The Philadelphia Convention.The first day’s proceedings of the Philadelphia Convention have reached us in detail in the Northern papers. We condense the following.The Southern Loyalists formed a line in Chesnut Street, at an early hour and marched in the following order, 41 amid a thundershower of cheers,” to meet the Northern delegations :Gov. Brownlow of Tennessee, with 130 delegates.James Speed of Kentucky, with fifteen delegates.Madison Mills of Missouri with thirty delegates.Gov. Boreinan of West Virginia, with one hundred and thirty delegates.Burnham Ward well of Virginia, with seventy delegates. -John L. Thomas of Maryland, with two hundred and ten delegates.N. B. Smithers of Delaware, with ten delegates.A. A. Tourgce of North-Carolina, with twelve delegates.J. L. Dunning, of Georgia, with nine delegates.Col. D. O. Bingham of Alabama, with fourdelegates.- ^ a • • • • fit ^