COMPOSITION OF HUMAN MILK IN AUSTRALIA. 183 



unchanged. Under these circumstances, when the measure- 

 ments are all made with equal care, there is no reason to 

 believe that any one of them is nearer the truth than any 

 other and the arithmetic mean of the whole number of 

 measurements is taken as representing a value which is 

 probably nearer to that of the quantity itself than the value 

 obtained from any isolated measurement. The arithmetic 

 mean of the results in this case has a very definite meaning. 



But when the quantity measured itself varies, each value 

 which it takes cannot be regarded as an equally probable 

 approximation to a hypothetical "true" value, but itself 

 has a real existence. To take the arithmetic mean of a 

 series of measurements of such a quantity, then, is to obtain 

 a figure which only has a meaning on the basis of assump- 

 tions which do not hold in this case. As the arithmetic 

 mean of a series of measurements of a quantity which varies 

 has thus, of itself, no significance, how then is a series of 

 measurements of such a quantity to be briefly described? 

 Attention seems to have been first directed to this ques- 

 tion by Francis Galton (1879). 



Quantities which are observed to vary are of two main 

 types: (1) those whose variations bear a definite relation to 

 the variations of a second quantity or group of quantities, 

 and (2) those in which no such relation to other quantities 

 has been detected. A series of measurements of a quantity 

 of the first type may be briefly and completely described by 

 stating the relation which exists between this quantity 

 and the second quantity or group of quantities. Such a 

 relation is expressed by the mathematical function which 

 the values of the first quantity are of the values of the 

 second quantity. Numerous intermediate stages occur 

 between the extreme cases where all the values taken by 

 one quantity are a function of the values of other quanti- 

 ties and where no definite relation has been discerned 



