A cyclopaedia of physical sciences : comprising acoustics, astronomy, dynamics, electricity, heat, hydrodynamics, magnetism, philosophy of mathematics, meteorology, optics, pneumatics, statics &c. &c / by J.P. Nichol with the assistance of eminent scientific men.

  • Nichol, J. P. (John Pringle), 1804-1859.
Date:
1860
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Licence: Public Domain Mark

Credit: A cyclopaedia of physical sciences : comprising acoustics, astronomy, dynamics, electricity, heat, hydrodynamics, magnetism, philosophy of mathematics, meteorology, optics, pneumatics, statics &c. &c / by J.P. Nichol with the assistance of eminent scientific men. Source: Wellcome Collection.

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    fringes which result from these interferences for all the colours are superimposed in the sky; and bands analogous to those in the coloured rings of thin plates result. Space compels us to refer for detailed experiments, and explanations of these supernumerary bands, and of much of the whole theory and history of the subject, to an article by Bravais, in the Anuaire Meteorologique for 1849; and to the Graphical Representations of Engel and Schellbach, of which we have spoken. Rain-Crauge, or Pluviometer. An in- strument whose object it is to measure the depths of rain falling within certain intervals on the earth's surface, at the locality where it is placed. No meteorological instrument, generally speak- ing, is so imperfect and little trustworthy as rain- gauges in general. The simplest form is the best; nor can a better be devised than that sug- gested by the Rev. Professor Fleming, of Edin- burgh. It consists simply of a cup or receiver, whose opening should be flush with the soil's sur- face, and which by a funnel delivers the rain into a jar below. The liquid can at any time be jjoured into a graduated vessel, and mea- sured ; or the jar itself may be graduated. ThiS arrangement, which costs only a few shillings, is superior, in point of accuracy, to every com- plex apparatus that men of over-ingenuity have from time to time proposed. The right placing <jf the rain-gauge is of paramount consequence. The writer of this has seen one on the top of a pavilion or tent roof, and across which any cur- rent of air whatever—necessarily deflected by the roof—simply carried both rain and snow in a fine scientific smrl! The extreme imperfection of our knowledge as to the distribution of rain is imquestionably owing, in most part, to the imper- fection of this instrument, and the careless way in which it is used. Range. A technical term connected with yunnery and projectiles (q. v.) Rarefaction. The laws of rarefaction under increased heat, and under diminished pressure, and under both combined, are given as Dalton's, Marriotte's, and Amonton's laws in Pneumatics. Ratio. The ratio of two quantities simply signifies the number of times that the one quan- tify is contained in the other. Sometimes this number cannot be stated, t e., the one quantity is not contained in the other amj definite number (if times. The quantities are then said to be m- romviensurable. Euclid's Fifth Book contains the general Geometrical Doctrine of Ratios; and jierhaps no portion of that remarkable volume is more worthv of the ingenuity of the Greek In- K'Hect It'is very clear that no ratio or propor- tion can exist between quantities of different Unds; for instance, between a solid and a sur- face, or between an angle and a line. Hence that general principle in geometry termed the J'rinciple of Hmiogeneity, A Principle quite un- (|uestionable, if it be kept in view that in Func- tional Equations between magnitudes of appa rently different classes, constants may exist that convert, by their presence, magnitudes apparently heterogeneous into Ratios. Ratio Harmonic: Harmonic Pencilx : Aiiiiarmonic Ratio. The foregoing termri have now acquired so important a significance in the Modern Geometry, that an exact definition of them is necessary here. (1.) In Arithmetical proportion the diflferences of any two consecutive terms are equal. In Geometrical proportion, the quotients of two consecutive terms are the con- stants. The nature of Harmonic proportion Ls as follows:—Let the line ab be cut internally Fig. 1. at o and externally at o', so that A o : B o = A o' : B o', it is said to be cut harmonically: o o' is an har- monic mean between a o' and b o'; and if A b be supposed invariable, while o and o' change, these two points are named harmonic conjugates—A Harmonic Pencil is this: from any point, o, let four straight lines be drawn cuttmg the line a d harmonically, or so that AD:DC = AB:BC. It may A' Ml Fig. 2. These four lines are an harmonic pencil easily be proved that they will also cut harmonically any other trans- versal line, such as a'd'—Ratio Anharmonic. If four fixed right lines V A, V B, V c, V D be drawn from the same point, and any trans- verse right line a D be cut by them in foiu- points A, B, c, d, the ratio of the rectangle a d • b c to the rectangle a b - c d is constant. (This ratio is called ihcanhaimonic ratio of the four points A, B, C, D.) For, through c draw m n parallel to A V; then, a d . b c : a b • (BC : ab\. Jmo ; av). ^ ^ = • |ad : cdI ■ ■ (ay : CNi : : Ji c c n; but this last ratio remains constant when the point c changes its position along the line V c; the proposition is there- fore proved. When the transversal coincides with si N, a b and a n become infinite, and are in a ratio of equalitv, and therefore A d . b c : a 1! • c 1) : : B c: c D:: 31 c: c K, as before. Fig. 3. If