"By foot" vs. "on foot"

• Which one is correct?

1. I go to school by foot.
2. I go to school on foot.

• Are there instances when the expression by foot is preferred?

My last question is the following:

• Why is the singular noun, foot, used?

If a person goes to school by bus/train/car they are using only one means of transport, they are travelling in one car not two. But people use both feet for walking, so why would the following expressions be ungrammatical?

1. I go to school by feet
2. I go to school on feet

I read the answers on this question why is it always "on foot" not "on feet"? but they did not convince me.

Solution 1:

"By" in this context normally refers to a mode of transportation whereas "in" or "on" would refer to your position whilst travelling.

We travel by car

This suggests we are using a car to travel.

We travel in a car

This implies we are inside of a car while traveling.

EDIT

Adding quotes around the phrase in google makes a big difference in results. The following reflects a more accurate search:

When it comes to using "on foot" or "by foot," either would be correct; however, a quick google search demonstrated that "on foot" is more commonly used (34M hits vs. 7.9M hits).

Solution 2:

1. Which one is correct?

a) I go to school by foot. b) I go to school on foot.

The original question and the additional questions are easily answered quoting the authoritative Oxford Dictionaries

a) OED records on foot from XIV century:

(c1325 in G. L. Brook Harley Lyrics (1968) 62 ): Þe is bettere on fote gon þen wycked hors to ryde.

b) Oxford Dictionaries (also) record by foot as a variant of on foot:

The first time he came was in 1945 when the main means of transport was by foot or rickshaw.

Therefore both forms are correct

2. Why is the singular noun, foot, used?

If a person goes to school by bus/train/car they are using only one means of transport, they are travelling in one car not two. But people use both feet for walking, so why would the following expressions be ungrammatical?

The singular form is preferred when not the concrete part[s] of the human body is/are considered, but the abstract meaning, i.e. the organ of sense, or any other figurative sense:

• eye: The appropriate form is used when referring to the physical organ: one would give one's left/ right eye, to turn a blind eye, up to (one's) eyes in, to shut one's eyes , to be all eyes; but:
  at first eye, in the eye of the law/ logic, beauty is in the eye of the beholder, through/ with the eye(s) of, (sight), or: to do .. in the eye, one in the eye for (humiliating blow); to give an eye to, to catch the eye (attention) to keep an/ one's eye on (watch); to see eye to eye (agree); to give .. the eye (warning glance/ sexual interest); to have an eye to (object/ view/ regard for); to have/ get one's eye[s] in (judge distance/ direction);

In sing. and pl. The action or function of perception by the ears; the sense of hearing or listening (OED)

• ear: “He sow'd a slander in the common ear”, “Does my ear deceive me? A shrill whistle coming over the water!”, “Clocks should be in beat, not only because they sound pleasant to the ear, but because they are less likely to stop”, “For later ventriloquists, the dummy would become a fixture.., funnelling the audience's attention on what they saw in front of them, and knitting together the evidence of eye and ear”. to come to somebody's ear, at first ear, (to play) by ear, etc.

foot, on its own, can be used in the singular instead of feet

a. Viewed with regard to its function, as the organ of locomotion. In rhetorical and poetical use often (in sing. or pl.) qualified by adjs. denoting the kind of movement (as swift, slow, stealthy, etc.), or employed as the subject of verbs of motion. (OED)

(1667 Milton Paradise Lost) "Tripping ebbe, that stole With soft foot towards the deep", "I was not aware of your presence... Your foot is so light", "Dogs..swift of foot", "Useful as is Nature, to attract the tourist's foot", (a1616 Shakespeare Coriolanus) "Unless by using means I lame the foot Of our design". With reference to walking or running: to pull foot (depart), to take one's foot in one's hand (also, to make a journey). Mr. Foot's horse (one's feet),to catch.. on the wrong foot (to catch unaware), to get off on the wrong/right foot (to start un/successfully)

• on foot refers to a way of locomotion:

to go on foot: to walk as opposed to ‘ride.’ (OED)

and, according to Oxford Dictionaries

to go on/by foot: walking rather than travelling by car or using other transport.

This explains why the singular form is used

3. Are there instances when the expression by foot is preferred?

As we have seen, the phrase originated in XIV century when one could only choose between walking and riding

on foot : a. on one's own feet, walking or running, in opposition to on horseback (OED)

therefore the preposition on was chosen to express both ways. When other means of locomotion where invented the preposition by was appropriately chosen (to go… by bike/bus/car/train, etc.)

Walking rather than travelling by car or using other transport. (Oxford Dictionaries)

Therefore it was natural to change the preposition ("I won't go by bike/ car/ bus ....but by foot") adding by foot to the long-established on foot. That explains why the latter is more popular and can be used in most contexts:

" I drove up..(fearful of being late, or I should have come on foot". "Motorists were forced to abandon their vehicles in the road and walk the remaining distance on foot". "In the past, hockey fans could walk on foot for miles to watch their favourite stars".

In conclusion, by foot is (to be) preferred when another modern means of transport is mentioned:

"The first time he came was in 1945 when the main means of transport was by foot or rickshaw". (quoted above: Oxford Dictionaries)

EDIT:

I added the other two questions to make it more "complete" but could you please say which is more the common between "by foot" and "on foot", which is basically why I set up the bounty in the first place. Mary-Lou A.

I thought that was obvious, from my post and, above all, from Siva's answer that unmistakably showed which is more common:

• by foot (0.00003[5] %) is over a hundred times less common then the original form (0.001-0.00031 %)¹ even though not a recent coinage. Probably, it is an educated guess to imagine that it gained currency with the advent of railway, when people started traveling by train: the phrase has in fact a first (modest) peak (0.000015 %) around 1764, and at that time also by horse became more popular

I can only add, that it is not mentioned in the OED at all, and, what is worse, it is not listed, not even as a variant, in the updated SOED version. I also said that it is used mainly when another means of transport that requires that preposition is mentioned or understood.

¹Ngram percentages respectively in 1900 and in 1999

The preposition by was used with different means of transport, long before manual or motor vehicles (bikes, cars, trains, and buses) came into existence, e.g. by ship, "to travel by land, or by sea". – Mari-Lou A

I'll make a last attempt to clarify it all. The structure we are discussing is "to go (travel) on/by foot" vs. other means of transport: "to travel by car/train etc...", since we have ascertained that "on foot" does not refer to a part of the body but (idiomatically) to a means of transport.

• "I am on a train... " has nothing to do with the issue, its alleged meaning
• "I am travelling on a train" has nothing to do with "I travel by train", and roughly would correspond to "I am travelling on a foot"
• "He is on () horseback / on the train / on a ship" is utter confusion: the first noun has no article (idiomatic use), the second a definite and the third an indefinite article (literal use). The copula is does not link to a means of transport. A horse is a means of transport. Considering on (foot/horseback) in its literal sense gives the weird conclusion that one is leaning on the horseback or on one's own foot (and not on the land, both one's and the horse's foot/back lean on the land)
• "to travel by land/ sea", land and sea are not means of transport, (same as Sven's water), when one travels on horseback/foot they are travelling by land, That is a separate idiom that has nothing to to do with our issue.

I am not convinced that "by" was employed when later means of transport became available. I think it is much older than you suggested

I only reported facts and not personal convictions, did not suggest anything. If one has evidence that by foot is older than the XIX century, they should put it forward. What I noticed is actually that also other ancient means of transport like by horse and by ship become popular roughly at the same time, that is after the advent of railway. It is really surprising that very old means of transport like ‘horse’ and ‘ship’ were associated to the preposition by only after people started travelling by train (and actually by foot is slightly older than by ship and by horse). The incredulity might have been disbanded by an Ngram search.

This odd circumstance can be fully be explained by my guess (which was outside the scope the answer), if anyone can find a better explanation it will be welcome.