The invention relates to a method for improving the pivotal movement of a mobile body (1) for a scientific instrument, comprising a shaft (10) pivoting or oscillating about an axis (D), wherein said method comprises: statically balancing said mobile so as to bring the center of gravity thereof onto said axis (D); determining a target value of the resulting imbalance momentum of the mobile body about said axis (D), which corresponds to a predetermined divergence between a first longitudinal main axis of inertia of said mobile body and said axis (D); rotating said mobile body about said axis (D) at a predetermined speed, and measuring the resulting imbalance momentum relative to said axis (D); and adjusting the value of the resulting imbalance momentum of said mobile body about said axis (D) to within a given predetermined tolerance relative to said target value, wherein said adjustment is carried out by machining on either side of a median plane (P) comprising the two secondary axes of inertia of said mobile body.