TEANSACTIONS OF SUB-SECTION B. 589 



This affords an even more sensitive index of variation, since it depends on all 

 the conditions favouring plant growth — moisture, temperature, air-supply, and 

 foodstuffs, these being necessary for the production of nitrate — and also on the 

 amount of water washing through the soil, nitrates not being retained like 

 ammonium salts. Here, also, differences are found of the order of 5 or 10 per 

 cent, of the amount present on fields that appear to be uniform. These differences 

 may be accentuated where there is a dip in the field. 



Variations in the field arise partly from natural and partly from artificial 

 causes. So many agents come into play in soil formation that uniformity can 

 hardly be expected. Further, the purely artificial operations, such as tilling, 

 cropping, manuring, and folding, have a profound effect on the soil, persisting 

 for some years. Frequently the treatment has not been uniform over the whole 

 field. Drainage, whether artificial or natural, is rarely uniform : during a very 

 wet winter it is not uncommon to see places in the field where wheat has been 

 affected by differences arising either from lines of good drainage or patches of 

 bad drainage. In other seasons the differences still exist, though not to so 

 marked an extent. 



(b) Lack of uniformity in the conditions of growth. — The conditions of the 

 outside row of a plot differ from those obtaining inside the plot, and those on 

 the outside of the field are much modified by the competition of hedges and 

 trees. These difficulties can, however, be obviated. The unequal incidence of 

 disease is sometimes very troublesome. 



[c) Effect of season. — In manurial trials it is possible after a number of years 

 to allow for the effect of season in a general way, especially as our knowledge of 

 the properties of fertilisers increases. But in variety trials the problem is much 

 more difficult, and cannot yet be said to be solved. 



Total magnitude of the error of experiment. — An examination of the Rotham- 

 sted records shows that the error is 10 per cent, on plots where the past treat- 

 ment has for many years been uniform, where all weighing, measuring, and other 

 operations are performed with the utmost care, and where the general conditions 

 are favourable for experimental work. Having regard to these considerations 

 and the difficulties often encountered in field trials, the authors would not be 

 prepared, as a general rule, to lay stress on differences of less than 15 per cent. 



(vi) The Application of the Theory of Errors to Investigations on Milk. 



By S. H. Collins. 



This paper was intended as a demonstration of the uses to which the theory of 

 errors can be put. The theory of errors was applied to measurements of specific 

 gravity, fat and total solids, with compound measures derived from them. 



Lactometers were compared with a large plummet on a good balance giving 

 the probable variation from the plummet of a single reading on the lactometer with 

 the following results : — ■ 



1 small lactometer 1° = 1 mm., ± 2 degrees lactometer 

 6 special lactometers 1° = 3 mm., ± - 55 ,, ,, 



8 „ 1° = 1 cm., ± 0-18 



1 Westphall balance ± - 47 „ „ 



Total Solids. — There are many sources of error in this determination. The 

 rate of evaporation appears to be one of the large causes of error, but the rate 

 of evaporation is itself dependent on many causes. Without attempting extreme 

 variation of detail, but simply drying milk under such varying conditions as 

 prevail in good laboratories, the probable variation of a single determination from 

 the mean is found to be ± 0'068 per cent. Where work is carried out under 

 rigidly uniform conditions the variation from the mean of one laboratory will be 

 less, but for purposes of comparison between one laboratory and another the value 

 given is not unreasonable. 



Fat. — The probable variation of one determination by Gerber from the mean is 

 ± 0-036 per cent. fat. 



1910. Q Q 



