The correct answer is C) to remove deviation on the intercardinal headings. Quadrantal spheres are used to compensate for deviation on the intercardinal compass headings (NE, SE, SW, NW). This deviation is caused by the interaction between the Earth's magnetic field and the ferrous metals in the ship's structure. By placing spherical magnets in specific locations around the compass, the quadrantal spheres can counteract this deviation and improve the accuracy of the compass on the intercardinal headings. The other options are incorrect because: A) cardinal headings (N, E, S, W) are typically adjusted using other compass correction methods, B) vertical soft iron induces different types of deviation that require different compensation, and D) heeling error is corrected through separate means, not with quadrantal spheres.