S P I 



A a to the whole circumference can be afligned. See Mac- 

 lauriii, ibid. p. 33. 



Spiral, Parabolic. See Helicoid. 



Spiral, Proportional, is generated by fiippofing; the ra- 

 dius to revolve equably, and a point from the circumference 

 to move towards the centre with a motion decreafmg in a 

 geometric progreffion. See Logistic. 



From the nature of a decreafmg geometric proprenion, it 

 is eafy to conceive that the radius C A tfg. 8.) may be 

 continually divided ; and although each fuccelfive divifion 

 becomes fhorter than the next preceding one, yet there mull 

 be an indefinite number of divifions or terms before the lall 

 of them becomes of no finite magnitude. Whence it fol- 

 lows, that this fpiral winds continually round the centre, 

 and does not fall into it till after an indefinite number of re- 

 volutions : and alfo that the number of revolutions decreafes, 

 or the number of the equal parts into which the circum- 

 ference is divided increafes. 



It is alfo evident, that any proportional fpiral cuts the 

 intercepted radii at equal angles : for, if the divifions A <i, 

 de, ef, fg, &c. of the circumference be very fmall, the 

 feveral radii would be fo clofe to one another, that the in- 

 tercepted parts AD, DE, EF, F G, &c. of the fpiral 

 mighr bf taken ao right lines; and the triangles CAD, 

 C D E, C E F, &c. would bt- fimilar, having equal angles 

 at the point C. and the fides about thofe angles propor- 

 tional : confequently, the angles at A, D, E, F, &c. being 

 equal, the fpiral mult neceffarily cut the radii at equal angles. 

 Hobertfon's Elem. of Nav. book ii, p. 87. 



Proportional fpirals are fuch fpiral lines as the rhumb 

 lines on the terreitrial globe, whicli, becaufe they make 

 equal angles with every meridian, muil alfo make equal 

 angles with the meridians in the ftereographic projeftion on 

 the plane of the equator, and therefore will be, as Dr. 

 Halley obferves, proportional fpirals about the polar point. 

 From whence he demonftrates, that the meridian line is a 

 fcale of log. tangents of the half meridian complements of 

 the latitudes. See Rhumb, Loxodromy, and Meridional 

 Parts. 



Spiral, in ArchUeaure and Sculpture, denotes a curve 

 that afcendf, winding about a cone, or fpire, fo that all the 

 points of it continually approach the axis. 



By this it is diitinguifhcd from the helix, which winds, 

 after the fame manner, around a cylinder. Ignorant archi- 

 tefts confound the two, but the more knowing dillinguifli 

 them carefully. 



Spiral Pump. See Archimedes^ s Screw . 



Spiral Stairs, in Building. See Stairs- 

 Spiral Vejfili, in Vegetable Phyfwlogy, are found ranged 

 concentrically round the pith in the tender branches or llalks 

 of numerous plants, particularly the Elder, Syringa, Cor- 

 nel, Peony, and many of the Liliaceous order. If a branch 

 be partly cut tranfverfely, or gently broken, and the por- 

 tions fiowly drawn afundcr, a number of fine white fibres 

 will be perceived gradually to unroll, and thcfc will often 

 fupport a confidcrable piece of the divided italk. Thcfe 

 fibres originally formed the coat of the vellcls in quellion. 

 After the plant has acquired a certain firmnefs of texture, or 

 has finifhed its growth for the fealon, fuch can no longer be 

 unrolled. Mirbcl has delineated many fpucimcns of thefc 

 vellels, in which the fpiral fibre of each m more or lefs im- 

 perfeft, fhewiiig that, probably as they advance in age, the 

 velTels become entire tubes. 



The ufe of thcfc fpiral-coated veliels has been much dlf- 

 puted. Tiiey being commonly found on dideftion to con- 

 tain fcarccly any fluid but air, Malpighi, Grew, and others, 



S P 1 



have called them air-vefiels, fuppofing they were the lungs 

 of plants, and imbibed air from the atmofphere, through 

 another more external fet of roundilh or oval air-veUels, of 

 which leaves, petal;-, &c. are full. But the experiments of 

 Darwin and Knight rather (hew the fpiral-coated tubes to 

 be the true fap-vclTels, in which light we have confidered 

 them in the article Circulation of Sap, to which we refer 

 the reader. No fuch fpiral veflels are found in the bark of 

 plants, at any period of its growth. 



SPIRATION. See E.\piration, Inspiration, Per- 

 spiration, Respiration, and Transpiration. 



S PI ration, in Scholq/lic Theology, a term ufed by the 

 popith fchoolmen to fignify the manner in which the per- 

 fonality of the Holy Spirit was derived from the Father and 

 the Son. See Procession and Holy Spirit. 



SPIRDING See, in Geography, a large lake of Pruffia ; 

 30 miles S. of Bartcnftein. 



SPIRE, in Agriculture, a term fignifying to fprout, as 

 grain in the malting procefs, &c. The fpiring in this procefs 

 fliould neither be carried too far nor hopped too fuddcnly, 

 as in both cafes the malt fuffers injury. See Malt. 



Spire, Spira, in the Ancient ArchiteSure, is fometime* 

 ufed for the bafe of a column, and fometimes for the allra- 

 gal, or tore. 



The word is formed from the Latin fpirte, the folds of a 

 ferpent, which bear fome refemblance to it ; or from the 

 Greek o-irsipa, the coil of a rope. 



Spire is alfo a pyramidical termination of the tower of 

 a church or other building. This ornament, being the ge- 

 nuine offspring of the pointed arch, and not occurring in 

 the monuments of Greece or Rome, ought to be confined 

 to its proper ityle. It is an incongruity to introduce it 

 into Grecian architedure. 



Spire, in Geography, a city of France, and principal 

 place of a diltriiit, in the department of Mont Tonnerre, 

 containing 3744 inhabitants, (its canton having 7894,) in 

 9 communes. This was, before the French revolution, an 

 imperial city of Germany, and the capital of a bilhopric of 

 the fame name. Spire is an ancient city, (aid to have been 

 founded before the commencement of the Chriilian era, and 

 receives its name from the fmall river Spirebacii, which runs 

 into the Rhine, about 500 paces below it. It contains a ca- 

 thedral, thrte collegiate churclies, and (everal convents, be- 

 fides two churches belonging to the Lutherans, of which 

 clafs the magiltrate^ and greater number of the inhabitants 

 confiU. The Franks took this city from the Romans, and 

 it became one of the original imperial cities. In the year 

 1529, a diet was held here, in which the reformers firil ob- 

 tained the name of Protellants. It was dillroyed by the 

 French in 1689, and lay wade for ten years, nor was it re- 

 built till after tlic peace of Ryfwick. Before this difaller, 

 it was tiie feat of the imperi.il clamber. In December 

 1793, it furrendered to the republican troops of France. 

 The bilhopric of Spire is of conliderable antiquity. Its 

 territories were fituated on the Rhine, between the Palatinate, 

 the duchy of Wurtemburg, the niargraviatc of Baden, and 

 the princi|)ality of Deux-Ponts, about 18 leagues in length, 

 and 12 in breadth. It is mountainous, and covered with 

 forelts ; nevorthckfs it produces corn, wine, chelnuts, and 

 alniMuds. The bifliop was luftragan of Mentz, and refided 

 at BruchfaL The territories on the left bank of the Rhine 

 have been united to France, and in 1802, thofe on the right 

 were given as indemnities to the margrave of Baden ; 12 

 miles S.W. of Heidelberg. N. lat. 49^ 18'. E. long. 

 8^^ 30'. 



SPIRES, 



