In spring 1907 and 1908, the authors of this note participated in a geological excursion along the northern coast of Lake Ladoga. The excursion began with an inspection of the Imatra Waterfall and the surrounding rocks, which exhibit characteristic signs of the glacial period. From Imatra, we traveled to the town of Serdobol and from here we set off on foot along the shore of Lake Ladoga, getting acquainted along the way with the rocks of this area and with two ore deposits, Välimäki and Pitkäranta, the latter being the final destination of our trip. Without having in mind to describe all the material, for our brief note we selected only the rock samples that we gathered along the way from the town of Serdobol to the Välimäki iron mine inclusive, the most interesting from a petrographic point of view.

This note examines the expression of the length of the arcs of an ellipse and a hyperbola using infinite series (see the article). Adding all these equalities and making reductions, we obtain the following formula, which is none other than the Wallis formula. The same result could be obtained by finding the arc length of a hyperbola.