Researchers have found that Eiffel used empirical and graphical methods accounting for the effects of wind rather than a specific mathematical formula. Careful examination of the tower shows a basically exponential shape; actually two different exponentials, the lower section overdesigned to ensure resistance to wind forces. Several mathematical explanations have been proposed over the years for the success of the design; the most recent is described as a nonlinear integral equation based on counterbalancing the wind pressure on any point on the tower with the tension between the construction elements at that point.[39][40] As a demonstration of the tower's effectiveness in wind resistance, it sways only 6–7 cm (2–3 in) in the wind.[5][39][40]