Cows are ruminants ie they have a rumen. a pre-stomach if you will.
The advantage in this for the cow is that it allows them to break down crude cellulose which is poor feed for grazers with a simple stomach. There is the added advantage that the heard can venture out on the grass plains and swallow copious quantities of grass and then retire to cover where they regurgitate their "cud" and chew it carefully with digestive juices before swallowing. Ever seen a cow peacefully chewing away? The saliva runs out of it's mouth.
The CH4 is produced by enteric fermentation, 87% to 90% happens in the rumen which is BELCHED out. Only the remainder is from farting.
So these geniuses don't even know which end of the cow produces the offending gasses. Enter
