Which preposition to use with fixation

of Occurrences 13%

Quite recently, however, one of the electro-chemical companies at Niagara Falls has succeeded in commercially solving the important problem of the fixation of the nitrogen of the atmosphere; it being claimed that the cost of thus producing one ton of commercial nitric acid, of a market value of over eighty dollars, does not greatly exceed twenty dollars.

by Occurrences 1%

After some hesitation we attempted the method of fixation by means of steel plates, which was introduced with such success by Sir Arbuthnot Lane in the case of simple fractures.

Which preposition to use with  fixation