S L I 



3.6, wliich is a near approximation to the required root ; 

 and accordingly, 3T6^ '• ' =100. 



Our author's inllrument admits of being applied in various 

 forms to the feveral purpofes above recited, as well as to 

 others which he has enumerated : but the following deferves 

 particular mention, on account of the pecuhanties that at- 

 tend them. If to the upper fcale, which we may fuppofe 

 to be fixed, and to be graduated logometrically, conftitutmg 

 the line of exponents, a Aider be adjulled, graduated on 

 both edges, according to the logometric logarithms ; and 

 the line below, which, like the upper one, is fuppofed to be 

 fixed, be graduated in the fame manner as the Aider, the 

 inftrument will poilefs tlie fallowing property. When the 

 divifion 10 on the Aider is fet againft any particular number, 

 or exponent, in the upper line, all the numbers on the lower 

 line will be the powers, to the fame degree, of the numbers 

 oppofite to them on the Aider ; the degree of the power being 

 marked by the exponent on the upper Hne, which is above 

 the 10 on the Aider. The lower line will, therefore, exhi- 

 bit the whole feries of fimilar powers belonging to all poAi- 

 ble roots ; and converfely, the Aider will exhibit all the 

 roots of the fame dimenfions, with regard to all poffible 

 numbers. Thus, if the 10 on the Aider be under 3 in the 

 line of exponents, it will itfelf be above 1000 (which is its 

 cube) in the lower line ; all the other numbers in that line 

 will be the cubes of their oppofites on the Aider ; and, con- 

 verfely, the former will every where be the cube-roots of the 

 latter. This will fufficiently appear, when it is recolkaed 

 that the addition or fubtraftion of logometric logarithms, 

 anfwers to the multiplication or divifion of fimple logarithms, 

 and therefore to the involution and evolution of numbers. 

 The rule in this form of it, therefore, bears a clofer analogy 

 to the common Aiding-rule ; fince in every pofition it exhibits 

 the feries of fimilar powers and roots, exaftly in the fame 

 way as the latter exhibits the feries of fimilar produfts and 

 quotients. 



Dr. Roget has alfo contrived to give another form to the 

 inftrument, by throwing the whole fcale, like Gunter's line, 

 into a circular form : and of this form he has given a draw- 

 ing. The circle on the outfide being logometrically divided 

 from I to 10 round the circumference, will conftitute the 

 line of exponents. The line of powers, being difpofed in a 

 fpiral, will occupy the interior fpace, which may be made 

 to revolve within the former, and fhould be provided with 

 one or more threads, extending from the centre to the cir- 

 cumference, and ferving as radii to mark the pofition of all 

 the parts of the fpiral line with regard to the divifions of the 

 outer circle. One of thefc threads may be fixed at the unit 

 or beginning of the fcale, and will ferve to mark the pofi- 

 tion for the root of any required power. The fpiral itfelf 

 muft be graduated exactly as the upper line in the firft de- 

 fcribed rule ; that is, thefituation of the divifion 10 muft be 

 firft determined upon, and then brought under the unit in 

 the circle of exponents ; that is, under the fixed thread. 

 Every other divifion mull then be marked with reference to 

 the place of its logarithm on the circle, or muft be made to 

 occupy the fame angular diftance from the thread. This 

 graduation will be moft conveniently made by means of the 

 moveable leg of a fedor revolving on the centre of the cir- 

 cle. The comparifon of the divifions of the fpiral with 

 thofe of the circle may be made, either with this moveable 

 feftor, or with the threads already mentioned. The num- 

 bers on the fpiral will increafe as they recede from the centre, 

 and each turn will carry on the powers to an exponent ten 

 times higher than the preceding ; and the converfe will ob- 



S L I 



tain with regard to the defcending portion. Thus, imme- 

 diately in a line with the 10, on the fuperior branch of the 

 fpiral, is found the number loooooooooo, or 10' °; below 

 it, on the inferior branches, we find fucceflively 1.258926 



= lo"-', 1.023293 = io|°'°', 1.00230524= loV"', 

 1.000230285 = To) •"'"", 1. 0000230261 =iol*''°°°', 

 &c. of which the decimal figures approach nearer and nearer 

 to 2.302585093, &c. the reciprocal of the modulus of the 

 logarithmic fyftem. Oar ingenious author has further ftiewn 

 how to exhibit in one view the whole feries of roots, powers, 

 and exponents, in all their pofiible relations, by a fuitable 

 difpofition of lines. For further particulars we refer to the 

 Phil. Tranf. for 1815, part i. p. 9, &c. For an account 

 of Mr. W. Nicholfon's improvements of the Gunter's 

 fcale, &c. fee the Phil. Tranf. for 1787, vol. Ixxvii. part 2. 

 See Gunter'j Line and Scale. 



StlDlttG-Keels, in Ship-Building, an invention of the in- 

 genious captain Schank, of the royal navy, to prevent vef- 

 fcls from driving to leeward. They were compofed of plank 

 of various widths, erefted vertically by a winch, fo as to 

 Aide up and down in a trunk, and through the keel. Many 

 veAels were built with no lefs than three of thefe keels ; but 

 it has not feemed to have anfwered. 



Sliding- P/an/fj, are the flat forms upon which the bilge- 

 ways Aide in launching the ftiip. 



SLIDING-GUNTER-SAIL, in Sail-Making, a tri- 

 angular fail, uied in boats, bent at its foremoft leech to 

 loops or grommets that Aide on the lower maft : the peek or 

 head is attached to a fmall top-inaft, that Aides up in the 

 diredion of the lower maft, through two hoops fixed at its 

 head, about three feet afunder. When the top-mall is 

 lowered, the fail furls up clofe to the lower maft. 



SLIEBH, or Sliabh, the Irifli name for a range of 

 mountains, or a fingle one, covered with heath. O'Brien 

 lays it fignifies heath-land, whether mountain or plain. It 

 is prefixed to the names of many IriAi hills. 



SLIEBH-AN-ERIN, in Geography, a range of moun- 

 tains in the county of Leitrim, Ireland, extending in a N.E. 

 direftion from Lough Allen. 



SLIEBH-EN-EWR, called alfo Dartry mountains, a 

 clufter of hills, covering almoft the whole of the northern 

 barony of the county of Leitrim, Ireland. Of thefe and 

 the preceding it is obferved by Dr. Beaufort, that they are 

 far from unprofitable ; for producing abundance of coarfe 

 grafs, they annually pour forth immenfe droves of young 

 cattle. 



SLIEVE-BAUGHT Mountains, a chain of moun- 

 tains on the confines of the counties of Monaghan and Ty- 

 rone, and extending in-to both. They form an uninterrupt- 

 ed ridge of high land, the higheft part of which is called 

 Cairn-more. They have, in general, neither a fruitful foil, 

 nor any natural beauties to recommend them, being an un- 

 interefting wafte, and almoft always wet and moory. There 

 are parts, however, which have beds of the richeft lime- 

 ftone, and abundance of marie, particularly on the eaftern 

 fide of Cairn-more. This mountain is famous for its mill- 

 ftone quarry : thofe moft valued confift of a red and very 

 hard grit or fand-ftone, the grain of which is clofe : there is 

 alfo a foft whitilh fand-ftone, more eafily procured, but 

 which foon waftes away. Potters' clay found in the neigh- 

 bourhood is carried to the pottery at Dundalk. Stat. Ac. 

 of Monaghan. 



SLIEBH-BAUGHTA Mountains, an extenfive 



range of rather low hills, which cover the fouthern part of 



° the 



