We saw a similar picture on Shorpy earlier. Look for the differences:
Class of '92

Update: I realized that the way I had described where the future four-star admiral is sitting, in this photo, might be confusing, so I rewrote it, and am adding a closeup of him.

I found out that the Naval Academy has put out a yearbook, called "The Lucky Bag" for many years. It's our luck that the first issue was produced by the class of 1894! Furthermore, it has been published on the internet. There are no individual pictures but, since Reeves was an athlete, there are three group pictures that include him. There is one very good photo, however, in which he is wearing the first football helmet (which we know was made for him) and holding the ball, since he was the team captain. I am posting a closeup from it. The man sitting in front of him was Winston Churchill (not the English one), who also made a name for himself, although he did so in literature.

So, where are they, in this group shot from when they were (most likely) plebes? Churchill is easy to pick out, third row from the bottom, fourth from the left. To the left of the man to the left of Churchill is, I'm 98% certain, our future Adm. Reeves. I never would have recognized him without the yearbook photos of him, clean shaven, or his football helmet! https://archive.org/stream/luckybag1894unse#page/n0/mode/2up

DavidK, I was saying that the classes of 1892 and 1894 are separate, too! The two classes would have been at the academy together, for two years,but these pictures are all of a single class. The guy with the mustache was from the class of '92 and the pictures that were labeled as being from 1894 were obviously taken in 1892.

As for the guy I first thought might be Reeves, I was able to identify him, through several pictures in the yearbook, as Roscoe Charles Moody. He also made the Navy a career and retired as a Captain (O6 in the Navy). Earlier in his career, he was an instructor at the academy and published a book called "The Oscillations of Ships", which was used for many years, at the academy. It was recently selected to be republished, all these years later, and is available on Amazon.com

ALEX-the men in the picture you posted the closeup from were two years ahead of the men in this one. There are several other photos, which are dated 1894, but had to have been taken earlier, because the men in them are all in the class of 1892 photo. Some of them are very easy to pick out.

I am now royally confused, noelani. It would seem to me that the classes of '92 and '94 are entirely separate, but you suggest otherwise. Here's what I do notice: the fellow SMSgt Mac picks as Reeves (moustache) appears in two Class of 1894 photos, both taken in 1894 -- on the left (below) from https://www.shorpy.com/node/8053, and in the middle from https://www.shorpy.com/node/12341. Is it possible that your choice on the right (from the photo in this post of the same class, taken two years earlier) is the same guy?

Davidk, the two photos that you posted are not of the same men. If you look at the picture taken at the Gazebo, with "92" spelled out in the caps, you will see that the same men are in all of the following pictures, which say they are from 1894.

https://www.shorpy.com/node/16714
https://www.shorpy.com/node/16714
https://www.shorpy.com/node/12341
https://www.shorpy.com/node/10164

Also, none of the men in this picture, with the caps spelling "94" are in any of the other pictures.

UPDATE
I found two more pictures of the class of 1894, one of the whole class and one of the men who sang in the choir. The quality isn't as good, but these are the same men as in the gazebo picture. Both were obviously taken somewhat later. Besides the fact that many of them have earned various insignias and decor for their uniforms, the large group picture has fewer men. There were some resignations, dismissals, and deaths each year.

http://upload.wikimedia.org/wikipedia/commons/5/5d/United_States_Naval_A...
http://media-cache-ec0.pinimg.com/originals/15/15/8b/15158b886e21709a854...

http://media-cache-ec0.pinimg.com/originals/15/15/8b/15158b886e21709a854...

From what I've been able to find, so far, Cadet Joseph Mason Reeves did not distinguish himself at the academy, except on the football field. There was certainly nothing that would have made anyone predict that he would end up as a four-star admiral, with a phenomenally long career, to boot!

UPDATE #2- I have recently identified another of the young men in this photo, who also retired as a "full" or "four-star" admiral. In this photo, Cadet David Foote Sellers is, coincidentally, seated in between Cadets Reeves and Churchill, in the third row up, third from the left. He looks a bit nervous and shy, in this picture, but that is understandable, considering that he was only 16! Adm. Sellers served as superintendent of his Alma Mater, before his retirement, in 1938. For more information, go here: http://www.quarterdeck.org/book/cencoms/sellers.html

Photos of the young Reeves are hard to come by, but I have found one (unfortunately low-resolution) from about 1908 which I have paired with a photo of the later Reeves. The photo with three men is an enlargement from the current post (Class of ’94 in 1892): noelani’s choice is the guy on the left, while Kabukikitsune’s is (I think) the guy on the right. The photo with the two full heads is an enlargement from The Belle of Annapolis: 1894, linked below by StanFlouride. In the comments to that post, SMSgt Mac proposes the man on the left (with moustache) as Reeves. I don’t know who the guy on the right is, but he looks to me like he may be Kabukikitsune’s Reeves. But which is the actual one? Will the real Reeves please stand up!

Comparing photos of Reeves with this, I believe that the future admiral is the chap reclining directly above the fellow with his hand in his jacket.

Dutch's comment inspired me to learn more about the member of the class of 1894 who was still on active duty while well into his 70s. As the daughter of a career Marine, I know that very few men are still on active duty by age 60, so this was quite a career! He had retired in 1936, after a very long career. He was recalled to active duty, at the beginning of WWII. I don't think they were recalling many retirees who were in their 70s. Adm. Reeves, however, was a pioneer of carrier aviation, which was so important in the Pacific theater during WWII.

There aren't many pictures I could find, but by comparing features, I believe he is sixth from the left, on the second row from the bottom, with his arms folded. Anyone else care to guess?

And one more thing: The men in the other pictures that are identified as being the class of 1894 match each other, but do not match the men in this picture. They do, however, match the one identified as the class of 1892. Another thing that is obvious, here, is that lower classmen were required to be clean shaven, but upper classmen were permitted to have facial hair. Therefore, I believe the gazebo pictures were taken during the freshman years of those classes. That would have to mean that something is incorrect in the years identified in the others pictures. Most likely, IMO, the other pictures were of the class of 1892 and not 1894. Anyone else care to try to clear that up?

One may assume that, a few years after graduation, more than a couple of these Mids saw interesting service under an admiral named Dewey.

A previous visit with '94:

https://www.shorpy.com/node/8053

What was the origin/meaning of slipping one hand into the jacket for photos as we see here?

Buried in the US Naval Academy Cemetery is Joseph Mason Reeves (Class of 1894) who became a pioneer in naval aviation, an admiral and called the "Father of Carrier Aviation." Served in the Spanish-American War, WWI and WWII. A football hero at the Academy, he is credited with inventing the modern football helmet. Little did this group know that one of their classmates would achieve notoriety.

Among the graduates, though I don't know which one, is Joseph "Bull" Reeves (1872 - 1948). Although he had a long career in the Navy, and was one of the pioneers of naval aviation, he's best known for inventing the football helmet.