Emphasis /edits for clarity:
To formally cooperate in the sin of another is to be associated with him in the performance of a bad deed in so far forth as it is bad, that is, to share in the perverse frame of mind of that other. On the contrary, to materially cooperate in another's crime is to participate in the action so far as its physical entity is concerned, but not in so far as it is motived by the malice of the principal in the case. For example, to persuade another to absent himself without reason from Mass on Sunday would be an instance of formal cooperation. To sell a person in an ordinary business transaction a revolver which he presently uses to kill himself is a case of material cooperation. Then it must be borne in mind that the cooperation may be described as proximate or remote in proportion to the closeness of relation between the action of the principal and that of his helper. The teaching with regard to this subject matter is very plain, and may be stated in this wise: Formal cooperation is never lawful, since it presupposes a manifestly sinful attitude on the part of the will of the accomplice. Material complicity is held to be justified when it is brought about by an action which is in itself either morally good or at any rate indifferent, and when there is a sufficient reason for permitting on the part of another the sin which is a consequence of the action. The reason for this assertion is patent; for the action of the accomplice is assumed to be unexceptionable, his intention is already bespoken to be proper, and he cannot be burdened with the sin of the principal agent, since there is supposed to be a commensurately weighty reason for not preventing it. Practically, however, it is often difficult to apply these principles, because it is hard to determine whether the cooperation is formal or only material, and also whether the reason alleged for a case of material cooperation bears due proportion to the grievousness of the sin committed by the principal, and the intimacy of the association with him. It is especially the last-named factor which is a fruitful source of perplexity. In general, however, the following considerations will be of value in discerning whether in an instance of material cooperation the reason avowed is valid or not. The necessity for a more and more powerful reason is accentuated in proportion as there is (I) a greater likelihood that the sin would not be committed without the act of material cooperation; (2) a closer relationship between the two; and (3) a greater seriousness in the sin, especially in regard to harm done either to the common weal or some un offending third party. It is to be observed that, when damage has been done to a third person, the question is raised not only of the lawfulness of the cooperation, but also of restitution to be made for the violation of a strict right. Whether in that case the accomplice has shared in the perpetration of the injustice physically or morally (i.e. by giving a command, by persuasion, etc.) whether positively or negatively (i.e. by failing to prevent it) the obligation of restitution is determined in accordance with the following principle. All are bound to reparation who in any way are accounted to be the actual efficient causes of the injury wrought, or who, being obliged by contract, express or implied, to prevent it, have not done so. There are circumstances in which fellowship in the working of damage to another makes the accomplice liable to restitution in solidum; that is, he is then responsible for the entire loss in so far as his partners have failed to make good for their share.
