Derby Day today ! 
I would use the big grin smiley but it's green and might be disloyal to the Jambos on a day like today
Thanks both for the research. Green with a red toorie ! I guess that was during the time of the Great War etc. Perhaps the change to dark blue came in 1948 when they adopted the kilt, though I suspect at that time they wore the coloured Tam O'Shanter for best-dress, as did the other Scottish regiments at the time in the 1950's. The glengarry did hover in the background though eg the 1st Argylls were photographed wearing them for "out of the line" and parades during their time in the Korean War 1950-51 with 27th British Commonwealth Infantry Brigade (where Major Kenny Muir won the posthumous VC during the fight for Hill 282) .
I like the photo of the serjeants of the 15th HLI and the typical Scottish WW1 "pancake" bunnet ! Looking at their sleeves, they seem to be wearing horizontal coloured stripes below a shape. Usually (but not always), infantry didn't wear divisional insignia below the shoulders, it was normally worn by divisional artillery, engineers, ASC etc, plus divisional vehicles and direction signs. Infantry usually used "battle badges", often geometric shapes or combinations of stripes and colours to determine brigades and the order of the battalion within it. Examples are the small horizontal stripes used by the 51st Highland Division - one, two or three stripes identified the brigade, while the colour, red, blue, green or yellow, identified the seniority of the battalion in the brigade. For example, the 4th Gordons wore three horizontal blue stripes identifying it as the 2nd senior battalion of the 3rd brigade (153 Bde). The 52nd Lowland Division had something similar, but were long horizontal stripes above the cuff of the sleeves. The 9th Scottish had a different system - I've forgotten most of it but I recall the 8th Black Watch (in 26th Bde - senior battalion of the senior brigade of the most senior Kitchener division of the British Army) wore a yellow arc along the shoulder seams. The use of divisional insignia by infantry became pretty well universal though in mid-late 1918. Funny enough, the 51st took a long time to adopt any form of formation insignia of any type, a similar stance taken by the regular divisions. In the case of the regular BEF divisions (1 - 8), they believed their status did not stoop to plastering their sleeves with badges. In the case of the 51st, it was pretty bloody obvious that when a division appeared, nearly all wearing kilts, it had to be them. What further recognition was needed ? But conformation took over and by 1917 they were wearing the wee strips mentioned above. I used to own a WW1 Brodie steel helmet, rough, dark khaki finish with 3 painted blue stripes each side (the 4th Gordons).
In this HLI photo of the 15th Batt, the 4 stripes could represent either the battalion (there were 4 battalions per brigade, reduced to 3 in early 1918) or the company within the battalion (4 company structure) - more likely the battalion, while one of 3 colours might identify the brigade. The shape above looks a bit like the 32nd Div insignia, like a rounded four-leaf clover. In fact, it was 4 x numeral 8's, each numeral arranged at 90 degrees with the lower "bubble" of each "8" superimposed to give a 4 leaf clover effect. But it's hard to tell on the photo.
The hackle on the old HLI glengarry is unusual - white over red, granted to the regiment (I believe after WW2) and similar to the hackle of the Royal Fusiliers (until they became Royal Regt of Fusiliers when they amalgamated with the Royal Northumberland Fusiliers, Warwickshire Fusiliers and Lancashire Fusiliers and the hackle colours were reversed). I wonder if the owner of the glengarry added it at a later date, perhaps for re-unions ?
That's why I love military history, the more you dig and the more answers you find, the more new questions pop up !