SPINKT. 



SPIKK. 



Relief from pressing occupation!, a nutritious diet, change of air, 

 oold bathing, the preparations of iron and quinine, are the great means 

 that roust be looked to for the cure of the duordered state* of the 

 nervous system. When the painful symptoms arUe from over-exertion 

 of the muscle*, as is often the case, artificial support may be given 

 with advantage to the particular muscle*. Friction over the seat of 

 pain, and the application of stimulants, as turpentine, ammonia, and 

 brandy, in the form of embrocation with oil or glycerine, has been 

 found very beneficial. Where the pain is very acute, or the muscular 

 action excessive, sedatives, as opium, henbane, and belladonna, may be 

 given internally and applied externally. 



(Lay cock On Ike Servant Ditnua of Women ; Bennett, Tkt Pri*cipltt 

 and Practice of Medicine; Inman, The Plunomena of Spinal Irrita- 

 tion,) 



s I '1 NET, a musical instrument of the harpsichord kind, but differing 

 in shape and power, formerly much in use, though now entirely 

 superseded by the piano-forte. The fyinet had but one string to each 

 note, which was struck by a quilled jack, the latter acted on in the 

 usual manner by a key. The tone was, of course, comparatively weak, 

 but pleasing, and as the instrument was small in dimensions and cheap 

 in price, it answered the purpose of those who did not find it con 

 to purchase a harpsichord. The outline of its ordinary form was 

 nearly that of a harp laid horizontally, supposing the clavier, or key- 

 board, to be placed on the outside of the trunk, or sounding port, of 

 the last-named instrument. 



SPINNING. There are two entirely distinct manufacturing opera- 

 tions to which this name is given the one relating to animal and 

 vegetable fibres, and the other to certain soft metals. 



l-'il'i-e !<i-i iming. This kind of spinning consists in forming a flexible 

 cylinder of greater or lees diameter, and of indeterminate length, out 

 of vegetable or animal fibres, arranged as equally as possible alongside 

 and at the ends of each other, so that, when twisted together, they 

 may form an uniform continuous thread. The primitive modes of 

 spinning by the spindle and distaff, and by the spinning-wheel, which 

 are still extensively practised in the East, and not entirely superseded 

 in some remote districts of Scotland, only enable the spinner to produce 

 a single thread ; but with the almost automatic spinning-machinery 

 which has been called into existence by the cotton manufacture, one 

 individual may produce nearly two thousand threads at the same time. 

 The history of the series of inventions by which this result has been 

 gradually attained has been already given under COTTON MAM 'i AC- 

 TUB*; together with wood-cuts and descriptions of some of the 

 chief machines. The spinning of flax, silk, and wool partake of the 

 same general character as that of cotton ; so far as they differ they will 

 be found noticed under LINEN MANUFACTURE ; SILK MANUFACTURE ; 

 and WOOLLEX A so WOIISTED MANUFACTriu:. 



Metal Spinning. This is a peculiar branch of Birmingham and 

 Sheffield manufacture, in which articles of use and ornament are pro- 

 duced without forging, casting, stamping, or cutting, by bringing into 

 play the ductility of the metal. The metal employed is chiefly one or 

 other of the soft mixed white metals, such as Britannia metal. Tea- 

 pots, and such-like articles, are shaped in this metal almost entirely by 

 the process of spinning. There is first prepared a wooden mould, of 

 the exact size and shape ; and this mould is fixed upon a lathe. Then a 

 circular piece of the thin sheet metal is taken and fixed temporarily 

 in contact with the bottom or flat surface of the lathe. Burnishers 

 and smooth tools are then pressed cautiously against the metal, while 

 the mould is rotating, and made to conform to all its curvatures 

 stretching out a little to cover the convexities, and compressing a little 

 to cover the concavities. Tlie ductility of the metal alone enables it 

 to do this ; the bending takes place gradually, so as to enable the 

 particles of the metal to accommodate themselves to their altered 

 position. Teapots, plated candlesticks, dish-covers, bell mouths of 

 musical instruments, &c., are made by a succession of processes of 

 which this is the chief; and a large quantity of cheap Birmingham 

 jewellery is worked into form in a similar way. 



e SPIRAL, a name belonging properly to curves which wind round a 

 point in successive convolutions. The easiest mode of representing 

 such curves algebraically is by means of polar CooitmNAi -i -,- : hence, in 

 many of the older English works, any curve referred to such coordi- 

 nates is said to be considered as a spiral. Thus we have the circle 

 considered as a spiral ; the- ellipse considered as a spiral, and so on. 

 The rest of this article is intended only for those who have some 

 knowledge of the mathematical part of the subject. 



1 1 < be the radius vector of a curve, 8 the angle which it makes with 

 a given line, and r=$> (9) the equation of the curve, it i obvious that 

 if 4>0 be a common trigonometrical function of sin 9, cos 9, &c., the 

 curve will not have an unlimited number of convolutions. The whole 

 of tho curve from =2 to fl=4, will be merely a repetition .,f that 

 from 0=0 to 9='2r. Thus, r = sin9is tho equation of a circle of a 

 unit diameter, tangent at the origin to the line from which r sets out ; 

 the fifteenth half-revolution of the radius vector is only the fifteenth 

 description of this circle. It is then only when the angle 9 occurs 

 indeiwndeutly of trigonometrical quantities, that any curve i 

 aented which can properly be called a spiral. Thus, the spiral of 

 Archimedes, or Conon, of which the equation is r=a9, has a c 

 tion in which r changes from to 2wo, while changes from to 2 ; 

 another, in which r changes from 2a to 4iro, while 9 changes 



from 2* to 4, and so on. The principal spirals to which ii 

 names have been given, 



1. Spiral of Archimedes . . . 



2. Reciprocal Spiral . . . . 



3. Lituus ...... 



4. Logarithmic or Equiangular Spiral 



r=9 

 r = a 

 i"0 - a . 



r = 06 



with some others of less note. The figures of these spirals are given 

 in all books on the application of algebra to geometry. 



It has hitherto been universal to consider spirals in a manner whieh 

 has deprived these curves of half their convolutions ; this has been 

 done by refusing to entertain negative values of tin- ladiu*. For 

 example, in the spiral of Archimedes r=a9,o beinK a positive quantity, 

 the curve is supposed to have no convolutions when 9 i* negn- 

 when the radius revolves negatively. The consequence 

 curve begins abruptly at tho origin. It would l>e a matter of little 

 importance to insist on the existence of the additional branches which 

 belong to the negative radii, if it were not that the other mode of 

 representing curves, by means of rectangular coordin 

 the additional branches : so that, if we refuse to receive the latter as 

 coming from the polar equation, we have only the alternative of sup- 

 posing that the mere transformation of coordinates destroys a 

 the curve. In the spiral of Archimedes, for example, the rectangular 

 and polar equations are 



y = u- tan 



r = off. 



The first, treated in Uie usual way, gives a curve of which there i< 



one succession of convolutions beginning with o A B c r>, and another 

 beginning with o A 6 c rf. But the second equation, which is only the 

 first in a different form, does not yield any of the second set of con- 

 volutions, unless by means of the negative values of the radius vector 

 answering to negative values of 8. 



The manner in which the negative value of r is to be treated, is as 

 follows: Every line passing through the origin, as POQ, makes two 

 angles with the } lositive side of the axis of x, POD, less than a right angle in 

 1 he diagram, and Q o D, between two and three right angles : the second 

 of which may be considered as the common angle Q o D, taken nega- 

 tively. The bounding directions of these angles are different, o p and 

 o Q : the rule is, whichever angle the straight line Q o P is supposed to 

 make with c. n, let the bounding direction of that angle be the positive 

 direction, and the other direction negative. Thus, \\heii POD is the 

 angle, o p is positive and o Q negative : when Q o D is the angle, o Q is 

 positive and o P negative. In this manner it will be found that the 

 first three of the four spirals above enumerated have never been com- 

 pletely drawn. There is little need to insist much on the necessity of 

 the extension here described : one more instance may suttice. Let the 

 reader trace the curve whose equation is 



2y- = 1 - ix - 2.i ! VI &c, 



d> i-hed from r = l 2 cos 9. The rectangular equation gives a curve 

 of two loops, of which the polar equation will only yield one. un- 

 less negative values of r be employed, in the manner above 

 described. Nevertheless, if the process had been inverted, and the 

 polar equation deduced from the rectangular, we should have found 

 r= +12 cos 9 for the former ; and the effect of the double sign is 

 that~the positive values of r only, in the two equations r . 1 2 cos 9, 

 and r = 1 2 cos 9, will give the complete curve deduced from the 

 rectangillar equation. As far as this instance goes, it might seem as if 

 the complete polar equation, as reduced from the rectangular 1 , would 

 give the whole curve by means of p.-.-itive radii ; thouuh at the .-ami- 

 time a single instance hardly proves anything. Hut even granting 

 that the passage from the rectangular to the polar equation will 

 give forms enough to the hitter to trace the whole curve from positive 

 radii, it remains indisputable that the other transition, from the 

 polar to the rectangular, requires the negative radii to be taken into 

 account. 



SPIKAL OF ARCHIMEli: AL.] 



SI'IKE (in (icruian, Spitzf, or I'l : in French, 7-'/<'</n I, in 



Gothic architecture, is used to designate the I mass 



erected on a tower by way "f finish and ornament. The origin of the 



