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"The Method of Brezina" — A Quick Method of Modal (Mineral Percent) Analysis

Brezina, Jiri, 1959c: A quick method of modal analysis (Czech, English summary); Vestnik of the Central Geological Survey, Praha, vol. 34, No. 3/March, p. 161 - 169.

The article is based on a simple fact, that the microscope eyepiece view with a 100 portions scale has an area of 100 by 100 portions = 10,000 square portions. It is true for the same shape of the eyepiece view as the shape of the portions: both may be squares, circles etc.. Therefore, a component-percent in the circle eyepiece view, such as a mineral-percent, equals

% = n.y^{2}/100 , where |
n is the particle number in each eyepiece view |

y is the particle circle-equivalent diameter in the eyepiece portions |

I recommend to average both values per each eyepiece-view in order to increase the representativity and accuracy of this simple method.

In the time when I wrote the article (1958), there were no calculators and smart-phones. This is why I constructed a simple nomograph of the above formula, in which the co-ordinates cross-section gives the component (mineral) percent (diagonal scale).

You are welcome to print out my nomograph either in format A4 here (or in format Letter here) — enjoy it.

This common-sense method has three advantages:

- It is very fast and economic;
- One does not need to determine all components up to 100 percent;
- It is accurate, and for accessoric components
*most*accurate.

In these days, it may be easy to design a simple smart-phone application or an Excel table for the above formula.

However, I believe that even when using the most sophisticated image analysis programs, you may enjoy this rapid, economic and common-sense method, for example — to check the results of your object recognition routine.

The Spreadsheet Excel Table can be used according to the following example showing calculation of ten eyepiece views. Here is an *active* Excel Table example: you may fill in the columns "size" and "number" with your data and the Table will display immediately the results - the calculated percentages in the column "%" .

Good luck!