I think you have a bit of a misunderstanding as to what this quote is saying. It does not support your argument, and actually supports mine (which would be the same as Adam Smith's in this case).

SUPPLY SIDE: "send him to study [x], it as at least twenty to one if he ever makes such proficiency as will enable him to live by the business." He is making is quite clear that the supply of qualified [x] is low (and giving a reason as to why it is low, but as Adam Smith himself would surely admit, the laws of supply and demand do not [directly] care about the 'why').

DEMAND SIDE: There is no explicit mention of the demand for these services, but as educated readers, we are able to deduce that during the time of Adam Smith, the demand for certain [x] heavily outweighed the supply.

*[x] blocked out because its specific value is not germane to the underlying logic of the argument.

I also think you have a misunderstanding. Adam Smith is clearly explaining the reason for the more liberal wages from the perspective of the one who is to commence the study, and his likelihood of succeeding. Smith is pointing to the fact that liberal professions are inherently more difficult to master, and often provide a value that is more rare (and therefore worth more money).

You cannot turn this quote into a formula, because it's a description of how wages ought to be, and the reasons therefore. And it is completely irrelevant to discussion, as I'm sure if Smith were alive today, he would count the art of programming among the liberal professions. There is more to making a useful application than to be able to think mechanically. Because programmers create and shoemakers copy.

I wasn't addressing lawers v. programmers, but just the relationship between the cost of education and the wages expected from undertaking it.

Of course, today you could point to a plethora of professions for which a long and expensive education is required, but for which compensation lags, often painfully. Though in some cases job security may be higher.