Whenever any portion of said work shall be completed to the satisfaction of said board of control, and it is so far useful that in the opinion of said board of control tolls should be paid for the use thereof, said board may fix the tolls to be paid for the use of such portion until the whole of said work is completed; and whenever said improvements have been completed and accepted by said board of control, the rates of toll which any company organized under this act may charge for running rafts, timbers, logs or lumber through said improved stream shall be fixed by said board of control, and may be graduated with reference to the distance run upon the portion of said stream improved by said company, and shall not be increased without the consent of said board, but may be changed from time to time by said board; but such toll shall not at any time be increased so that the sum shall amount to more than 15 per cent a year upon the actual cost of such improvements after deducting the necessary expenses and repairs; and the said board shall, as far as may be practicable, so fix the rates of toll on timber, logs, and lumber, that the same shall not at any time exceed the sum of 25 cents per 1,000 feet, board measure, on any stream where 10,000,000 of feet or less are run in any 1 year; 20 cents per 1,000 feet, board measure, on any stream where 30,000,000 of feet or less are run in any 1 year; nor more than 15 cents per 1,000 feet, board measure, on any stream where from 30,000,000 to 50,000,000 of feet are run in any 1 year; nor more than 10 cents per 1,000 feet, board measure, on any stream where from 50,000,000 to 100,000,000 of feet are run in any 1 year; nor more than 5 cents per 1,000 feet, board measure, on any stream where from 100,000,000 to 200,000,000 of feet or more are run in any 1 year; and the collection of such tolls shall be confined strictly to that part or portion of a river or stream so improved, and to that class of floatables benefited by the improvement; and nothing in this act shall be construed to give jurisdiction to any corporation over any portion of a river or stream other than the portion specifically improved by such corporation. Such corporation shall cause to be made out and filed with said board of control, at or before its meeting on the last Wednesday in March, each year, the affidavit of its president or 1 of its directors, setting forth in detail, upon his best information and belief, what amount of timber, logs, and lumber will be run through any section or sections of the river improved by the company during that year, and that the official has made due and reasonable inquiry on the subject from persons lumbering on the river, and otherwise.