Writers before me have concluded that Matthew most probably was influenced by the writings of Malthus - the man who both Darwin and Wallace claimed as a most important influence on their "own" work. Dempster (1983, p. 51) writes that both Malthus and Paley were influenced by Franklin's essay of 1755. From that cause, it is worth looking at what Franklin wrote that may have influenced Matthew directly, or else indirectly through knowledge contamination.
In 1751, Franklin penned an essay that was finally published in Boston, USA, in 1755. It is entitled: Observations Concerning the Increase of Mankind and the Peopling of Countries.
The relevant sections of Franklin's essay are the very final ones 22 to 24:
22. There is in short, no bound to the prolific nature of plants or animals, but what is made by their crowding and interfering with each others means of subsistence. Was the face of the earth vacant of other plants, it might be gradually sowed and overspread with one kind only; as, for instance, with Fennel; and were it empty of other inhabitants, it might in a few Ages be replenish d from one nation only; as for Instance, with Englishmen. Thus there are suppos d to be now upwards of One Million English Souls in North America, (tho tis thought scarce 80,000 have been brought over sea) and yet perhaps there is not one the fewer in Britain, but rather many more, on Account of the employment the Colonies afford to manufacturers at home. This million doubling, suppose but once in twenty-five years, will in another century be more than the peo ple of England, and the greatest Number of Englishmen will be on this side the water. What an accession of Power to the British empire by the Sea as well as Land! What increase of trade and navi gation! What numbers of ships and seamen! We have been here but little more than one hundred years, and yet the force of our Privateers in the late war, united, was greater, both in men and guns, than that of the whole British Navy in Queen Elizabeth s time. How important an affair then to Britain, is the present treaty for settling the bounds between her Colonies and the French, and how careful should she be to secure room enough, since on the room de pends so much the increase of her people? 223 10 OBSERVATIONS CONCERNING THE INCREASE OF MANKIND 23. In fine, A nation well regulated is like a Polypus; take away a limb, its place is soon supply d; cut it in two, and each de ficient part shall speedily grow out of the part remaining. Thus if you have room and subsistence enough, as you may by dividing make ten Polypes out of one, you may of one make ten nations, equally populous and powerful; or rather, increase a nation ten fold in numbers and strength. And since detachments of English horn Britain sent to America, will have their places at home so soon supply d and increase so large ly here; why should the Palatine Boors be suffered to swarm into our settlements, and by herding together establish their languages and manners to the exclusion of ours? Why should Pennsylvania, founded by the English, become a colony of Aliens, who will shortly be so numerous as to Germanize us instead of our Anglifying them, and will never adopt our language or customs, any more than they can acquire our complexion? 24. Which leads me to add one remark: That the number of purely white people in the world is proportionably very small. All Africa is black or tawny. Asia chiefly tawny. America (ex clusive of the new comers) wholly so. And in Europe, the Span iards, Italians, French, Russians and Swedes are generally of what we call a swarthy complexion ; as are the Germans also, the Saxons only excepted, who with the English make the principal body of white people on the face of the earth. I could wish their numbers were increased. And while we are, as I may call it, scouring our planet, by clearing America of woods, and so making this side of our globe reflect a brighter light to the eyes of inhabitants in Mars or Venus, why should we in the sight of superior beings, darken its people? why increase the sons of Africa, by planting them in Ameri ca, where we have so fair an opportunity, by excluding all blacks and tawneys, of increasing the lovely white and red? But perhaps I am partial to the complexion of my Country, for such kind of partiality is natural to Mankind.
If these three sections of Franklin's (1755) essay, with what Zirkle (1941) saw as the texts that influenced Malthus, that so by 'knowledge contamination' influenced Darwin (and also Wallace) did not inspire Matthew to write "On Naval Timber" in 1831 and "Emigration Fields" in 1839 then the coincidences are astounding. For Franklin writes on so many of Matthew's key themes: (1) A belief in the superiority of the Saxon's (2) The importance of trade and navigation, (3) The voracious need of the British to obtain timber (4) The fact that some varieties of the human species suffer overcrowding and so need to emigrate so as not to be 'interfering with each other's means of subsistence' (5) The likelihood that by emigration Anglo Saxon's would overtop existing populations in colonies. (6) The ability for any species to have an ecological power of occupancy in the most circumstance suited environment - namely one that is supportive of life and devoid of superior competitors (think Dodo - until humans turned up).
See PatrickMathew.com for more information on the discovery of Natural Selection