Almost a decade ago, with the rapid world-wide development of air transportation, came the demand for new types of aircraft. It became evident that a plane capable of operating from land or water was the logical step needed to open up larger areas for air transportation. The proximity of water compared with the remoteness of available landing fields to the centres of population was the deciding factor in amphibian development.

While the advantages of the amphibian are obvious, the limitations and; difficulties of creating an efficient plane of this type are also evident. Compared to the seaplane or landplane, the amphibian must take care of the extra weight and parasitic resistance, as well as solve various other problems connected with combining the characteristics of the land and seaplane in one aeroplane.

In the spring of 1904, when echoes of the Brothers Wright first flights began to be known in Europe, the author founded at Koutchino, near Moscow, on his family estate, the Aerodynamic Institute of Koutchino.

Air is the fluid meant by the term “aerodynamic” and artificial flight was the most important of the applications included in the programme of the Institute; foreseeing, however, the importance of comparative researches in air and water, the author chose intentionally a location particularly suitable for hydraulic experiments. A small river, dammed so as to form a pond, afforded the possibility of regulating the speed of the current at will, and since 1905 parallel researches were carried on in the wind tunnel and in the stream of water.

The idea of such an institute was very favourably received in the Russian scientific circles. When the author asked N. E. Joukovsky, V . V . Kouznetzoff and S. S. Nejdanovsky to participate in the organisation of this institution, they willingly gave their assent.

Simultaneous equations of three or more variables are notoriously trouble some to solve numerically and, moreover, are frequently sensitive for certain relative values of the variables. This usually precludes the use of the slide rule and in consequence resort has to be had to accurate working to an increasing number of decimal places involving much labour even with a calculating machine.

A method is here given which is applicable to certain classes of equations of frequent occurrence in mathematical physics and engineering science, which method is a combination of what is knovwi as the Iteration process and the means of applying this principle to end moment distribution devised by Professor Hardy Cross.