Curves like those seen in Fig. 163 are properly drawn as smooth curves because they are based upon some definite laws of nature. It is only because of the crudity of the observations of mankind that the dots are so widely scattered. If human knowledge were sufficient to obtain measurements with exactness, curves for data relating to the laws of nature would fall exactly on points plotted according to the observations and there would be no difficulty in getting smooth curves. The curves in this book are nearly all plotted from statistical data for which there are ordinarilj^ some hundreds of variables, of which many do not follow any definite laws of nature. For most statistical work it is much better to join the points showing the observations by straight lines without any attempt to draw smooth

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curves. Smooth curves would by their smoothness implj' a degree of accuracy in the data much greater than would ordinarily be justifiable. By using the straight lines instead of the smooth curves to connect points, the reader is warned that the chart represents facts as found, rather than facts which are assumed to be in accordance with any definite laws. Where smooth curves are proper, as in Fig. 163, it is feasible to have a mathematical formula to represent the shape of the smooth curve. As the determination of mathematical . formulas to suit the shape of any curve is a whole study in itself, there will be no attempt to cover that subject in this book.