The court case of Grayson v. Lynch is significant because it involves a dispute over loss and damage to a herd of cattle between the firms of Lynch Bros and Grayson & Co. The case was originally brought before the District Court for the Third Judicial District in Dona Ana County, New Mexico. The case eventually made its way to the Supreme Court of the United States, where it was reviewed in 1896.
From the information provided, it appears that the case involved a determination of liability for the loss of the cattle, which had been affected by a disease known as Texas cattle. The Supreme Court's decision in the case may have had implications for the liability of parties for losses resulting from the spread of livestock diseases. However, without access to the full text of the Supreme Court's opinion, it is difficult to provide a more detailed analysis of the case's significance.
As for the legal proceedings, it is expected that the Supreme Court will review the lower court's decision and determine whether the appellants (Grayson & Co) are liable for the loss and damage to the appellees' (Lynch Bros) herd of cattle. The Supreme Court may affirm the lower court's decision, reverse it, or modify it. The Court may also remand the case back to the lower court for further proceedings. Ultimately, the Supreme Court's decision will provide a final resolution to the legal dispute between the parties and may establish legal precedent for similar cases in the future.