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## Pearson square or rectangle

Because the concentration of fat and protein in milk vary with season, and other well documented factors, it is necessary to adjust the composition of milk for use in the manufacture of cheese and other dairy products. This process, called milk standardisation (standardization in the US) is designed to ensure that product quality is maintained at a consistent level throughout the year. This area will be dealt with in more detail elsewhere in this website.

Increasingly standardisation is being done automatically using on line instrumentation. In small dairies this is still done 'manually' including calculating the volumes (or weights) of skim milk and whole milk required to produce a particular quantity of milk of a defined fat concentration.

One of the simplest methods of routinely adjusting the fat concentration of milk for cheese, ice cream or whole milk powder manufacture is to use the Pearson Square or Rectangle. This method may also be called Pearson's Square or Pearson's Rectangle. This is a simplified method for solving a two variable simultaneous equation. While it is being used here with milk it is is a tool that can be used to help processors calculate the amounts of two components that need to be mixed together to give a final known concentration. For example, it can be used to calculate the amounts of fruit juice and sugar syrup to be mixed to make a fruit squash or fruit pulp and sugar to make a jam. It is also used in mixing rations for animal feeding and in the meat industry to produce meat products e.g. sausages to a particular fat content. Wines and other alcoholic beverages are also blended to give products of a specified alcohol concentration. Microsoft Excel spreadsheets for undertaking these calculations can be downloaded.

This tool can only be used for blending two components. When more than two components are involved, more complex mass balance equations have to be used. The first step in using this method is to draw a rectangle. At the centre of the rectangle write the concentration of fat required in the cheese milk. At the upper left hand side write the % fat concentration of the milk; the most concentrated fat source used. At the bottom left hand corner place the fat concentration of the skim-milk used. On the top right hand side write 'parts milk' and on the bottom left hand side write 'parts skim'.

The 'parts milk or skim' are obtained by subtracting the lowest value number, working diagonally, from either the desired final fat concentration in the case of milk or by subtracting the value for final fat concentration from the concentration of fat in the milk.

This process gives the proportions of milk and skim that must be mixed together to give the desired fat concentration. Knowing the weight or volume of the final mix, the actual quantities of milk and skim required can be obtained by a simple proportional calculation. Note this method can also be used to standardise protein, SNF and/or casein in milk.

Browsers can test their understanding of this basic calculation by using the calculator below. More information on Milk Standardisation is available in the Answers to cheese science and technology self assessment section.