The Manchester Euterprisé publishes the following letter dated Sibouey, Jnly 2, from Dr. Fred Palmer, of the 33d Michigan hospital oorpsaud a U. of M. gradúate, now in Brooklyn, Mich. : We had onr first battle yesterday and I shall not atteropt to describe it, as it was too awfol. It bappened tbat we got the worst of it. Onr regiment tried to take a fortified town tbat had only a small forcé bnt bad a machine gun that was too mach for us, and it is a wonder tbat bundreds were not killed instead of two, and seven wonnded, but it was a terrible sight. I was oarrying a dead man when a snell struok witbin 10 feet of me and abont five feet from Dennis Donahae. When we went back to Siboney, we of the hospital oorps were the last to leave. as we had to luok after the killed and wonnded. The Spaniards paid no attention to the red flag and we are in bad shape as we are not armed, neither did we have anytthing to eat or drink all day yesterday. Last night I helped Dr. Nanoreda do a lot of operations, and I want you to know that Dr. Vangban is the man who looks after the welfare of yonrs trnly and if I get out alive it will be largely due to his considérate care and attention. It is estiinated that in yesterday's engagement 1,500 Americans were lost near Santiago and I saw several hundreds of them myself. You may all talk abont bravery; I saw instanoes yesterday that made me sbed tears more than once. My tears were not all from fright either, although I was badly scared I haven't gotten over it yet,in faot, we are in considerable danger of au attack at present. I never saw anything more disgusting thau the aotions of the Cubans - natives for whom this "humane" war was instituted. All the wbile our troops were fighting yesterday the dirty whelps were lying around in oaves asleep while onr men did all the fighting, or they would rush out and steal anything in the way of olothing, or food that happened to be dropped by our men. I snppose, however, that is the result of starvation for I, myself, have stolen enough since I left Miohigan to keep me in prison the rest of my life, even if I get ont of this alive. yesterday I lost my blankets, tent, ersack and rations, in faot everytbing I had exoept my hospital ponoh and oaDteen. Yon roay think I did this so I conld ron, bnt I didn't. The only safety was to crawl nnder a rock. I had to help oare for the wounded and dropped all impedimenta so that I oould get nnder a new rook. Hnndreds of otbers threw away their traps aud pioked np another set, bnt when we got throngb operating I was so dead tired I took a drink of hot beef tea and slept the rest of tbe night on the rocka without blankets or tent.