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Glagolev builds a device for point counting with a microscope. Steinhaus develops stereological principles for measuring length of curves in 2D. Wicksell formulates the general problem of particle size – inferring the distribution of sizes of 3-D particles from the observed distribution of sizes of their 2-D profiles – and solves it for spherical particles.

1919 committee of ASTM (American Society for Testing and Materials) established to standardise measurement of grain size.

Shand builds the first integrating linear accumulator to automate stereological work.

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Rosiwal explains how to determine volume fraction from length fraction on linear transects. 1895 first known description of a correct method for counting cells in microscopy.1885 mathematician Morgan Crofton publishes theory of `geometrical probability' including stereological methods.Delesse invents the first technique (Delesse's principle) for determining volume fraction in 3D from area fraction on sections.

Buffon discovers connections between geometry and probability, that ultimately lay the foundations for stereology. This allows us to extrapolate from the sample to the entire material, to obtain estimates of total quantities such as the absolute surface area of lung and the absolute number of cells in the brain. Using techniques such as systematic sampling and cluster sampling we can effectively sample a fixed fraction of the entire material (without the need to delineate a reference volume). Sampling principles also make it possible to estimate total quantities such as the total surface area of lung. This has caused the method of construction to be rethought as well as methods of restoration. Stereological studies demonstrated that the sand was obtained from dunes facing the bays.

the construction of historic Tabby buildings in the Carolinas was assumed to be done with sand obtained from sand pits.

(Number in 2D is related to length or height in 3D). So it is possible that the disease process simply involves an increase in the size of cells, without any proliferation. However, the number of cell profiles seen on a section depends both on the number of cells and on their sizes. They conclude that the disease involves proliferation of these cells. They find that a certain type of cell is seen more frequently in the diseased tissue.

researchers compare plane sections of normal and diseased tissue from an organ.

(Number in 2D is related to length in 3D). This is an error because the number of capillary profiles on a plane section is related to the length of capillaries, not to their number (which may not even be well-defined). Researchers count the number of profiles of capillaries that are visible in a microscope field, and report the 'number of capillaries' or 'number of capillaries per unit area'.

a biological tissue containing capillaries is sectioned.

the internal structure of mammalian liver was misunderstood for 100 years (1848–1948) because of a similar error.

(Length on sections is related to area in 3D).

But if every plane section shows linear profiles, then the Martensite inclusions must be plate-like, rather than needle-like. For many years this was interpreted as demonstrating that the Martensite inclusions are 'needle-like'. plane sections of quenched steel contain thin linear streaks of Martensite.Stereologists have helped todetect many fundamental scientific errors arising from the misinterpretation of plane sections.

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