Part 94

Chapter 942,721 wordsPublic domain

MATHEMATICS, originally signified any kind of discipline or learning; but, at present, denotes that science which teaches, or contemplates, whatever is capable of being numbered or measured; and accordingly is subdivided into arithmetic, which has numbers for its object; and geometry, which treats of magnitude.

MATHEMATICS are commonly distinguished into pure and speculative, which consider quantity abstractedly; and mixed, which treat of magnitude as subsisting in material bodies, and consequently are interwoven every where with physical considerations.

_Mixed_ Mathematics are very comprehensive, since to them may be referred astronomy, optics, geography, hydrography, hydrostatics, mechanics, fortification, gunnery, projectiles, mining, engineering, and navigation.

Pure mathematics have one peculiar advantage, that they occasion no disputes among wrangling disputants, as in other branches of knowlege; and the reason is, because the definitions of the terms are premised, and every one that reads a proposition has the same idea of every part of it. Hence it is easy to put an end to all mathematical controversies, by shewing, that our adversary has not stuck to his definitions, or has not laid down true premises, or else that he has drawn false conclusions from true principles; and, in case we are able to do neither of these, we must acknowlege the truth of what he has proved.

It is true, that in mixed mathematics, where we reason mathematically upon physical subjects, we cannot give such just definitions as the geometricians; we must therefore rest content with descriptions; and they will be of the same use as definitions, provided we are consistent with ourselves, and always mean the same thing by those terms we have once explained.

Dr. Barrow gives a most elegant description of the excellence and usefulness of mathematical knowlege, in his inaugural oration upon being appointed professor of mathematics at Cambridge.

The mathematics, he observes, effectually exercise, not vainly delude, nor vexatiously torment studious minds with obscure subtleties; but plainly demonstrate every thing within their reach, draw certain conclusions, instruct by profitable rules, and unfold pleasant questions. These disciplines likewise enure and corroborate the mind to constant diligence in study; they wholly deliver us from a credulous simplicity, most strongly fortify us against the vanity of scepticism, effectually restrain us from a rash presumption, most easily incline us to a due assent, perfectly subject us to the government of right reason. While the mind is abstracted and elevated from sensible matter, distinctly views pure forms, conceives the beauty of ideas, and investigates the harmony of proportions; the manners themselves are sensibly corrected and improved, the affections composed and rectified, the fancy calmed and settled, and the understanding raised and excited to nobler contemplations.

MATRAS, _Fr._ a sort of dart which was anciently used, and which was not sufficiently pointed to occasion any thing more than a bruise.

MATRON, a woman, generally the wife of some well behaved and good soldier, who is employed to assist in the regimental hospital. She is under the direction of the surgeon, by whom she is originally appointed to the situation. See NURSE.

MATROSSES, are properly assistants to the gunner, being soldiers in the British regiments of artillery, and next to them: they assist in loading, firing, and spunging the great guns. They carry firelocks, and march along with the guns and store-waggons, both as a guard, and to give their assistance on every emergency.

MATTER _of Deed_, in law, denotes something to be proved by witnesses, in contradistinction from _matter of record_, which may be proved by some process, &c. appearing in any court of record.

MATTER, in a military sense, especially with regard to courts-martial, consists of the specific charges which are brought against a prisoner, and to which the president and members most strictly confine themselves. It has been very properly observed, in a small pamphlet upon martial law, that unacquainted with the serious consequence of a strict attention to the minutiæ of form in criminal proceedings, general courts-martial have looked upon the first swearing in of the court, as a sufficient authority to warrant their proceeding on the trial of a variety of offences; whereas, in propriety, the court should be sworn afresh at the commencement of every new prosecution: for though, as judges, (in the manner of a court of common law) once swearing would be sufficient; yet, as jurors, who are sworn on every different trial, though identically the same men, so are the members of general courts-martial to be considered, when a new criminal and fresh _matter_ are brought before them. Lest, however, an established, and therefore an undisputed practice, should have acquired a force still difficult to be eradicated, we shall endeavor to point out those reasons which induce us to maintain this opinion. In the oath which is taken by each of the several members of a general court-martial, the words _matter_ and _prisoner_, are cautiously inserted. These words, therefore, being absolutely confined to a single matter, and a single prisoner, and _matters_ and _prisoners_ not being subjected to their jurisdiction, how is it possible that men, with propriety, can proceed upon a trial which they are not warranted by law to decide upon? Were the obligation in the Articles of War decisive as to the trial of all matters, and all persons, and in all cases; or were the court possessed of the authority of extending the meaning of the oath, once swearing would undoubtedly be sufficient; but, as in every respect, the contrary is evident, as the very words of the oath express that “_they shall well and truly try and determine according to their evidence, in the matter before them, &c._” How can it be otherwise than an unwarrantable irregularity in them, to proceed upon the trial of offenders, who, in the eye of the law, are not amenable to their authority? For, if the _first_ prisoner to be tried, has a right to challenge an officer, who may be appointed to sit on an investigation of his offence, as a member of a court of enquiry, or who may be liable to any exceptions, why shall not the _second_ and _third_ prisoner be entitled to the same merciful indulgence? See Thoughts on Martial Law, pages 25, 26, 27, 28.

_Combustible_ MATTER, _and_ MATTER _of composition_. All solids and fluids are so called which are of an inflammable nature themselves, and can communicate fire to other substances.

MATTUCASHLASH, an ancient Scotch weapon, sometimes called armpit dagger, which was worn there, ready to be used on coming to close quarters. This, with a broad sword and shield, completely armed the highlanders. Since the use of fire arms, this weapon has been laid aside.

MATTOCK. An instrument somewhat resembling a pickax, but having two broad sharp edges instead of points.

MATTRESS, a sort of quilted bed of straw, used by officers on service, instead of the feather bed, differing from the paillasse in one particular only; the straw in the latter being loose, whereas that of the mattress is quilted in.

MAUG, _Ind._ The name of a month which partly agrees with our January and February.

MAUL, a heavy beater or hammer, generally shod with iron, used in driving piles, &c.

MAWANY, _Ind._ See KISTBUNDY.

MAXIMS, in _fortification_. See FORTIFICATION.

MEALED, pulverized, or reduced to powder.

MEAN _Fortification_. See FORTIFICATION.

MEANA, _Ind._ A machine or vehicle, a species of palankeen, but only used for carrying one person. It is borne by four men, and supported by means of a bamboo extended from the ends; being generally seven feet long, and three wide, with Venetian blinds, which slide and act as doors. Persons in India sometimes travel to a considerable distance in these vehicles; the number of bearers being increased, and successively relieved. It is computed that they will easily go at the rate of six miles in the hour.

MEASURE, in _geometry_, any quantity assumed as one, to which the ratio of other homogeneous or similar quantities is expressed.

MEASURE _of an angle_, the length of an arch described from the vertex to any place between its legs: hence angles are distinguished by the ratio of the arches between the legs to the peripheries. See ANGLE.

MEASURE _of a figure_, is a square, whose side is an inch, foot, yard, or other determinate measure. Hence square measures.

Among geometricians it is usually a square rod, called _decempeda_, divided into 10 square feet, and those into square digits, and those again into 10 lines, &c.

MEASURE _of a line_, any right line taken at pleasure, and considered as unity.

MEASURE _of the mass or quantity of matter_, in _mechanics_, is its weight: it being apparent that all the matter which coheres with a body, gravitates with it; and it being found by experiment, that the gravities of homogeneal bodies are in proportion to their bulks: hence while the mass continues the same, the absolute weight will be the same, whatever figure it puts on; for as to its specific weight, it varies as the quantity of its surface does.

MEASURE _of a number_, in _arithmetic_, such a number as divides another without leaving a fraction: thus 9 is a measure of 27.

MEASURE _of a solid_, is a cube, whose side is an inch, foot, yard, or other determinate length: in geometry, it is a cubic perch, divided into cubic feet, digits, &c. Hence cubic measure, or measures of capacity.

MEASURE _of velocity_, in _projectiles_, and _mechanics_, the space passed over by a moving body in any given time. The space therefore must be divided into as many equal parts, as the time is conceived to be divided into: the quantity of space answering to such portion of time, is the measure of the velocity.

_Measures_ then are various, according to the different kinds and dimensions of things measured. Hence arise lineal and longitudinal measures for lines or lengths; for square areas; and solid or cubic, for bodies and their capacities: all which again are very different in different countries and ages, and even many of them for different commodities. Hence also arise other divisions, of domestic and foreign, ancient and modern, dry and wet (or liquid) measures, &c.

_Long_ MEASURE. The English standard long measure, or that whereby the quantities of things are ordinarily estimated, is the yard containing three English feet, equal to three Paris feet one inch and ³⁄₁₂ths of an inch, or ⁷⁄₉ths of a Paris ell. Its subdivisions are the foot, span, palm, inch, and barley-corn: its multipliers are the pace, fathom, pole, furlong, and mile.

TABLE, _which shews the length in English lines of the several long measures, and the relation of foreign measures to 100 English feet_.

LONG MEASURE.

The following examples will shew in what manner the proportion between the long measures of any two given countries may be ascertained.

_Examples._

It is required to reduce 100 metres new measure of France into feet of Hamburgh.

The French metre measuring 472,27 English lines, and the Hamburgh foot 135,30, according to the table prefixed, I state the following equation:

100 metres = _x_ 1 metre = 472,27 lines 135,30 lines = 1 foot Result 349,05 feet.

Reduce 100 feet of Hamburgh into metres of France.

100 feet = _x_ 1 foot = 135,30 lines 472,27 lines = 1 metre Result 28,65 metres.

TABLE, _which shews the contents in English square feet of the several land measures, and the relations of foreign measures to 100 acres English measure_.

LAND MEASURE.