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A NYONE who has constructed isarithmic maps has at one time or another been faced with the question as to how closely his isarithms should fit the plotted data on which they are based. Quite properly, closeness of fit is in large part a matter of judgment in the sense that the investigator, knowing the factors that influence the values of the variable, will apply this knowledge in making decisions as to the location of a single isarithm or a group of isarithms. An obvious example of such exercise of judgment is found in the drawing of isohyets for a plains region that includes within its borders a prominent isolated mountain. Because it is known that such a mountain usually produces increased rainfall on its slopes through forced lifting of moisture-bearing air, an investigator drawing an isohyetal map for such an area would quite properly bunch the higher-valued isohyets around the, mountain rather than space them in direct interpolative manner with respect to lower-valued rainfall observation points on the surrounding plain. Similarly, on isarithmic maps pertaining to cultural factors, as on a map showing mean income or land in crops, an investigator would apply his judgment in the bunching of isarithms in zones where he had reason to believe unusually rapid transition would occur. The fitting of isarithms to plotted data is not, however, simply a matter of understanding the factors that influence a variable andof applying this understanding in a judgment sense. There is also the problem of the reliability of the data themselves as that reliability relates to the precision with which the isarithms should fit the plotted values. To take an extreme and hypothetical example, if there is a 50 per cent chance that any plotted value may be as much as 100 per cent in error, then clearly a close fitting of the isarithms is not warranted. This study examines the relationship between the reliability of plotted data and the degree of precision that should reasonably be exercised in the drawing of isarithms to fit the data. A simple statistical method is developed for estimating goodness of fit of isarithms and this method is applied for illustrative purposes to the drawing of a map showing mean July temperatures in the state of Kansas.