(4) need be set only on the initial first entry and represents the size of the buffer provided by the user. It must be an integer equal to the dimension of the buffer. -9- 3.3 END OF CURVE CALLS : The following arguments must be set when CASPER is called with the last point in a curve: A(9); 1(1), I(3). A(9) controls the size of the plotted symbols in the case of a point plot; I(1) must be set to 1 to indicate end of curve; I(3) must be set to the type of point (see Appendix A for those available) or line plot desired for that particular curve. 3.4 END OF PICTURE CALLS : The following additional arguments must be set when the last point of the last curve of a graph is called: A(10--129); I(2). A(10--57) is the title of the graph, A(58--93) the y axis label, A(94--129) the x axis label. These should be read into the array in Al format or set equal to left adjusted boolean constants representing the desired BCD characters. If blanks are read into the y or x label portion of the array CASPER will print 'abscissa' or 'ordinate' on the respective axis. I(2) must be set to -1 to indicate end of picture. Every call of Casper will result in the plotting of the values of x and y which are then in A(1) and A(2). The arguments for first entry, end of curve entry and end of picture entry are in addition to the x and y values. For complete information concerning the possible values of the arguments and the limitations on them see Table 1. 4. CONTROL CARDS Control cards for the IBM 7090 monitor must include an absolute *ASSIGN(8,A6), and a tape control card: tape assignment card: *TAPE (8, POOL, SAVE), (27, POOL), (10, INPUT), (9, OUTPUT). Scratch -10- tape 27 will be written if the number of points to be plotted is greater than one-half the dimension given to BUFFER, but it must be specified in any case. The logical tape numbers 8,9,10, and 27 are fixed. 5. OUTPUT MESSAGES An error message will be written on output tape 9 if the proper first entry arguments are not set, and the program will call exit. If either the x or y values are such that the range, maximum minus minimum, is zero a message will be written, no plotting will be done, and control will be returned to the calling program. If the program finds points outside the range specified by the user, it will write a message that the nth point of the plot has been rejected and give the values of x and y. At the end of each plot the actual maxima and minima, delta x, delta y, the number of points, and the number of curves will be written on the output tape. See Appendix A for a sample calling program of SUBROUTINE CASPER. DESCRIPTION AND USE OF THE CALLING PROGRAM A "packaged" CASPER (Fortran calling program and subroutines) is available for plotting data from punched cards. All the options available with subroutine CASPER are also available with the calling package. The first five data cards for each plot must contain initial- izing information as follows: the title; y label; x label; arguments A(3), A(4), A(5), A(6), A(7), A(8), A(9); the first point to be plotted and an integer indicating lined paper or blank paper with d -11- A varying. grid or indicated intervals. All the limitations on arguments listed in Table 1 apply here also. The data cards following these five should each contain the x and y coordinates of a point and a control integer which may indicate end of curve or end of picture, and type of plot. See Table 2 for data input, Table 3 for use of the control integer. The use of the calling package with various options is illustrated in figures 2 through 8. The same data were used in these plots with only the options as to paper type, range specification and plot size ADDITIONAL LABELING If the programmer wishes to label curves or write out additional material on the finished plot, he can make use of the sub- routine LEGEND to write the information at the desired point on the graph. Care must be exercised in using LEGEND for this purpose. The calling program must set up an array of right adjusted BCD characters, one per word. The call statement must be made after the first entry call of CASPER but before the end of plot call, and appears as follows: CALL LEGEND (XP, YP, LEAN, SCALE, NUMBER, ARRAY) where XP and YP are the coordinates in floating point inches at which the first character is to be printed; LEAN = 1 indicates horizontal printing, 2 indicates vartical printing with top of character toward left; SCALE is the factor which sets the character size to 4 SCALE wide by 7 SCALE high (.01 ≤ SCALE≤ 1.5); NUMBER is the number of characters to be printed (1 ≤ NUMBER ≤ 48); ARRAY is the name of a highly subscripted variable containing characters to be plotted. -12- To set up XP add 1.5 inches to the desired distance from the left y axis; for YP add 1.0 inch in the case of blank paper, 0.5 inch for lined paper. $ -13- Array Position A(1) A(2) A(3) A(4) A(5) A(6) Input Number x value y value x max O x min ARGUMENTS FOR CASPER SUBROUTINE: O y max Table 1 Effect x coordinate of point to be plotted y coordinate of point to be plotted if A(4) = 0, hunt x max, x min if A(4) = x min, x range is specified; points outside range will be ignored if A(3) = 0, hunt x max, x min if A(3) = x max, x range is specified; points outside range will be ignored if A(6) – 0, hunt y max, y min if A(6) = y min, y range is specified; points outside range will be ignored if A(5) = 0, hunt y max, y min CALL CASPER (A, I, BUFFER) Must be Set For every call every call first entry for plot first entry for plot first entry for plot first entry for plot first entry for plot first entry for plot first entry for plot Limitations floating point f.p. f.p. f.p. f.p. f.p.; A(3) f.p. f.p. f.p. = x max -14- Array Position Input Number A(7) A(8) A(9) A(10-- 57) y min x axis y axis ARGUMENTS FOR CASPER SUBROUTINE: pos. no. alpha- numeric characters and blanks blanks Table 1 (continued) www if A(5) y max, y range is specified; points outside range will be ignored no title Effect CALL CASPER (A, I, BUFFER) 11 length of x axis (plotting area) will be set to 12". length of x axis will be set to input number length of y axis (plotting area) will be set to 9' length of y axis will be set to input number point scaling factor set to .05 (larger size) point scaling factor set to .03 (smaller size) title of graph printed across top Must be Set For first entry for plot first entry for plot first entry for plot first entry for plot first entry for plot end of curve call end of curve call end of picture call end of picture call Limitations f.p. A(5) f.p.; 8 ≤ x axis ≤ 120 y max f.p.; 5 ≤ y axis ≤9 f.p. f.p. number of characters not > 48; if x axis shortened, reduce number of char. by 4 for each inch -15- Array Position A(58-- 93) A(94-- 129) I(1) Input Number alpha- numeric characters blanks alpha- numeric characters blanks -2 ལ -1 O ARGUMENTS FOR CASPER SUBROUTINE: GND 1 Table 1 (continued) Effect y label printed on side of plot y axis labeled 'ordinate' x axis label printed across bottom of graph x axis labeled 'abscissa' CALL CASPER (A, I, BUFFER) Indicate initial first entry; initializes counters, rewinds scratch tape; calls PLOTS indicates beginning of new graph; initialization, check- ing of arguments no effect indicates end of curve; sets counters, stores informa- tion about curve Must be Set For end of picture call end of picture call end of picture call end of picture call set ONLY on initial first entry. (first call of CASPER in a series of plots) set ONLY on first entry for plot all entries except first, last, end of curve end of curve call ONLY Limitations number of characters not > 36; if y axis reduced by more than .75", limit is greatest integer of (8.3 x 4.0)) (y axis CONS number of characters not > 36; if x axis reduced by more than 1.25", limit is greatest integer of (8.3 x (x axis - 6.5)) fixed point fixed point fixed point -16- Array Position I(2) I(3) I(3) Input Number -1 1 2 1 + no 4 5 6 7 8 Table 1 (continued) ARGUMENTS FOR CASPER SUBROUTINE: Effect CALL CASPER (A, I, BUFFER) indicates end of graph; causes CASPER to scale data and write CALCOMP tape sets up graph for lined paper, with intervals in- dicated on inch or half-inch lines sets up graph for blank paper and maximum sensitivity; draws entire grid sets up graph for blank paper and maximum sensitivity; indicates intervals along axis points in curve will be connected by straight lines; continuous plot points in curve will be plotted by point centered symbol: See Fig. 1. 4 corresponds to bottom line 19 to top line Must be Set For end of picture call ONLY first entry for plot first entry plot first entry for plot end of curve call end of curve call end of curve call end of curve call end of curve call end of curve call Limitations fixed point fixed point fixed point fixed point fixed point fixed point fixed point fixed point fixed point -17- Array Position I(4) BUFFER Input Number ୨ 10 11 12 13 14 15 16 17 18 19 buffer size Table 1 (continued) ARGUMENTS FOR CASPER SUBROUTINE: CALL CASPER (A, I, BUFFER) array name Effect size of buffer region supplied to CASPER by calling program assigns buffer region Must be Set For end of curve call end of curve call end of curve call end of curve call end of curve call end of curve call end of curve call end of curve call end of curve call end of curve call end of curve call initial first entry all entries Limitations fixed point fixed point fixed point fixed point fixed point fixed point fixed point fixed point fixed point fixed point fixed point MUST be same number as dimension of array BUFFER and < 32,768 MUST be dimensioned in calling program; -18- Card No. 1 2 3 4 5 6--K Field 1--48 1--36 1--36 1--10 11--20 21--30 31--40 41--50 51--60 61--70 1--10 11--20 21--30 1--10 11--20 Table 2: INPUT DATA FOR CALLING PROGRAM 21--30 Variable Title y label x label A(3) A(4) A(5) A(6) A(7) A(8) A(9) x value y value NCHECK x value y value NCHECK Type BCD BCD BCD f.p. f.p. f.p. f.p. f.p. f.p. f.p. f.p. f.p. INT f.p. f.p. INT. number of characters not > 48; if x axis shortened, reduce number of characters by 4 for each inch number of characters not > 36; if y axis reduced by more than .75", limit is greatest integer of (8.3 x (y axis - 4.0)) number of characters not > 36; if x axis reduced by more than 1.24", limit is greatest integer of (8.3 x (x axis 6.5)) decimal point indicated 11 11 "T ft 11 11 = = 11 !! 11 }} 11 TI !! 1: 11 11 #1 ?? 11 }! 11 11 right-adjusted data points and a controlling integer are input on sub- sequent cards; if a series of plots is desired simply stack decks with input data in this form. (Cards 1-K) -19- Value of NCHECK O 2 NO 1 2 न न्वे 1 4 567 8 9 10 11 12 13 14 15 16 17 18 19 -1 -4 to -19 with first point of a graph (Card 5) 11 * 11 with all points except first, end of curve, and end of picture end of curve 11 11 11 11 11 1 11 11 !! {1 11 11 11 Table 3: CONTROL INTEGER FOR CASPER PACKAGE When Used #1 !! 11 11 11 11 !! }: 11 !! 11 11 11 ff 11 11 ?! 11 end of picutre end of picture Effect lined paper graph blank paper graph; complete grid blank paper graph; indicated intervals indicates more data to be read indicates end of curve and line plot indicates end of curve and point- centered plotting symbol as shown in figure 1 indicates end of curve and end of picture; line plot of last curve indicates end of curve and end of picture; last curve will be plotted according to NCHECK as above -20- J NAME CASPER LEGEND SQUASH PLOT SUBROUTINE NAMES AND LENGTHS PLOTS THREE SIND SYMBL2 RADJ SET PLOTL TRW BCDFL BCDFX LINK OUT TOTAL Table 4 DECIMAL 3264 105 145 336 279 10 44 21 32 29 19 4284 LENGTH OCTAL 6300 151 221 520 427 12 54 25 40 35 23 10274 -21- 1. 200+ 3[ 2 1.000+ DY ORDINATE POINT OPTIONS AVAILABLE FOR SUBROUTINE CASPER 0.000 ✪ ****** + + + + + + + + + + + + + + + + + + + + + + + + + + ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ A 又 ​◊ ◊ ← ← ← ← ← 0. 000 ххххххххххххххххо * 4 ด 1 13 C Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z ZZZZ + ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ B xlxx * อ ว 4 G ← ← ← ← ← ← ← ← ← ← ← X X X X 1 ABSCISSA Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y ххххх ***** 3 H 4 4 4 4 4 4 ព ~ хххххх X X X X X X X X X X X X X X X X X × × × × × × × × × X X X X X X X X X X X X X X X X X X X * * * * x 44 1 **** T 口 ​ххххххххххххххххххххххххххххххххххххххххххххххххх * * * * * * * * * * * * * X X X X X X X X × × × × × × × × × × X X X X X X X X X X X X X X X X хххххххххххххххх → → → → → → → → → → → ← ← ← ← ← ** 4 4 4 4 4 * ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑++++++ 6 6 6 4 6 4 6 4 6 ถ Figure 1 ล $ + 13 *** E + B ✦ ✦ ✦ ✦ ✦ ✦ ✦ ✦ + + + + + + + + + + + + 4444444 ท Q + 4 4 4 4 4 4 &&&& DX 2.500 *************** 口 ​ххххххххххж + + + D D D D P ✪ & 6 6 6 6 6 6 * * * * * * * * * $ ← × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × + 5. 000+ 1 -22- 3.000 - 3.000 5.000- 1 DY 3SIN(X) AND SIN(2X) CASPER PACKAGE, BLANK PAPER STANDARD GRAPH x X 0.000 X X x X X x X X X X ABSCISSA X X x X X X Figure 2 x X X X X x x x x X DX 1.000 x x x X x x x x 1. 300+ 1 SSIN XI AND SIN(2X) CASPER PACKAGE, LINED PAPER STANDARD GRAPH 0.000 x be ECH DX XX X X Ex X Et ABSCISSA X Las XXX X EX EX DE x 24 EXPLEX St Figure 3 DX 000 2, 400+ -23- -24- 3.000 5.000- 1 DY 3SIN(X) AND SIN(2X) -3.000 CASPER PACKAGE SIZE ALTERED X X * X X x 0.000 X X x X X X x X x X x X X ABSCISSA Figure 4 X X X X x DX 1.000 x x x # X Xx X X X x X X x X 1.300+ X- 6. 000 BSIN(X) AND SIN(280 CASPER PACKAGE! 0 000 * * EX X RANGE REDUCED INED X Est X PAPER RANGE SPECIFIED X Figure 5 X * X DX 1.000 A TA 1. 200+ -25- -26- 2.000 1 -2.000 2. 500- DY Y RANGE REDUCED CASPER PACKAGE, BLANK PAPER, RANGE SPECIFIED X X X 0.000 X X X X ABSCISSA X X Figure 6 x x × X X DX 1.000 * * X X 1. 300+ 1 -27- 3.000 1 DY 5.000- AND SIN(2X) 3SIN(X) -3.000 CASPER PACKAGE, BLANK PAPER, RANGE ENLARGED -3.000 x x X x X x x X x X RANGE ENLARGED x X x X X x * X X X Figure 7 X x X X x x X x ४ X 其 ​x PARA x DX 1.000 x x X x X X 1.500+ 1 -28- 3.000 1 -3.000 -000 'S DY 3SIN(X) AND SIN(2X) CASPER PACKAGE, BLANK PAPER, NO GRID 0.000 CURVE PLOT WITH LINE AND SYMBOL SYMBOL Figure 8 DX 1.000 1. 300+ 1 -29- 29. P. A. Agron 30. N. B. Alexander 31. E. D. Arnold 32. G. J. Atta 33. S. E. Atta 34. R. Baldock 35. J. B. Ball 36. R. H. Bassel 37. R. S. Bender 38. N. Betz 39. J. E. Bigelow 40. J. C. Bresee 41. R. E. Biggers 42. A. R. Brosi 43. G. Broyles 44. R. D. Bundy 45. C. T. Butler 46. H. P. Carter 47. A. Culkowski 48. M. H. Davis (K-25) 49. W. Davis, Jr. 50. H. J. de Bruin 51. G. deSaussure 52. A. C. Downing 53. L. Dresner 1. Biology Library 2-3. Central Research Library 4. Reactor Division Library 5-6. ORNLY-12 Technical Library Document Reference Section 7-26. Laboratory Records Department 27. Laboratory Records, ORNL R.C. 28. R. K. Adams 54. J. H. Durfee 55. F. F. Dyer 56. R. G. Edwards (K-25) 57. H. B. Eldridge 58. L. C. Emerson 59. M. Feliciano 60. R. L. Ferguson 61. B. R. Fish 62. B. A. Flores 63. T. B. Fowler 64. D. A. Gardiner 65. C. D. Goodman INTERNAL DISTRIBUTION ORNL-3394 UC-32- Mathematics and Computers TID-4500 (18th ed.) 66. A. A. Grau 67. C. D. Griffies 68. D. A. Griffin 69. W. L. Griffith 70. E. Halbert 71. M. L. Halbert 72. J. A. Harvey 73. F. F. Haywood 74. C. A. Horton 75. A. S. Householder 76. W. H. Jordan 77. H. W. Joy 78. L. J. King 79. G. B. Knight (K-25) 80. M. 0. Labhart 81. C. E. Larson 82. J. G. La Torre 83. M. E. LaVerne 84. E. Leach 85. E. J. Lee 86. W. W. Lee 87. R. P. Leinius 88. M. H. Lietzke 89-108. M. P. Lietzke 109. E. C. Long 110. G. A. Long 111. F. K. McGowan 112. M. J. Mader 113. F. C. Maienschien 114. C. D. Martin, Jr. 115. J. A. Martin 116. D. N. Mashburn 117. R. P. Milford 118. R. V. Miskell 119. E. C. Moncrief 120. S. E. Moore 121. C. W. Nestor, Jr. 122. G. D. O'Kelley 123. J. S. Olson 124. V. K. Pare 125. C. E. Parker 126. I. R. Parsley (K-25) 127. A. M. Perry 128. W. W. Pitt 129. C. A. Preskitt -30- 130. D. Ramsey 131. M. Rankin 132. E. D. Rather 133. M. T. Robinson 134. J. E. Rowe (K-25) 135. R. M. Rush 136-137. 0. W. Russ (K-25) 138. H. C. Schweinler 139. L. M. Scott 140. C. S. Shoup, Jr. 141. E. G. Silver 142. J. E. Simpkins 143. K. M. Simpson 144. M. J. Skinner 145. G. P. Smith 146. R. E. Smith 147. B. Srite (K-25) 148. F. J. Stanek 149. W. J. Stelzman 150. R. W. Stoughton 151. J. G. Sullivan 152. C. D. Susano 153. J. A. Swartout 154. F. Sweeton 155. D. K. Trubey 156. A. M. Weinberg 157. M. E. Whatley 158. C. S. Williams EXTERNAL DISTRIBUTION 159. F. J. Witt 160. H. Wright 161. J. H. Zeigler (K-25) 162-166. A. Zucker 167. Martin Hochdorf, Tennessee Valley Authority, Old Post Office, Chattanooga, Tennessee 168. Research and Development Division, AEC, ORO . 169-777. Given distribution as shown in TID-4500 (18th ed.) under Mathematics and Computers category (75 copies. OTS) UNIVERSITY OF MINNESOTA 3 1951 D04 030 503 F