017 



SLIDE RULE. 



SLIP. 



CIS 



oi consulting the ' Biographia Britannica,' and there we found, in the 

 middle of a very full life of Oughtred, the whole account of the 

 invention of the sliding-rule, exactly as above, and from the same 

 authorities. On looking at Dr. Hutton's account in the Dictionary, 

 we perceive that he has either used this memoir or some copy of it ; 

 but without giving any information on the subject of the present 

 article. 



We shall conclude this article by some account of a new species 

 of sliding-rule, invented by Dr. Roget (' Phil. Trans.' for 1815), which 

 would be very useful in the hands of writers on statistics, and would 

 sometimes save much trouble to the mathematician. The slide con- 

 tains a common logarithmic line of two radii, each 10 inches in length. 

 The fixed ruler has not logarithms, but logarithms of logarithms 

 denoted by its spaces. For instance, reckoning from 10 (remembering 

 that log log 10 = 0), the space from 10 to 100 is log log 100, or fog 2, 

 :ue space as from 1 to 2 on the slide. And since log log .< is 

 ve or negative, according as x is greater or less than 10, we 

 have the loyoliMjarilhms laid down on the left for numbers less than 

 10, and on the right for numbers greater. This instrument is 

 constructed by Mr. Hooker, and in this manner : 10 is on the 

 middle of the upper ruler, which ends on the right at 10', or 

 ten thousand millions; and oil the left at 1'25. At the ex- 

 treme right of the lower ruler we find 1'25 again, from which we 

 recede to 1'0025 on the extreme left. The upper and lower rulers 

 are so adjusted that from the end of one to the beginning of the 

 other it is exactly two radii, so that a setting on the upper ruler 

 applies also to the lower, but it may be necessary first to slip the slide 

 a whole radius forwards or backwards, in the manner described in the 

 preceding part of the article. And here again the meaning of the 

 reading qn the slide must frequently be determined by common sense 

 applied to the problem. 



When 1 on the slide is placed opposite to a on the ruler, we 

 have 4 on the slide opposite to a* on the ruler. Or using the pre- 

 ceding rotation 



Rule a o' 

 Slide 1 6 



a %- 

 6 1 



The approximations of this rule are equally easy whether applied 

 to fractional or integer exponents, and Dr. lioget justly observes 

 that it gives a much better idea of the rapid increase of powers 

 than simple reflexion. It is so little known even to mathematicians, 

 that we put down some of its results as specimens of its powers. 

 Set 1 on the slide opposite to 3'14 on the rule, and we find for 

 the approximate powers of this number by simple inspection 9*85, 31, 

 97, 300, 060, 3000, 9500, 29,500, 93,000, 4c. The square root is 1772, 

 the cube root 1-463, the fourth root 1-331, the fifth root 1'257. We 

 must now change the slide, aa above directed, so as to put it in con- 

 nection with the lower scale, and the proceeding roots are 1-215, 1-178, 

 &c. All questions of increase of money, population, ic., are in this 

 manner reduced to simple inspection, and very easy trial gives that 

 approximate solution of exponential equations which the mathema- 

 tician must find before he applies his more extensive methods. 

 Thus, to form the table of logarithms in SCALE the base of which 

 - : Set 12 on the slide opposite to 2 on the ruler, and the 

 table is ready, as far as the instrument will give it. Thus, oppo- 

 site to 3, 4, 5, 4c., we find 19'0, 21, 27'9, 31-0, 337, 38'0, &c., 

 almost exactly as in the table cited. It is also worth notice that each 

 division of the upper fixed ruler answers to the hundredth power of 

 the division directly beneath it on the lower fixed ruler. Thus, 

 wishing to know what effect would be produced in 100 years upon 

 a population which increases 3'18 per cent., we set unity to 

 1-OulG on the lower scale, and find at once 30-025 on the upper 

 ruler, being the number by which the present population must be 

 multiplied. 



The late Mr. Woollgar (to whom we were indebted for much infor- 

 mation in this article, and who made a particular study of the slid- 

 ing-rule) carried to a considerable extent the principle of making the 

 slide or the rule (no matter which) bear, not the logarithms of the 

 number* marked on its graduation, but those of the values of a func- 

 tion of those numbers J(' Mechanics' Magazine,' No. 849, vol. xxxii.) 

 Let a slide be so graduated that the interval from a given point to the 

 graduation f represents log ifac. When x is then ascertained (by the 

 common scale, if necessary), the formula a<t>x U immediately deduced 

 from the common scale and the new slide. Nor need there be a new 

 slide : for any scale being laid down in the groove, the common slide, 

 by having its end made to coincide with one or another division of the 

 scale in the groove, may be rendered capable of answering the pur- 

 pose of a new slide. 



We long since obtained from Paris a circular logarithmic scale in 

 brass, altogether resembling the one figured and described in the pre- 

 ceding part of this article, with the addition only of a clamping 

 screw. This instrument, the scale of which is 4J inches in diameter, 

 \ so well divided that it will stand tests which the wooden rules 

 would not bear without showing the error of the divisions. But here arise 

 disadvantages which we had not contemplated. In the first place, no 

 subdivision can be well made or read by estimation, unless the part of the 

 scale on which it comes i* uppermost or undermost, which requires a 



continual and wearisome turning of the instrument. In the next 

 place, to make the best use of it, and bring out all its power, requires 

 (we should rather say renders worth while) such care in setting and 

 reading, as, unless a microscope and tangent screw were used, makes 

 the employment of the four-figure logarithm card both shorter and 

 less toilsome. For rough purposes, then, a wooden rule is as good ; 

 for more exact ones, the card is better. We made a fair trial of both 

 on e tables in SOLAR SYSTEM, and are perfectly satisfied that though 

 the French brass arithmometer did, with great care, bring out the 

 results required, the four-figure card did the work more easily. But, 

 bad we wished to abandon two or three units in the last places of 

 figures, there would then have been no doubt that the instrument 

 would have been the easier of the two : but then a straight wooden 

 rule of the same radius would have done quite as well, and been more 

 convenient still. (' Mechanics' Magazine,' No. 949.) 



SLIDING SCALE. [SLIDE or SLIDING RULE.] 



SLING, an instrument with which stones or other missiles may be 

 thrown to a great distance. In its simplest form the sling consists of 

 a thong of leather, or a piece of cord or some woven fabric, both ends 

 of which are held in the hand of the slinger. The stone or missile is 

 placed in the fold or double of the thong, which is made wide at that 

 part, and sometimes furnished with a slit or socket for the purpose of 

 holding it ; and the sling is then whirled round to gain an impetus. 

 When a sufficient degree of centrifugal force is thus generated, the 

 slinger allows one end of the thong to escape, and the stone, being 

 thereby released, flies off with considerable velocity. In the hands of 

 an expert slinger, this instrument may be made to project missiles to a 

 great distance, and with surprising accuracy. 



The simplicity and portability of the sling, and the facility with 

 which supplies of ammunition for it might be obtained, led to its 

 extensive use among the ancients as a weapon of war, as well as for 

 other purposes. Its common use among the Jews is intimated by 

 several passages of scripture. Several ancient paintings represent the 

 use of the sling at an early period by the Egyptians. Some of these 

 are given by Wilkinson. In the Greek and lloman armies the light 

 troops consisted in great part of slingers, who were called ffQfvSovyTcu, 

 or funditorts, from aipfMtni, and/Knrfa, the Greek and Latin names of 

 the weapon. The Carduchi, according to Xenophon, annoyed the 

 retreating army of the Ten Thousand by their powerful slings. 

 (' Anab.', iv. 1, 4c.) There are no slingers mentioned in Homer ; and 

 the word which usually means sling (fffyevbiirri) occurs only once 

 (' Iliad,' book xiii., line 599), and then not in the sense of sling, but in 

 the primary sense of the word, which means a broad band or bandage. 

 This passage has sometimes been strangely misunderstood. The sling 

 is not mentioned by Herodotus ; and it is an error to assign the use of 

 it to the Persians, for which there appears no evidence but a loose 

 expression in Diodorus (xviii. 51), where he speaks of ' Persians, 

 bowmen and slingers, five hundred." The natives of the Balearic 

 Islands attained the highest reputation for their skill in its manage- 

 ment ; which is attributed to their custom of teaching their children, 

 while very young, to wield it, and forbidding them, it is said, to taste 

 their food until they had dislodged it from a post or beam by means of 

 a sling. Besides stones, leaden plummets, cast in moulds, were used 

 as projectiles for the sling. These, which were called glandcs, or 

 lw\v0$iSfs, were of an elongated spheroidal form ; somewhat resembling 

 that of olives or acorns. They have been often discovered in various 

 parts of Greece, and frequently bear on one side a figure of a thunder- 

 bolt, and on the other side either the word AESAI (take this), the 

 name of their owner, or some other inscription or device. Some of 

 these were of considerable size, weighing as much as an Attic pound, 

 or 100 drachma;. Fireballs also have been thrown by slings. Some of 

 the slings used by the ancients were managed by more than one cord ; 

 one, two, or three being used, according to the size of the missiles to 

 be thrown. 



The sling was long used in England. The Saxons certainly used it, 

 and seem to have been skilful in ita management. Besides the 

 ordinary sling, they used one attached to a staff or truncheon three or 

 four feet long, wielded with both hands. This kind of sling, with 

 which large stones were thrown, appears to have been used principally 

 in sieges and in naval warfare. It is represented in an old drawing, 

 supposed to be by Matthew Paris. Slingers formed a part also of the 

 Anglo-Norman soldiery ; and the sling had not fallen into disuse as a 

 military weapon at the commencement of the 15th century The use 

 of the sling may now be considered obsolete in this country as an 

 offensive weapon. 



(Wilkinson's Manners and Custom* of the Ancient Egyptians, first 

 series, vol. i. ; Strutt's Sports and Pastimes.) 



SLIP, Earthwork. When in an embankment, or cutting, the 

 materials move laterally in consequence of some dynamical action, they 

 are said to slip, and they do so occasionally under circumstances which 

 can only be overcome with great difficulty, and at great expense. 

 Slips occur either when heavy loads are placed on incoherent materials, 

 which under such circumstances are simply displaced ; or they occur 

 when the earth is of such a nature as to absorb so much water as to 

 become a semi-fluid mud ; or when there are intercalated between 

 more impermeable strata beds of sand, or other open materials suscep- 

 tible of being removed. The former of these sources of danger can 

 easily be avoided by carrying the foundations of the intended load to 



