I want to write:
"On its original formulation, the method uses ..."
However, I am not sure if it is "On its original formulation" or "In its original formulation".
Searching in Google for both cases I found that "in its original" is more common (250,000 hits versus 76,000), but not by a margin big enough to make a conclusion.
Which one is the right one?
I would use "In its original formulation" because it is more contextually correct.
On and in have many nearly identical definitions, and thus are many times used interchangeably, but as prepositions they still retain distinct meanings. One of the many definitions of 'in' reads
expressing inclusion or involvement
which I think fits best in this instance, because you wish to express a situation that took place within the context of the original formulation (i.e. it is included in the original formulation).
The most relevant definitions of 'on' that I could find for this issue read could be either of the follwing:
2 forming a distinctive or marked part of (the surface of something)
3 having (the thing mentioned) as a topic
6 having (the thing mentioned) as a medium for transmitting or storing
The problem with definition 2 is that it is mostly used when (as the parenthetical note specifies) when describing something on the surface of something else. For example, I was scratched on my arm.
Definition 3 indicates that the second noun is the subject of the preceding noun. For example, one could say The book on ornithology was interesting. Here, ornithology is the subject of the book. In your sentence, the method is not the subject of the formulation.
The final definition could only be used if the formulation was the mechanism by which the method performed its purpose or something of that nature, which is false.
*definitions from the New Oxford American Dictionary
Just drop -ulation and use in as opposed to on:
In its original form, the method uses...
I think you want to talk about the ingredients, like this:
In its original formulation, the method uses sugar, water, and tea.
It would sound odd to use "on" here; we're talking about what's included in - physically inside - the preparation.
I think most of the Google hits you're seeing for "on" are other uses. Contrast:
On its original formulation, the drink was welcomed as a success, but today it has been surpassed.
The new method, based on its original formulation, uses sugar, water, tea, and lemon.
In the first case, we're using "on" to reference a time, like "upon the date of its original formulation" (note that without some context to indicate that it's about a date, this use may still sound old-fashioned or awkward); in the second, we're using "on" in a phrase like "based on," "depending on."
Confusingly, if you're talking about what's written, it sounds best to use "on" instead, because things are usually in a formula but written on a page:
On the original recipe page, sugar, water, and tea are listed.
They mean different things (to me): "On its original formulation, the method used ..." is talking about the time the thing was first formulated (On its formulation). "In its original formulation" is saying the thing has had a number of different formulations, and you are describing the original one.
