If, on the contrary, it is the purpose of the investigation to furnish information to the cultivator concerning the fields which are worked, it is necessary to approach the problem from a different point of view. In this case the earth which is under cultivation should be first of all considered with all the modifications which nature causes or practical culture has caused, in it. But it often happens that upon the same farm the natural soil is variable, caused either by the washings from the adjacent soils, by the accumulation at certain points of deposits formed from standing water, or from other reasons. In such a case it would be necessary to take samples from every part of the field which exhibited any variation from the general type, in order to get a complete mean sample of the whole. It is necessary to be on guard against making a mixture of these different lots which would neither represent the different soils constituting the farm nor their mean composition. It would be better to examine each of these samples alone and then from those parts which appear to have a similar composition, to take a general sample for the mean analysis. Most often it is necessary to confine our studies to the really important part of the farm the composition of which would have a practical interest. The aspect of the spontaneous vegetation in such a case, will often serve as a guide to determine the parts of the farms which are similar in nature. The sample should represent the arable layer, properly so-called, that is, that part of it which is stirred by the agricultural implements in use and in which the root system of the plant takes its greatest development and which is the true reservoir of the fertilizing materials. When a trench is dug in the soil it is easy to distinguish the arable layer from the subsoil. In the first place, its color is different, generally being modified by vegetable débris which forms the supply of humus. The depth of the arable layer is variable, but it is most frequently between 200 and 300 millimeters. In the analysis the depth and layers should be indicated since the chemical composition of the earth varies according as the sample is taken to a greater or less depth. As an example of this it may be said that the quantity of nitrogen decreases in general in proportion as the depth of the layer is increased. The sample, therefore, should be limited exactly to the arable layer of soil. =61. Caldwell=[44] advises that according to the purpose of the analysis samples be taken: _a_, from one or from several spots in the field, in order to subject each sample to a separate analysis; or _b_, for an average representation of the soil of the whole field; in this case, several portions of earth are taken from points distributed in a regular manner over the field, all of which are most carefully mixed together, and 4–6 kilograms of the mixture, free from any large stones, are preserved as the average sample.