Was Kant incorrect to assert 'natural sciences' as 'a priori'?

Question

[Source :] In natural science no less than in mathematics, Kant held, synthetic a priori judgments provide the necessary foundations for human knowledge. The most general laws of nature, like the truths of mathematics, cannot be justified by experience, yet must apply to it universally. In this case, the negative portion of Hume's analysis—his demonstration that matters of fact rest upon an unjustifiable belief that there is a necessary connection between causes and their effects—was entirely correct. But of course Kant's more constructive approach is to offer a transcendental argument from the fact that we do have knowledge of the natural world to the truth of synthetic a priori propositions about the structure of our experience of it.

I challenge not that natural sciences are synthetic, but only that they are a priori.

I exemplify my confusion with universal constants, whose existence (I understand) is a priori. However, how can a person's knowledge of them be a priori? Only some external experience can inform you which rational numbers describe them. For example, every human experiences atmospheric pressure, but you cannot know the unit of standard atmosphere somewhere until you experience some measure of it (eg: a barometer or a report about atmospheric pressure).
So your knowledge of natural sciences (eg: atmospheric pressure) must be a posteriori?

Answer 1

The reference you cited doesn't assert that Kant held that the natural science are a priori. Rather, "synthetic a priori judgments provide the necessary foundations for human knowledge." In the Preface to the Second Edition to the Critique of Pure Reason, Kant made it clear that although the objects of investigation are to be determined a priori, such information is insufficient for empirical science:

"Mathematics and physics are the two theoretical sciences which have to determine their objects a priori. The former is purely a priori, the latter is partially so, but is also dependent on other sources of cognition." [Bix]

The transcendental argument which is the heart of the Critique is aimed at establishing that all objects of experience are subject to the categories and, consequently, to related a priori principles such as causation. Such principles provide the necessary foundation for understanding the natural sciences, but that is only the beginning of what is required. In fact, Kant gives a nice description of the scientific method in which he asserts that reason must direct us in forming hypothesis, but our understanding of physical laws is ultimately determined through experimentation:

"[Natural philosophers] learned that reason only perceives that which it produces after its own design; that it must not be content to follow, as it were, in the leading-strings of nature, but must proceed in advance with principles of judgement according to unvarying laws, and compel nature to reply its questions. For accidental observations, made according to no preconceived plan, cannot be united under a necessary law. But it is this that reason seeks for and requires. It is only the principles of reason which can give to concordant phenomena the validity of laws, and it is only when experiment is directed by these rational principles that it can have any real utility. Reason must approach nature with the view, indeed, of receiving information from it, not, however, in the character of a pupil, who listens to all that his master chooses to tell him, but in that of a judge, who compels the witnesses to reply to those questions which he himself thinks fit to propose." [Bxi]