Here is the history:
https://www-perscom.army.mil/tagd/tioh/ROTC Misc NGB page/Silver and Gold Insignia.htm
USE OF SILVER AND GOLD
OFFICER INSIGNIA OF RANK
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The precedence of silver over gold in officer insignia of grade was not the result of deliberate intent, but arose from the desire to avoid unnecessary changes. Although the background discussed below is for Army insignia, the Navy and Marine Corps metal insignia of grade for officers have paralleled those of the Army. When the Air Force was established in 1947, it adopted the officers’ insignia of grade already in used by the Army.
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___ Since 1780, when insignia was embroidered on the epaulettes, the grade of general officers has been denoted by a number of silver stars. This was the beginning of the present system of officers’ grade insignia.
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___ Epaulettes were specified for all officers in 1832; for the infantry they were silver and all others had gold epaulettes. In order that the rank insignia would be clearly discernible, they were of the opposite color; that is, the infantry colonels had an eagle of gold because it was placed on a silver epaulette and all other colonels had silver eagles on gold epaulettes. At that time the only grade insignia were the stars for general officers and eagles for colonels. Epaulettes for lieutenant colonels, majors, captains, and lieutenants had no insignia -- the length and size of the fringe showing the difference of grade.
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___ Shoulder straps were adopted to replace the epaulette for field duty in 1836. The straps followed the same color combination as the epaulettes; that is, the border was gold with silver insignia for all officers except those of infantry which had silver border with gold insignia. At that time majors were authorized leaves; captains were authorized two bars and first lieutenants were authorized one bars on the shoulder straps.
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___ In 1851, the colonel’s eagle was prescribed in silver only. Apparently when it was decided to use only one color, the silver eagle was selected based on the fact that there were more colonels with the silver eagle that those with gold. At that time on the shoulder straps, lieutenant colonels wore an embroidered silver leaf; majors wore a gold embroidered leaf; and captains and first lieutenants wore gold bars. The second lieutenant had no grade insignia, but the epaulette or shoulder strap identified him as a commissioned officer.
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___ In 1872, epaulettes were abolished for officers and replaced by shoulder knots. As the shoulder knots had no fringe, it was necessary that some change in the insignia on the dress uniform be made in order to distinguish the major from the second lieutenant. It was natural to use the gold leaf which the major had worn on the shoulder strap for the previous twenty-one years. In the same year, the bars on the shoulder straps of the captains and first lieutenants were changed from gold to silver to correspond with the silver devices of the senior officers.
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___ The service uniform of olive drab gradually came to be used more frequently and by the time of World War I, the blue uniform was worn only in the evenings and on dress occasions. As a result, metal insignia was authorized for wear on the service uniform on the shoulder loop and on the collar of the shirt when worn without a jacket. Shortly after the United States entered World War I, only the service olive drab uniform was being worn. The need for an insignia for the second lieutenant became urgent. Among the proposals was one to authorized for that grade one bar, the first lieutenant two bars, and the captain three bars. However, the policy of making as little change as possible prevailed, and a gold bar was adopted in 1917, following the precedent previously established by the adoption of the major’s insignia.
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___ Although silver outranks gold insofar as the Armed Forces metal insignia of grade, gold can be considered as outranking silver in medals and decorations and their appurtenances. The order of precedence in establishing medals when using the same design is gold, silver and bronze.
