of the horizon; but when we draw near to them, we find they are no vapours, but firm land, fit for culture and inhabitation. Some misunderstandings may arise from inexperience; others from prejudice and disaffection. It is our great misfortune in this country, that we are so much inclined to party and faction upon every occasion. In Religion we are broken into sects, and disturbed with fanaticism in various shapes. In Politics we have parties, whose opposite views weaken the force of the strongest kingdom in Europe, and endanger the vitals of the constitution. And even in Philosophy, where nothing but candour and serenity should prevail, we are still subject to an intolerant spirit, which either absolutely hinders the advancement of science, or obliges it to run in one narrow channel. From the observations I have been able to make on mankind, I find them always more intolerant for error than for truth, which is great without the aids of worldly power or policy, and will prevail in the end by its own strength. Hitherto I have been informing my reader what he is to expect: I must now tell him what he is not to expect. The nature of my work would seldom admit of an historie cal account of experiments. When they are delivered in detail, they take up much room, and if wantonly amplified, are more like the history of a man's own self, than a treatise upon Philosophy. The result of any trial is generally very short, and its doctrine is more to my purpose than its history; which, if the experiment is common, is to be met with in writers who have pursued a different plan. It is possible I may have carried this reserve too far; and I am apprehensive I shall be suspected of inaccuracy, because I have so studiously avoided minute descriptions. Having much matter to offer, and of various sorts, and having promised to confine myself to the compass of two volumes in quarto, I am under the necessity of compressing my matter into as small a compass as I conveniently can. The description of the machine to shew the force and heat of burning fire, would have been thrice as long as it is, if it had extended minutely to all particulars but I did not mean to write as a mechanic; I have contented myself frequently with throwing out a general truth, leaving others to correct it with proper distinctions. Thus, in explaining the consonance of musical strings, I have said that the vibrations vibrations of the same pendulum compared among themselves, are isochronous; which is not true, except in small arcs of a circle, not sensibly differing from the arcs of a cycloid; but it is true so far as I have occasion for it, because the ordinary vibrations of musical strings are in exceeding small arcs, and it would have carried me out to a subject not before me, if I had distinguished more accurately. To some, my plan may appear defective, because it does not abound with diagrams and demonstrations: but in these discourses I have little concern with that mixt Philosophy, which has been so well and so copiously treated of in. several modern systems of great merit and I have reason to believe that the public will be gratified with the best work of that kind by an ingenious mathematician of the university of Cambridge, who is qualified in every respect to answer their expectations. My work is of a more humble and popular nature; it is properly physiological, and its demonstrations are from facts; a sort of reasoning, which, if inferior on some occasions to the geometrical, is yet unexceptionable in Philosophy, and best accommodated to the capacities of all sorts of readers. readers. Mathematical demonstration, when applied to the properties and powers of matter, partakes of uncertainty, from our imperfect knowledge of the subject to which it is applied; and it has been extended injudiciously and affectedly to subjects where it has no place; for some have taught Divinity, and others have administered Medicines, upon mathematical principles. When Mr. Robins made his experiments on the resistance of the air to bodies in motion, Sir Isaac Newton had demonstrated that this resistance was as the square of the velocity; and it was reasonable to believe that the demonstration was universal: but when experiments were carried on to very high velocities, the rule failed entirely, and another took place, never till then suspected. As bodies lose their motion from the resistance of a fluid, it was supposed demonstrable, from thence, that a Vacuum is necessary to motion; but the contrary appears from other experiments, and the demonstration is but partial. Muschenbroek demonstrates, from Hydrostatics, that all bodies would be at rest in a fluid æther capable of occupying their pores, because a body of the same specific gravity with water is at rest in water; whence he concludes It is concludes there can be no such æther. But if we begin the other way, and shew there actually is an æther in the pores of bodies, then it is found that the demonstration does not hold; and that the author, in stating the case, did not follow nature. Men can always prove with great ease what they already believe, or wish to be true. Pure Mathematics yield absolute demonstration; but when they are mixed with physical suppositions, then the demonstrations are conditional at best, and may be absolutely false. dangerous to call such mixt reasonings by the name of demonstrations; because they may exclude all farther inquiry by experiment; and they may likewise discourage the studies of some readers, who, under a persuasion that all philosophy lies deeply intrenched and fortified against common understandings, give up the whole science in despair. But there is a vast field open to all persons of a liberal education, wherein they may employ their minds with pleasure and profit, free from those terrors which stop the progress of many students. The Astronomer, the Navigator, the Engineer, must be Mathematicians; and it will be good for the Philosopher |