From Letters to the Editor

N. A. MOROZOV AS THE FOUNDER OF DIMENSIONAL ANALYSIS

Alongside other methods of investigation in physics, dimensional analysis is also used.

Academician S. I. Vavilov drew attention to the importance of applying the method of dimensional analysis. “It is customary to regard dimensionality only as a convenient method for passing from one system to another and, at best, as a means of preliminary checking of the correctness of physical equations”¹. Meanwhile, in private practice, “physicists make extensive use of dimensional analysis as a simple reconnaissance theoretical device that makes it possible to predict the solution of a difficult problem, except for a constant factor”².

Few, however, know that dimensional analysis was first substantiated and widely used in the 1890s by the Russian scientist, honorary academician Nikolai Aleksandrovich Morozov.

In a letter to his mother in 1902, Nikolai Aleksandrovich wrote: “Now I am already engaged in new investigations in mathematical physics, because some few years earlier, when working on The Structure of Matter *) I noticed that, by two or three relations, and often even by one, among several complex physical agents in nature, one can determine mathematically all the remaining relations as well, just as in zoology one can outline the whole of an animal’s body from a single tooth. But for this it was necessary to develop a new method, which I called ‘qualitative physico-mathematical analysis,’ where, instead of the chemical formulas that filled the Periodic System, mathematical formulas are scattered over every page”².

This work by N. A. Morozov was published in 1908 (after his release from the Shlisselburg Fortress) under the title Fundamentals of Qualitative Physico-Mathematical Analysis. In the preface Nikolai Aleksandrovich writes: “Qualitative physico-mathematical analysis is a new method of scientific investigation”³.

Nikolai Aleksandrovich characterizes the essence of the proposed new scientific method as follows: “Indicate only any one of the many interrelated physical factors among several complex physical factors, and qualitative physico-mathematical analysis will reveal before you all the remaining factors as well, present in the given phenomenon of nature.”

Nikolai Aleksandrovich bases the method of dimensionality on the fundamental theorem of dimensional analysis. “Every mathematical equality conclu—

*) As is known, in 1899 N. A. Morozov completed the three-volume work The Structure of Matter, which he wrote over ten years while imprisoned in the fortress.

has a complete and finished logical meaning only in the case when both its parts are isotetic, i.e., represent the very same theses, consisting of quantities of the same name.”

N. A. Morozov proves this theorem and uses it to establish the connection between various physical quantities.

However, the method of dimensions, while providing the correct relation between physical quantities (with accuracy to a dimensionless coefficient), cannot replace rigorous mathematical methods.

Nikolai Aleksandrovich notes this limitation of the method of dimensions and considers the discovery of new regularities to be the chief purpose of his method.

“Simple reduction to isoteticity of one-sided empirical dependencies, noted between several phenomena of nature, may serve the natural scientist as an instrument for discovering still new, unforeseen dependencies between them”[^3].

Dimensional analysis is widely used not only for scientific but also for educational purposes. Yet the priority in the discovery of dimensional analysis belongs to N. A. Morozov. This is pointed out only in the work of K. Morozova, “Nikolai Aleksandrovich Morozov,” issued in a small print run.

In 1914 we specifically approached Nikolai Aleksandrovich regarding the establishment of his priority in developing the method of dimensional analysis, and received an affirmative reply.

M. Rozenkov

Cited Literature

1. Preface by S. I. Vavilov to Bridgman’s book Dimensional Analysis, 1933.
2. N. A. Morozov, The Tale of My Life, vol. 3, 1947.
3. N. A. Morozov, Foundations of Qualitative Physico-Mathematical Analysis, 1908.