In fixing the _exact_ position of the 30° line south of Memphis and Little Rock, the following considerations must be our guide: Memphis has 28°; Vicksburg has 35°. Neither of these stations has 30°. Suppose, however, that you had started from Memphis, with a thermometer, and had traveled very rapidly to Vicksburg. The thermometer reading at starting in Memphis would have been 28°, and at the end of your journey in Vicksburg it would have been 35°, presuming that no change in temperature at either station took place during the journey. Evidently the mercury rose during the journey, and in rising from 28° to 35° it must, somewhere on the way, have stood at exactly 30°. Now this place, where the temperature was exactly 30°, is the point through which our 30° line ought to pass. How are we to determine its location? Assume, as is always done in such cases, that the temperature increased at a uniform rate between Memphis and Vicksburg. The total rise was from 28° to 35° = 7°. In order to find a temperature 7° higher than at Memphis, you had to travel the whole distance from Memphis to Vicksburg. Suppose you had only wished to find a temperature 5° higher. Then, assuming a uniform rate of increase between the two stations, you would have had to travel only 5/7 of the distance, and your thermometer at that place would have read 28° + 5° = 33°. But assume you had wanted to find the place where the thermometer stood at 30°. In this case you would have been obliged to go but 2/7 of the total distance from Memphis to Vicksburg, and at that point your thermometer reading would have been 28° + 2° = 30°, which is the point we wish to find. In this way, then, when we do not find the _exact_ temperature we are looking for on the map, we can calculate where that temperature prevails by noting places which have temperatures somewhat higher and somewhat lower, and proceeding as in the case just described. Take another example. Little Rock, Ark., has 26°; Shreveport, La., has 40°. 40° - 26° = 14°, which is the total difference. From 26° to 30° is 4°. Therefore a point 4/14 or 2/7 of the distance from Little Rock to Shreveport should have a temperature of 26° + 4° = 30°, which is the point we wish to find, and through which our 30° line must pass.