In corolla length of Nicotiana longiflora, polygenic inheritance was studied by

The correct option is E.M. East.

Detailed Explanation:

Polygenic inheritance refers to the inheritance of quantitative traits that are controlled by two or more genes (polygenes), showing a continuous range of phenotypes. E.M. East conducted pioneering research on the inheritance of corolla length in the tobacco plant, Nicotiana longiflora, to study this phenomenon.
By crossing strains of Nicotiana longiflora with different corolla lengths, East demonstrated that the variation in corolla length was quantitative and governed by multiple genes, conforming to Mendelian principles when multiple alleles/genes are involved.

Why other options are incorrect:
- Joseph Kolreuter is known for early hybridization experiments in tobacco but did not establish the genetic basis of polygenic inheritance for this specific trait.
- Francis Galton studied quantitative traits in humans (like height) and developed statistical methods but did not work on the corolla length of Nicotiana longiflora.
- Nilsson-Ehle studied polygenic inheritance in wheat kernel color (kernel color in Triticum aestivum), not corolla length in tobacco.