"A family of chart-forms of great structural simplicity is that which is known under the general name of the 'proportional' or 'parallel alinement' type. The ease with which they may be laid out and the fact that they may be used with certain forms of equations which cannot be handled so conveniently by those types previously described are strong recom- mendations for their use in these cases." (John B Peddle, "The Construction of Graphical Charts", 1910)
"A more important case is where the divisions are laid off to a logarithmic scale. Paper ready ruled in this way may now be had from dealers in mathematical instruments and is valuable for many purposes. On it many problems which would have to be solved by tediously drawn curves, may be worked with ease by straight lines." (John B Peddle, "The Construction of Graphical Charts", 1910)
"A type of chart which has received considerable attention of late years and which differs radically from those 'already described is that known as the alinement chart. In the charts hitherto examined the necessary lines were plotted on what are known as rectangular coordinates; that is, the axes on which the values of x and y were plotted met at a right angle. This is by no means a necessary condition. The axes may be parallel [...]" (John B Peddle, "The Construction of Graphical Charts", 1910)
"Except in some of the simplest cases where the line connecting the plotted data is straight, it will generally be possible to fit a number of very different forms of equation to the same curve, none of them exactly, but all agreeing with the original about equally well. Interpolation on any of these curves will usually give results within the desired degree of accuracy. The greatest caution, however, should be observed in exterpolation, or the use of the equation outside of the limits of the observations." (John B Peddle, "The Construction of Graphical Charts", 1910)
"In fitting an equation to a given set of observations the first step is to draw through the plotted points a smooth curve. If the experimental work has been carefully and accurately done the curve may be made to pass through, or close to, almost all the points. If not, the curve must be drawn in such a way as to represent a good probable average; that is, so as to lea:ve about an equal number of points at about equal distances on either side of it, these distances, of course, being kept as small as possible. Such a curve is assumed to represent the most probable values of the observations, and we then attempt to get its equation." (John B Peddle, "The Construction of Graphical Charts", 1910)
"In getting an algebraic expression to show the relations between the components of a given set of data there may be two entirely distinct objects in view, one being to determine the physical law controlling the results and the other to get a mathematical expression, which may or may not have a physical basis, but which will enable us to calculate in a more or less accurate manner other results of a nature similar to those of the observations." (John B Peddle, "The Construction of Graphical Charts", 1910)
"The graduated lengths along the different axes may be anything we choose to make them. In general, they should be about equal and as long as possible while keeping the size of the chart within reasonable limits." (John B Peddle, "The Construction of Graphical Charts", 1910)
"The simplest form of graphical chart is that which is frequently used to compare different systems of units of the same character with each other. [...] It is exceedingly simple to construct and to use." (John B Peddle, "The Construction of Graphical Charts", 1910)
"[...] so far as I know, no systematic general method has ever been devised which will give the correct form of equation to be used. The discovery of the equation's form is to a large extent a matter of intuition which can only be acquired by long experience. Some persons seem to be peculiarly gifted in the ability to pick out the proper kind of equation for use in compensating a particularset of observations, but for the rank and file of the men engaged on experimental work this is, and probably always must be, a matter of pure guesswork, which must be verified by cut-and-try methods." (John B Peddle, "The Construction of Graphical Charts", 1910)
"Two dimensional charts for the representation of mathematical equations or experimental data are in very common use nowadays and are everywhere recognized as valuable devices for giving a clear conception of the manner in which the variables are related. Their application is generally restricted, however, to cases where there is but one variable and its function, if the variation to be shown is continuous. Nevertheless cases often arise in which there are two variables and a function to be represented and where it is desirable to show a continuousvariation for all three." (John B Peddle, "The Construction of Graphical Charts", 1910)
"When an alinement chart is intended to cover a considerable range of values we are confronted with the difficulty that it must be large, and therefore awkward to handle, or we must have scale divisions which are too small for accurate reading. These difficulties may be overcome with but little additional trouble by a system of double graduation of the axes." (John B Peddle, "The Construction of Graphical Charts", 1910) [on double axes]
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