Whilst arrows could “infect” wounds directly,
“Tallow” on Bullets had little or NO effect (it was sterilised by travelling down a Hot barrel at high speed and friction).
What did cause the infection was the Bullet, (slow, large diameter) smashing thru layers of often dirty clothing, carried these fragments into the wound, where of course, with the none-to-clean operating methods, were allowed to fester etc…with fatal results ( hence the “amputate to save life” principle of battlefield surgery, up to the US Civil war and early 1900s.) Even with the availability of Antiseptics etc.
In the Royal Navy, it was common practice for officers to don clean underwear and uniforms before a Sea-battle, to reduce the “wound potential” of Fibres etc being carried into an often messy wound by Gunfire and iron and Wood splinter effects…The common sailors of course, “were expendable”, although some more caring commanders issued new and hopefully clean slops ( fatigue uniforms) before an expected battle.
La Garde’s seminal treatise on battlefiled surgery (Gunshot Wounds, 1914 and 1917) recounts the instance in the Russo-Japanese War (Siege of Port Arthur, 1904) where Russan soldiers, issued with Sheep Fleece Winter Jackets ( Manchurian winters are rigid) were dying of Anthrax Infections when wounded by Japanese 8mm Murata and 6,5mm Arisaka jacketed projectiles…The Bullets and other shrapnel were carrying the Spores of the disease, from the Fleece of the jackets, into the wounds…but the Russians accused the Japanese of using “tainted” Bullets…the same as at the Span-Am war, the Hearst newspapers accused the Spanish of using “Poisoned Bullets” (Verdigris covered 11mm Spanish Reformado ammo) against the US Volunteers ( no such thing, again, the lead bullets carried dirty fibres from the Unhygienic conditions of Cuba into the wounds ( again, LaGarde comments on this.)
La Garde also utilised the “Wide debridement” rule with all wounds, which ensured the removal of all foreign matter from the wound track, thus reducing or eliminating the Infection Potential. THis practice is still done today, in iraq and Afghanistan…IN WW I, its use saved many a wounded soldier from death by gangrene or galloping septicaemia. The Introduction of universal Tetanus shots for soldiers before 1914, also reduced the incidence of “lockjaw” deaths from C. tetanii found in battlefiled dirt and Horse manure…of which battlefileds then wqere usually liberally supplied.