SLIDE 



SLIDK l; 



UJ 



uf the (Okie on which the divisor is marked, hu p*Jed to tho divisor 



: ' 



The following lint of slidiug-rules contains all, or nearly all, which 

 can be useful to any one : 



1. Common Engineer's Rule, or Carpenter's Rule in iU beat form. 

 A double 12-inch ride, a slide of two radii with the same scale on one 

 side, and a scale of one radius of double length on the other, with 

 divisor*. (Sold by all rule makers.) There is a description in Kentish's 

 Treatue on a Box of Instruments,' ftc., London, 183 U . 



2. Sevan's Engineer's Rule, 1 inches. Has slides on both faces 

 (which may be exchanged), and serres for squares, cubes, square 

 roots of cubes, Ac. There are scales on the backs of the slides 

 and in the grooves, for sines, tangents, inverted numbers, compound 

 interest and annuities at 5 per cent. (Cory, Strand, with an explanatory 

 treatise.) 



~8. Henderson'* Double-Slide Rule, 12 inches. Has two parallel con- 

 tiguous slides, with scales of number* fixed above and below, and 

 solves at one operation most sets of multiplications and division- nut 

 exceeding fire operations. At the back are tables of divisors for solids. 

 . Woollgar's Pocket Calculator, 8 inches. The two slide* work in 

 either of the grooves : the bocks and the grooves have scales of sines, 

 tangent*, areas of polygons, circular segments; interest, annuities, 

 certain and for lives, at several rates of interest. An addition may be 

 made by a metal slip, giving the solution of the some questions a the 

 hvst rule. 



5. Woollgar's Pocket-Book Rule, 6 and 8 incites. Two radii, one 

 under the other, as described in the preceding part of the article ; a 

 line for shies and duplicate proportions at the bock of the slide. At 

 the bottom of the groove are sometimes inserted lines for finding the 

 relations of right-angled triangles, for cask-gauging, and for cuttings 

 and embankments. 



6. Excise Officer's Sliding Rule, modern form. Sold at the Excise 

 Store-office, and by some of the instrument-makers. The old Excise 

 rule was a thick block, with a slide on each face. 



7. Barley's Rule, (Elliot, Strand) has a scale of numbers, squares, 

 and cubes, and a scale of equal parts, of the length of the line of 

 squares, from which the logarithm of a number can be approximately 

 read. This line is of considerable use in operations connected with 

 higher powers : it is found also in Sevan's rules. The constructor of 

 this scale, which is well divided and convenient, has a full treatise on 

 the whole subject in the press. 



Among separate treatises not yet noted are Flower's, Svo., London, 

 1768; Mackay's, 8vo., 2nd edit., London, 1811; do. Leith, 1812; 

 ' Instruction sur la Maniere de se servir de la Regie ti Calcul.,' petit-in- 

 8vo., Paris et Dijon, 1825 ; ' The Universal Ready-Reckoner,' by an 

 Idle Gentleman, 12mo., London, 1839 ; and there is a good deal on the 

 subject in Ingrain's 'Concise System of Mathematics,' 12ino., Edin- 

 burgh ; and Bateman's ' Excise Officer's Manual,' 12mo., London. 



Between the slicling-rule and the book of logarithms comes the card 

 of four-figure logarithms, published by Messrs. Taylor and Walton 

 (explained in the ' Companion to the Almanac ' for 1841), to which has 

 been added a similar card for sines and tangents. A sliding- rule, which 

 would in all parti compete with these tables in accuracy must have a 

 radius of from 8 to 10 feet, and would be unmanageable. At what 

 length the card begins to be more easily used than the rule we cannot 

 determine, but we should suspect that the former would be preferable 

 to a rule of four feet radius. We have found the rule of 24 inches 

 extremely useful in checking the material figures of more minute cal- 

 culations, particularly when there are many divisions by the same 

 divisor. 



The history of the sliding-rule, had it ever been properly given, 

 would be matter for a few lines of our work, in the way of abbrevia- 

 tion and reference. As it is, we have not only to establish the main 

 points, but also to point out a specimen of the manner in which the 

 account of early English science has been written. Harris's ' Lexicon 

 Technician ' (1710) informs us that sliding-rules ' are very ingeniously 

 contrived and applied by Ounter, Partridge, Cogsluill, Everard, Hunt, 

 and others, who have written particular treatises about their use and 

 application.' Stone's 'Mathematical Dictionary ' (1743) has the same 

 words. Dr. Hutton (' Math. Diet., 1815) informs us that they are 

 variously (not ingeniously) contrived and applied by different authors, 

 particuUirly Quntcr, Partridge, Hunt, Everard, and Cogglesboll. Other 

 writers repeat this sentence in their own ways, and the summing up 

 is this: the recognised history of the sliding-rule consists in the 

 names of five persons ; all our best English authorities are unanimous 

 in stating that these men 'contrived and applied* sliding-rules, either 

 ingeniously or variously ; but to the credit of this century be it spoken, 

 that it was our historian who altered the chronological order, and spelt 

 CoggleahaU's name right : had it not been for the research of Dr. 

 Hutton, it might have been Cogshall to this day. 



We now go on to something more like history. It is generally rtatcd 

 that Guntcr invented the sliding-rule. This is not correct ; Uuntcr 

 neither invented this rule nor wrote about it ; and though he was the 

 first (On He Crouc-itaffc, book i., cap. 6) who used a logarithmic scale, 

 ;. . i n the manner described at the beginning of this article, com- 



: 



passes being used to make the additions and subtractions. Quntcr 'H 

 The maker of this slide has them of ration* lengths up to 24 inches. 



rule is used up to the present time, under that name, in the navy, 

 without any slides. 



The real inventor of the slide was OuuliTBED [Bioo. Div.J, who was 

 also the first writer upon it He was a man who set but little value 

 upon instrumental aids, unless in the hands of those who had pre- 

 viously learned sound principles, which (as we have seen) he himself 

 testifies. In the year 1680 he showed it to his pupil William Forater, 

 who obtained his consent to translate and publish his own description 

 of the instrument, and rules for using it. This was done under the 

 following title : ' The Circles of Proportion and the Horizontal lustra- 

 ni. MI.' London, 1632; followed, in 1633, by an 'Addition, &c.,' with 

 an appendix, having title, ' The Declaration of the two Rulers for Cal- 

 culation.' The following extract from W. Forster's* dedication to Sir 

 Kth.hu Digl.y "ill explain the whole : 



" Being in tho the time of the long vacation 1C30, in the Country, at 

 the house of the Reverend, and my most worthy friend, and Teacher, 

 Mr. William Ocghtred (to whose instruction I owe both my initiation, 

 and whole progru*se in these Sciences), I upon occasion of speech told 

 him of a Ruler of Numbers, Sines, and Tangents, which one had be- 

 spoken to be made (such as is usually called Mr. Gunter's Ruler), ti feet 

 long, to bo used with a payre of beanie compasses. He answered that 

 was a poore invention, and the performance very troublesome : But, 

 said he, seeing you are taken with such rnechanicall waycs of Instru- 

 ments, I will show you what devises I have had by nice these many 

 yeares. And first, bee brought to nice two Rulers of that sort, to be 

 used by applying one to the other, without any compasses : and after 

 that he shewed inee those lines cast into a circle or Ring, with another 

 movcable circle upon it I seeing the great expeditenesse of both 

 those wayes, but especially of the latter, wherein it farre excelleth any 

 other Instrument which hath bin knowne ; told him, I wondered that 

 he could so many yeares conceale such usefull inventions, not onely 

 from the world, but from my selfe, to whom in other parts and mys- 

 teries of Art he had bin so liberal!. He answered, That the true way 

 of Art t is not by Instruments, but by Demonstration : and that it is 

 a preposterous course of vulgar Teachers, to begin with Instruments, 

 and not with the Sciences, and so instead of Artists, to moke their 

 Schollers only doers of tricks, and as it were Juglers : to the despite 

 of Art, losse of precious time, and betraying of willing and industrious 

 wits unto ignorance, and idlenesse. That the use of Instruments is 

 indeed excellent if a man be an Artist : but contemptible, being set 

 and opposed to Art. And lastly, that he meant to commend to me 

 the skill of Instruments, but first he would have me well instructed in 

 the Sciences. He also shewed me many notes, and Rules for the use 

 of those circles, and of his Horizontal! Instrument (which he had pro- 

 jected about 30 yeares before) the most part written in Latine. -Ml 

 which I obtained of him leave to translate into English, and make pub- 

 lique, for the use and benefit of such as were studious, and lovers of 

 these excellent Sciences." 



Oughtred gave his right in the invention (so soon as it was settled to 

 be published) to Elias Allen, a well-known instrument-maker, near 

 St. Clement's Church, in the Strand. In walking to and fro from his 

 shop, he communicated his invention to one Richard Delamain, a 

 mathematical teacher whom he used to assist in his studies. This 

 Delamaiu not only tried to appropriate the invention to himself, but 

 wrote a pamphlet of no small scurrility against Oughtred, which the 

 latter answered in an ' Apologeticall Epistle' fully as vituperative; 

 which epistle was printed at tho end of W. Forster's translation. It 

 contains some quantity of biographical allusion, and must not be for- 

 gotten by a mathematical historian of the tunes. W. Forster's work 

 was republished in 1660, by A. H. (Arthur Haughton, another pupil of 

 Oughtred), with Oughtred's consent, but the dedication and epistle 

 were omitted. 



The next writer whom we can find is Seth Partridge, in a 'IV 

 tiou, &c. of the Double Scale of Proportion,' London, 1685. DM 

 studiously conceals Oughtred's name : the rulers of the latter were 

 separate, and made to keep together in sliding by the hand ; perhaps 

 Partridge considered the invention his own, in right of one ruler 

 sliding between two others kept together by bits of brags. Coggle- 

 shnll's ruler was made in both ways, that is, with the rulers attached 

 and unattached; it appears to have come in at the end of the 17th 

 century. Since that time several works have been written, and 

 various modifications of the ruler proposed. Ward (' Lives of Greshaiu 

 Professors') is incorrect in saying that Wingate carried the sliding rule 

 into France in 1624 : it was Gunter's scale which he introduced there. 

 In fact the slide was little used and little known till the end of the 

 century. Leybourn, himself a fancier of instruments, and an inn 

 (as ho supposed) of the sector, has 30 folio pages of what he calls 

 instrumental arithmetic in his 'Cursus MathematZons' (1690), but not 

 one word of any sliding-rule, though he puts fixed lines of squares and 

 cubes against his line of numbers in his version of (Junior's scale. 



Finding so meagre an account on this matter in publications pro- 

 fessedly mathematical, we did not at first think of having recourse to 

 any others. When we hod finished the preceding however, we thought 



* This man must not be confounded with the Grcsham professor of his 

 name; nothing more than his connection with Ouphtrcd is known of him. 

 Tho cnc whose name is M> much connected with Ounter is Samuel Foster (died 

 1052), Grcihnm professor of astronomy. 



t litre Is the old use of the word art ; we should now say science. [SCIEKCI.] 





