SOL
[94]
SOL
If, then, thefe be applied in this Order, fa, fil, la, fa, fil, la, mi, fa, i$c. They exprefs the Natural Series from c ; and if 'that be to be repeated to a Second or Third Oftavc, we fee by them how to exprefs all the different Orders of Tones and Semi-tones in the Diatonic Scale ; and ftill above mi, will {land fa, fil, la; and below it, the fame reverfed, la, fil, fa 5 And one mi is always diftant from another by an Oftave ; which cannot be faid of any of the reft becaufe after rat afcending, comes always fa, fil, la, fa, which are repeated invertedly, defcending.
To conceive the Ufe of this : it is to be remember'd, that the firlt Thing in teaching to iing, is to make one raife a Scale of Notes by Tones and Semi-tones to an Oclave, and defend again by the fame Notes, and then to rife and fall by oreater Intervals, at a Leap, as a Third, Fourth and Filth, tfc. And to do all this, by beginning at Notes of different Fitch. Then, thefe Notes are reprefentcd by Lines and Spaces, to which thole Syllables arc applied, and the Learner taught to name each Line and Space, by its refpeftive Syllable; which makes what we call Sol-fa -ing ■■ The Ufe whereof is, that while they are learning to tunc the Degrees and Inter- vals of Sound, exprefs'd by Notes fet on Lines and Spaces ; or learning a Song, to which no Words are applied ; they may do it the better, by means of an articulate Sound : but, chiefly, that by knowing the Degrees and Intervals exprefs'd by thefe Syllables, they may more readily know the true Di- ftance of Notes. See Singing.
Mr. Malcolm obferves, that the Praclice of Solfa-ing, common as it is, is very uielefs and infignificant, either as to the Underftanding or Praflifingof Molic ; yet exceedingly perplexing : The various Application of the feveral Names, according to the various Signatures of the Clef, are enough to perplex any Learner ; There being no lefs than 72 various Ways of applying the Names fil, fa, S3c. to the Lines and Spaces of a particular Syftera. See Scale.
SOLID, in Phyficks, a Body whofe minute Parts are connected together, fo, as not to give Way, or flip from each other upon the fmalleft Impreffion. See Solidity.
The Word is ufed in this Senfe, in Contradiftinftion to Fluid. See Fluu> and Firmness.
For the Zones of Gravitation of-
Solitis immerged in Fluids
Specifically lighter than the
Sclids - - ) See Gravity,
"The Zaivs of Gravitation 0}
Solitis imraerg'd in Fluids
Specifically heavier - - - J
To find the Specific Gravity o/\
JfindThekatil of tieSpe'eifiS S « S ^'" c G ""^ Gravity of So li-ds to Fluids. )
tfle Laws of the Refinance of J
Solids moving in Fluids - > See Resistance, Solid of the leajt Refinance - - J
Solid, in Geometry, is a Magnitude indued with Three Di mentions ; or extended in Length, Breadth and Depth, See Dimension-
Hence, as all Bodies have thefe Three Dimensions, and nothing but Bodies ; Solid and Body are frequently uled in- difcriminately. See Body.
A Solid is terminated, or contained under one or more Planes or Surfaces ; as a Surface is under one or more Lines. See Surface and Line.
From the Circumftances of the terminating Lines, Solids become divided into Regular and Irregular.
Regular Solids, are thole terminated by regular and equal Planes. See Regular.
Under this Clafs come the Tetrae'dron, Hexaedron or Cube, OHffidton-, fDodecaedron and Icofiedron. See Tetraedron, Cube, &g. each under its proper Article.
Irregular Solids, are all fuch as do not come under the Definition of Regular Solids ; fuch are the Sphere, Cylinder, Cone, 'Parallelogram, <Prifm, Pyramid, 'Parallelopipid, &c. See Sphere, Cylinder, Cone, &C, each under its proper Article.
The Gcneies, Properties, Ratio's, Constructions, Di- tnenfions, ifc. of the feveral Solids, Regular and Irregular, Spherical, Elliptical, Conical, £?e. See under each refpe&ive Heads.
Cubature or Cubing of a Solid, is the meafuring of the Space comprehended under a Solid, i. e. the Solidity or Solid Content thereof. See Solidity.
Solid Angle, is that form'd by three or more plain Angles meeting in a Point : Or, more ftriftly, a Solid Angle, as B, (Tab. Geometry, Fig. qo-) is the Inclination of more than two 1 5nes, A B, B C, B F, which concur in the fame Point B, and are in the different Planes.
Hence, for Solid Angles to be equal, 'tis necejTary they be
contained under an equal Number, of equal Planes, difpofed in the lame manner.
And as Solid Angles are only diftinguifhable by the Planes under which they are contained 5 and as Planes thus equal s are only diftinguifhable by Comprslence, they are Similar - and confequently Similar Solid Angles, are equal, & vice verfa* See Similar.
The Sum of all the Plane Angles conftituting a Solid Angle, is always leis than 36o°5 otherwife they would conftitute ihe Plane of a Circle, and not a Solid. See Angle.
For the Method of Cubing the feveral Kinds of Solids 5 See Cubature.
Solid Baflion? g ee y Bastion. Solid 'Place 5 £ Locus.
Solid Numbers, are thofe which arife from the Multipli- cation of a Plain Number, by any other whatfbevcr. Thus 18 is a Solid Number, made of 6 (which is Plain) multiplied by 3 ; or of o multiplied by 2. See Number.
Solid 'Problem, in Mathematicks, is one which cannot be Geometrically folved, but by the Interferon of a Circle, and a Conic Section 5 or by the Interieftion of two other Conic Sections, befides the Circle.
Thus, to defcribe an Ifofceles Triangle on a given Right Line, whole Angle at the Bafe, fhall be triple to that at the "Vertex, is a Solid Problem. See Problem.
SOLIDITY, in Phyficks, a Property of Matter or Body, whereby it excludes every other Body from the Place itielf poflefTes.
Solidity is a Property common to all Bodies, whether Solid or Fluid. See Body.
The Idea of Solidity y Mr. Lock obferves, arifes from the Refiftance we find one Body make to the Entrance of another into its own Place. 'Tis ufually called Impenetrability ; but Solidity expreffes it beft ; as carrying ibmewhat more of pofitivewith it than the other, which is negative.
Solidity, he adds, feems the mod extenfive Property of Body; as being that whereby we conceive it to fill Space : 'Tis diflinguifli'd from meer Space, by this latter not being- capable of Refiftance or Motion. See Space.
J Tis diftingui/h'd from Hardnefs, which is only a firm Cohefion of the Solid Parts, fo as they mayn't eafily change their Situation. See Hardness.
The Difficulty of changing Situation, gives no more So- lidity to the hardeft Body than the fofteft ; nor is a Diamond a Jot more Solid than Water. By this we diftinguifh the Idea of the Extenfion of Body, from that of the Extension of Space : That of Body, is the Continuity or Cohefion ofc" folid, feparable, moveable Parts 5 that of Space, the Con- tinuity of unfolid, infeparable, immoveable Parts. See Extension.
The Cartejians, however, will, by all means, deduce Solidity-, or, as they call it, Impenetrability ', from the Nature of Extenfion ; and contend, that the Idea of the former, is contain'd in that of the latter 5 and hence argue againfl: a Vacuum. Thus, fay they, one Cubic Foot of Extenfion cannot be added to another, without having two Cubic Feet of Extenfion ; for each has in irfelf, all that is required to conftitute that Magnitude. And hence they conc!ude,that every Part of Space is Solid, or Impenetrable ; inafmuch as of its own Nature it excludes all orhers. But the Conclufion is falfe, and the Inftance they give follows from this, that the Parts of Space are immoveable ; not that they are Impene- trable or Solid. See Impenetrability.
Solidity, in Geometry, the Quantity of Space contain'd in a Solid Body ; call'd alio the Solid Content ', and the Cuts thereof. See Cubature.
The Solidity of a Cube, Prifm, Cylinder, or Parallelopipid, is had by multiplying its Balls into its Height. See Cube, Prism, Cylinder, £fJc.
The Solidity of a Pyramid or Cone, is had by multiplying either the whole Bale into a Third Part of the Height j or the whole Height into a third Part of the Bafe. See Pyra- mid and Cone.
<Tq find the So l i d i t y of any Irregular Body.
Put the Body in a hollow Parallelopipid, and pour Water or Sand upon it, and Note the Height of the Water or Sand AB (Tab. Geometry, Fig. 32.) then, taking out the Body, obferve at what Height the Water (or Sand when levell'd) ftands, as A C Subtract A C from A B j the Remainder will be B C. Thus is the irregular Body reduced to a Parallelopi- pid, whofe Bafe is F C G F 5 and Altitude B C. To find the Solidity whereof, fee Parallelopipid.
Suppole, E. gr. A B 8, A C 5; then will B C be 3 = $>*?' pofe, again, D B n, DE43 then will the Solidity of the irregular Body be found 144. ,
If the Body be fuch, as that it can't be well laid in Uch
a kind of Channel ; £, gr, if it be required to meafure the
? ° i Solidity
