I was preparing this as Barbara posted her response.
It would appear to be your 1st post on an Ancestry board but from your profile I assume the picture is of a British ancestor, if that is so he’s a British soldier in the 76th Regiment of Foot, with no rank insignia he’s a private.
The date you suggest is the latest that the style of tunic (cuffs) was worn (c1855-1868) so it may have been much earlier and the other details don’t help much.
Although dates can vary from regiment to regiment with some mention as early as 1830, generally the Kilmarnock aka “pill box” or “pork pie” style forage cap for infantry other ranks, where the regiments the badge was simply the regiment’s number in brass, was I believe introduced from around the late 1840’s early 1850’s and was worn up to around 1874, when the badge changed.
The upwards pointing chevrons on his lower left sleeve represent he was in receipt of 3 awards of good conduct pay; only private soldiers wore the badges and up to six could be earned. The regulations governing the award of good conduct pay changed over the years such that the minimum service for the award represented by 3 badges decreased from 15yrs service (1836-54) to 13yrs in 1860 and 12yrs from 1870; the minimum service would be for a soldier did not lose a badge for miss-conduct and have to serve additional time before it was restored.
At various times prior to WWI the crossed rifles have been used as a “prize badge”, an award for skill at arms and as part of a Musketry Instructors insignia. I’ve been trying to confirm the facts as to the meaning when they were first used, but have been unable to trace a reference to Musketry Regulations prior the 1869.
Although some opinion varies as to when specific rules changed, from the online information that is readily available, including forums on other web sites, as far as I can tell, the crossed rifles (or muskets) badge and one with a Crown above that formed part of Musketry Instructors rank insignia, was created by the same Royal Warrant of 1856 that created the Corps of Instructors of Musketry.
The initial regulations must have been revised between 1856 & 1869, but I can only say that the 1869 Regulations describe the badge without the crown in two styles, one in gold for the best shot in each company and regimental depot and the other in worsted for “each qualified marksman”; each badge earned a cash award.
The 1869 Regulations apparently describes the badge with a crown to be awarded to all the sergeants in the best shooting company and the best shot in the battalion. Sergeant Instructors of Musketry (who had passed a course at the Army’s School of Musketry) also wore it above their sergeant’s stripes.
Would it be safe to assume that prior to 1869 the badge without a crown in worsted was for the best shot in each company and regimental depot? I say worsted as if the one in the picture was gold it would surely have been coloured like the brass buttons.
By 1879 the crossed rifles badge was awarded to all ranks below sergeant whose score fell within the top 10% of a battalion or unit of a corps. In later years the badge was more a proficiency badge being awarded to every soldier who achieved the score as set down in Musketry Regulations.
Before 1883, unless he was discharged to pension (with common name, need full name, year and ideally place of birth to check), no record of his service will have survived and you would have to (or employ a researcher) check the 76th Regiment’s Muster lists and Pay Books at the National Archives, Kew; they are not online.
In 1881 the 76th Regiment of Foot merged with the 33rd (Duke of Wellington’s) Regiment of Foot to become the 2nd & 1st battalions respectively of the Duke of Wellington’s West Riding Regiment.