_Applied_ mathematics are not always sound; for example, in applying mathematics to Engineering problems, it is by no means uncommon to find that they appear to err most egregiously; so much so, as to give rise to the saying, that “theory and practice contradict one another.” The fact, in reality, being that theory has not been correctly applied; that innumerable small factors, which can only be ascertained by practice and experience, have been neglected in the application of theory; and even practice often fails to supply these factors. _Applied_ Political Economy is under similar conditions, but with this difference: _1st_, that _pure_ Political Economy is not infallible; _2nd_, that the application of Political Economy is affected by a greater number of intricate factors than any ordinary problem in Engineering; _3rd_, that the observation of results in a complex question of Applied Political Economy is far more difficult than in the case of those simple materials which are dealt with in Engineering problems. The eminent Italian Political Economist, Luigi Cossa, warns the student of this difficulty; but free-trading “fools rush in where angels fear to tread.” He says:-- “It is needful to hold ourselves aloof equally from the so-called Doctrinaires who refuse the assistance of practice, and from the Empiricists who obstinately close their eyes to the light of theory. _The Pure science_ explains phenomena and determines laws; the _Applied_ science gives guiding principles, which practice brings into conformity with the innumerable varieties of individual cases.”[15] Mill also says:-- “One of the peculiarities of modern times,--the separation of theory from practice,--of the studies of the closet from the outward business of the world,--has given a wrong bias to the ideas and feelings both of the student and of the man of business.[16] ... There is almost always room for a modest doubt as to our practical conclusions.” Let us take an example of pure and applied science. You, my Friend, quote an axiom of Pure Political Economy when you say:-- “It is unjust to tax all for the benefit of _one class_” So far I quite agree with you;--it is to your _application_ of the _axiom_ that I object, when you go on to say--“therefore protection in any shape is wrong.” Your application of pure science to the complex question of free trade is quite incorrect. I say “_it is just and expedient to tax all for the benefit of all_.” I hold that the employment of home and colonial labour, and the development of home and colonial produce and industries, is for the benefit of the community as a whole; and that, consequently, protection, if _carried only to the extent necessary to secure this, and no further_, is just and expedient.