Logos

Uh, yeah, this is a Supreme Court decision.

The goal here is to support an argument and they're using logic and reason to do it.

Take this thrilling paragraph:

Although the courts will afford the utmost deference to Presidential acts in the performance of an Art. II function. United States v. Burr, 25F. Cas. 187, 190, 191-192 (No. 12, 694), when a claim of Presidential privilege as to materials subpoenaed for use in a criminal trial is based, as it is here, not on the ground that military or diplomatic secrets are implicated, but merely on the ground of a generalized interest in confidentiality, the President's generalized assertion of privilege must yield to the demonstrated, specific need for evidence in a pending criminal trial and the fundamental demands of due process of law in the fair administration of criminal justice. (Opening.10)

Not exactly a page-turner, but it makes the point: this is serious business and we thought a lot about it.

Ethos

In Supreme Court cases, you might think that appeals to ethos aren't necessary. These are the Supremes; they know their stuff. We assume they're knowledgeable and credible. They're not writing to persuade anyone; the decision's already signed, sealed, and delivered.

Still, you can think of all the case-citing as an appeal to ethos as well as a map to the Court's careful reasoning, letting the rest of us know the extent of their (or their clerks') knowledge in order to lend credibility to their decisions.

They also invoke an ethos-oriented argument in their demonstration of respect for Nixon:

Since a President's communications encompass a vastly wider range of sensitive material than would be true of an ordinary individual, the public interest requires that Presidential confidentiality be afforded the greatest protection consistent with the fair administration of justice, and the District Court has a heavy responsibility to ensure that material involving Presidential conversations irrelevant to or inadmissible in the criminal prosecution be accorded the high degree of respect due a President and that such material be returned under seal to its lawful custodian. (Opening.12)