24 SCIENCE AND FRUIT GROWING 



a star is invalidated by some of the determinations of parallaxes 

 giving negative values. Misconception on this point is often 

 shown by horticulturists, who imagine that the general results of 

 a large number of experiments can be upset by producing results 

 of an opposite character in some one experiment with, perhaps, 

 half a dozen trees. 



Another difficulty of a serious nature is repeatedly met with 

 in dealing with horticultural experiments . The individual experi- 

 ments from which a mean has to be deduced are often varied in 

 character and, indeed, must be varied, if the conclusions are to 

 be generally applicable the number of the trees comprised in the 

 plots may be different, the varieties may be different, and their 

 general vigour may have differed. If it is only a case of differ- 

 ences in numbers, that may easily be dealt with by weighing each 

 result according to the number of trees under examination ; but 

 other differences cannot be dealt with so easily. To take an 

 instance : some special method of planting may have been 

 adopted in the case of three different varieties of apple trees, two 

 of them, I. and III., are vigorous growers, but have not shown 

 much increase in growth under the special treatment, whilst the 

 variety No. II. has shown very poor actual growth, but a relatively 

 large increase under the special treatment. The actual growth 

 measured in the check and experimental plots is given under 

 A and B below. 



A B Increase 



check. expt. per cent. 



I .... 100 I2O -f 20 



II .... 15 60 + 300 



III .... 300 330 + 10 



Sum . . . 415 510 + 23 



On working out the results with each variety separately, and 

 taking the mean ( -f no), it is evident that the results with the 

 feeble variety (II) influence the value much more than they ought 

 to do, considering the smallness of the actual amount of growth 

 measured ; whereas, if the sum of the measurements of the 

 check and experimental plots be taken, and treated as if the three 

 varieties were all one, we get a mean ( + 23) which almost entirely 

 swamps the large increase under treatment shown by the second 

 variety. 



The only safe rule for dealing with cases of this sort is to take 

 the mean in both these ways : if these prove to be very different, 

 the results must be considered as highly uncertain ; if they are 

 not so, the mean of them may be accepted with some confidence. 



