162 



THE AUKICULTUKAL NEWS, 



May 25, 1912. 



It happens sometimes, however, that the curve 

 that is obtained may possess more than one peak. In 

 such a case, it is indicated that more than one cause is 

 actively influencing the results, and that no reliance 

 can be placed upon their average alone, when an inter- 

 pretation of them is sought. There is, however, no 

 need to conclude, in such a case, that the results are 

 useless, for information may have been received which 

 will enable the separate factors causing variation to be 

 discovered, and the apparent incongruity may prove to 

 be of the greatest use in arriving at an interpretation 

 of the experimental figures that have been obtained. 



The next step is to find the value that may be 

 attached to any one result; this is done by ascertaining 

 its Probable Error, or the extent to which it may 

 vary from the average on account of the method 

 of experimentation employed. The determination of 

 the probable error is a matter of applying the 

 rules of mathematical chance; these must be taken for 

 granted in this discussion. It will suffice to say that 

 the probable error is found by adding together the 

 squares of all the amounts by which the results differ 

 from the average, dividing the figure obtained by the 

 number of results less one, taking the square loot of 

 the quotient, and multiplying this by the constant 

 quantity 067. To illustrate the use of the probable 

 error obtained by means of this simple arithmetical 

 process, suppose that it is found to be 2'3, in a certain 

 instance, and that the average of the results was 16-6, 

 it is most likely, under the conditions of the experiment 

 that any one result will fall between the limits differ- 

 ing by 23 on each side of 16'6; that is, between 143 

 and 18-9. 



Proceeding to the consideration of more than one 

 result in a given investigation, it is useful to know the 

 probable error of the average of all the results, or of 

 a certain number of them; this is obtained by dividing 

 the probable error of one result, found as above, by 

 the .square root of the number of results that are 

 being considered. For example, employing the prob- 

 able error just found, namely 23, the probable error of 

 the average of four results would be 2'3 divided by the 

 square root of four; that is 2•3-^2, or 1'2. In the same 

 way (to take another simple example) the probable 

 error of the average of nine results would be 0'8. 

 It is obvious that the probable error of the aver- 

 age of results decreases with increase in the number 

 of results taken. Further, using the application of the 

 last result as an illustration, it has been shown that, 



under the special circumstances, when nine results are 

 taken, the average is not likely to vary on each side of 

 It! (J by more than 08; that is, the chances are that it 

 will be between 1.5'8 and 17'4. It is instructive to 

 compare these limits of variation with those of the 

 similar limits for one restilt alone, as de termined above 

 namel}' 143 and 18'9. 



It is sometimes found convenient, in experimenta- 

 tion, to divide the experiments into two equal, inde- 

 pendent groups, to submit each to the same process of 

 investigation, and to take the average of each gToup, 

 instead of regarding the whole lot as being in one group 

 and finding the average of this. By doing this, a use- 

 ful check on the work is obtained, especially when the 

 results are employed for comparison in the two groups. 

 The value of the comparison is determined by finding 

 the probable error of the difference between the two 

 i-esults; and when this is done, it must be remembered 

 that each of the results, as it is obtained by the same 

 method, is liable to the same probable error. Taking 

 this into consideration, it may be said shortly, that the 

 probable error of the difference between any two such 

 results is obtained by multiplying the probable error of 

 each result by the square root of two. Thus, with the 

 figures given above, and taking two similar groups of 

 fifty, the probable error of the average of 100 results will 

 be 2'3 divided by 10 (the square root of 100), that is 

 023; and the probable error of the difference of the 

 averages of the two groups of fifty (making up the 

 hundred) will be 023 multiplied by .the square root of 

 two, giving as the result 026. 



Further development and illustration of these 

 matters may be found in the papers mentioned in the last 

 article, particularly in that entitled The Interpreta- 

 tion of Experimental Results, by T. B. Wood, M.A., of 

 the Cambridge University Department of Agriculture. 

 The purpose of the next article on the subject will be 

 to bring forward the practical value and results of the 

 methods, as they may be applied specially to schemes of 

 experimentation that are being carried out in the West 

 Indies. 



Information concerning the export of rubber from the 

 Federated Malay States is contained in the Govet nment Gazette 

 for March 1.5, 1912. This shows that the quantity shipped in 

 .January 1912 was 2,730,.576 ft) ; during the same month of the 

 previous year, it was 1,329,170 ft. By far the largest amount 

 oj rubber is being produced in the State of Negri Sembilan. 

 the weight for last January being 1,352,473 ft). 



