34 



THE AGRICULTURAL NKWS 



January 31, 1914 



In cases where homogeneous material has to be 

 dealt with, there is practically no difference between 

 the quality of the sample and the quality of the 

 whole. Analysis of the most minute samples of pure 

 common salt, for instance, will always give the same 

 results, or if there is some slight variation, it will 

 be due entirely to imperfections in the methods of 

 analysis. Nor is homogeneity confined only to specific 

 compounds: mixtures can also be homogeneous. For 

 instance, with a mixture of alcohol and water, the 

 smallest sample will be truly representative of the bulk. 

 But with materials of the class just mentioned agricul- 

 ture has practically nothing to do. Agriculture deals 

 typically with substances of extremely variable composi- 

 tion, and it is obviously one of the most pressing duties 

 of science to assist those who are commercially con- 

 cerned with sampling and those who are chemically 

 concerned, by introducing and familiarizing a dependa- 

 ble system. 



Those who follow science progress in relation 

 to agriculture will be aware that during recent years 

 the philosophy of sampling has not been ne,L;lected 

 in experimental work. In this connexion reference 

 may be made to the lucid writings of Wood and Stratton 

 at Cambridge in connexion with the sampling of 'roots' 

 from field plots, and in regard to the variability in the 

 results of feeding experiments; there is also Halls 

 and Russell's investigations at Rothamsted: Gavin's 

 statistical researches with milk records; Leather's work 

 in India; and coming nearer home, Harrison's investi- 

 gation of the probable error in sugar-cane experiments. 

 And underlying all this work, in spite of its being 

 extremely technical, there is a very practical and moral 

 motive. The aim is to interpret results rationally, 

 and to exercise the greatest cavition before laying 

 results before the agricultural public. 



Speaking generally, the principal thing in samp- 

 ling is to decide what the minimum quantity is that 

 may be taken to give a representative value to the 

 whole. In this respect there has been in the past, and 

 there is, too, at the present time, a grear, deal of 

 personal 'fancy' and 'rule of thumb' at work. Nothing 

 could be less in the interests of science and commerce. 

 One imagines that in a general way the size of the 

 sample selected by those who are not trained techni- 

 cally depends principally upon an a priori knowledge of 

 the degree of homogeneity of the material to be 

 examined; for instance, the degree of homogeneity in 

 a field of diseased sugar-canes will be greater than in 

 one which is entirely healthy; hence even an untrained 



investigator would know that a larger sample must be 

 taken in the former case. Incidentally the ques- 

 tion of sampling in relation to partially damaged pro- 

 ducts is a matter of great importance all round. 



The soil presents extremely difficult probleriis 

 as regards sampling, because no two samples will 

 be alike; hence in the case of the soil, com- 

 paratively large and numerous samples are needed 

 before accurate judgements can be formulated. It 

 is probable, indeed certain, that what we are calling 

 the degree of homogeneity, is an important factor 

 for consideration in regard to the valuation of 

 Plantation rubber. It is easy enough to determine 

 the proximate constituents in a sample of rubber, 

 and to subject the rubber to physical tests; but it 

 is not so easy to say to what extent these results 

 hold good for the entire cargo. Nor do we even know 

 whether these proximate constituents, like caoutchouc 

 for instance, have the same chemical composition in 

 themselves, throughout the whole bulk. 



The only way to form a true judgement of the value 

 of any bulk is to decide mathematically how much 

 must be examined to provide a representative sample, 

 or — what is generally retpiired in practice- -how many 

 small samples must be taken in order that the arithme- 

 tical mean of the quantitative results of their examina- 

 tion may be justifiably taken. We had hoped in the 

 course of this article, which professes to be popular, 

 to avoid a reference to Freijuenc}' curves and probable 

 error formulae. 3Ioreover. the mathematical aspect of 

 variability has already been explained in this journal* 

 But it would be an omission in the pi-etent connexion 

 not to invite the reader's attention to the use of 'he 

 Frequency curve as a simple means of ascertaining 

 the amount or dfe]iendence that may be placed on an 

 average, that is, as a means of deciding whether 

 enough small samples have been taken to enable 

 a correct average estimate to be struck. Closely 

 connected with the Frequency curve is the probable 

 error, which is a measure of the reliability either of 

 any one result, or of the mean of a number of resuhs. 

 The probable error of any one result is such than 

 taking any single result at random, the chances are 

 even for or against that result differing from the 

 average by the amount of the probable error. In 

 other words, half the results should differ from the 

 mean by less than the probable error, the other half by 

 more. The probable error of an average can be found 

 by dividing the probable error of one result by the 

 square root of the number of results averaged. The 

 * Vol. Xr, pp. 145, 161. 177. 



