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MACHINES, CALCCLATIN'0. 



MADDER, COLOURING MATTERS 



Tkk MehiM Mibodte UM prinoiplM of all UM ekleuUUng nuohinM 

 yet propoeed. A few word* oooocmiog other contrivances may, bow- 

 everTbe desirable. 



SuoVls arithmetical machine is about 18 Inches in length, 9 in 

 breadth. nd 4 in height. It contains. three rowi of small cylinders, 

 thirteen in the first row, and seven in each of the others ; upon each 

 cylinder are ton numerals, from to 9. Theae cylinders act upon each 

 other by means of small wheels, levers, sliders, and other delicate appa- 

 ratus. The upper surface of the machine presents seven small holes, 

 with moreable plates beneath them, marked by numerals, seven similar 

 holes over the peripheries of seven little vertical wheels, and thirteen 

 number-holes in a distinct row. Each set of seven holes has a traversing 

 movement, but the longer row is immovable. Every one of the twenty- 

 seven holes has ten numerals, from to 9, belonging to it In per 

 fanning any sum, the conditions of the question are arranged on the 

 two smaller rows : and then, by turning a handle, the result makes its 

 at the holes of the larger row. By different modes of 

 the two smaller rows of holes, and of turning the handle, the 

 performs addition, subtraction, multiplication, division, and 

 evolution. It can multiply seven digits by seven, or millions by millions, 

 A very beautiful part of the apparatus u a little bell, which rings when- 

 ever the operator attempt! to perform an impvuibU operation, such as 

 subtracting a larger number from a smaller, or dividing a smaller by a 

 larger ; the machine refuses to work, rings a bell, and stops. 



Colmar's arithmometer is rather larger than Staffel'g machine. It 

 has as many slides, each working in a groove, as there are digits in the 

 quantity which it is capable of calculating; and each groove is num- 

 bered with ten figures, from to 9. There are as many round holes 

 in a brass plate as there are possible places of figures in the result to 

 be produced ; and beneath each hole may appear any one of the ten 

 numerals. The machine U adjusted to any particular problem or sum 

 in addition, subtraction, multiplication, division, or evolution, by 

 moving some among the many slides ; these slides work upon cerb.in 

 wheels and levers underneath, which cause the proper figures for 

 the result to make their appearance at the row of holes in the brass 

 pUte. 



Wertheimer's machine, for the addition and subtraction of numbers 

 and moneys, consists of a box having a metal plate divided into nine 

 indexes, with semicircular notches, under which are placed a series of 

 boles. Numeral* are engraved round the indexes. The semicircular 

 notches are furnished with teeth, with a pointer to insert between 

 them, for the purpose of bringing the notch opposite to any particular 

 figure* 



Baranowski's Ready Reckoner U intended for the calculation of wages, 

 prices, interest, and other sums of money. If it be to calculate the 

 amount of wages at a given rate, the weekly rate, printed on paper, ia 

 brought to view in an opening in a brass plate, by means of a handle ; 

 a shde is withdrawn belonging to the particular number of days for 

 which the calculation is made, another for any extra hours, and another 

 for any odd quarters of an hour ; and the printed figures revealed by 

 the moving of these slides give the sum total of wages. 



Sehott's calculating marhine can perform addition only. Lalannc's 

 calculating-rule is a peculiar apparatus for solving the problems usually 

 worked by the sliding-rule. Dr. Roget's sliding-scale of involution is 

 like the apparatus just noticed, and bean more resemblance to the ordi- 

 nary sliding scale than to a calculating machine. Maurel's calculating 



' 



something like Colmar's, founded mainly on the action of 

 graduated slides. Moth's automaton calculator, and Slovinski's calcu- 

 lating marhine, an two other examples mainly dependent on the same 

 principle. Haurel's calculating machine works, like Colmar's, through 

 the medium of graduated slides. 



The most important calculating machine ever invented (next to 

 Babbage's), and decidedly the most important ever actually finished, 

 u ScbeuU'i. It presents another example of ingenuity ill rewarded. 

 In 1M4, after reading an account of Babbage's machine as at that time 

 proposed. M. SchraU, a technologist at Stockholm, conceived the idea 

 of sntnefhing to the same end on a different principle. Under SCUKCTZ, 

 GCOKOE, and EDWARD, in the BIOURAPUICAL DIVISION of this work, 

 will be found a narrative of the circumstances connected with the 

 invention and the difficulties which attended the construction of this 

 machine, as well as some particulars respecting ite prirciple, and the 

 share taken by Mr. Babbage. the inventor of the first calculating 

 machine, in directing the attention of the scientific men of this country 

 to lU value. The machine was exhibited in London in 1804, and in 

 Paris in 1855 ; and in 18(6 it was sold to the Dudley Observatory, at 

 Albany, in the United States, at a price quite inadequate to the labour 

 and thought bestowed upon it. Mr. Babbage deplored that the 

 machine had not been mured for and by England; he greatly 

 admired it, and attached high value to it* power of computing mathe- 

 matical tabUs. Not only can it do this, but it impresses each result on 

 a piece of lead, from which a clicU cast in type-metal can be obtained, 

 applicable to printing from. The machine, which U about the size of 

 a square pianoforte, calculates to sixteen places of figures, and prints to 

 eejbt. By taking out certain wheels and putting in others, the machine 

 can be readily caused to produce and record iU results in i.d.: 

 in degress, minutes, snd seconds ; in tons, cwte., and Ibs. ; or in any one 

 among a large number of d.flersot modes. When once the machine is 

 set with the conditions of the problem, a handle is turned, and the 



results appear at the rate of 25 figures per minute, not merely calou- 

 iatd and recorded, but actually stamped or impressed upon a plate of 

 lead. Mathematically speaking, this is a di/rmft engine, like Babbage's, 

 and depending on the same general principles, though worked out by 

 means of original details, 



A full and minute description by the inventors of the machinery of 

 this remarkable instrument is given in the specification of the English 

 patent, dated October 17, 1854. 



MACLAURIN'8 THEOKEM. [TAYLOR'S THEOREM.] 



MADDER, COLOURING MATTERS OF. The root of the madder 

 plant [RL-BIA titctanm, in NAT. HIST. Div ] is so extensively used for 

 the preparation of all shades of purple, red, brown, and even black dyes, 

 that in importance to the calico-printer and others, it is second to no 

 other dye-stuff, except perhaps indigo. 



Madder grows in the south of Europe, many parts of the Levant, 

 and is largely cultivated in Holland. It does not contain the colouring 

 matter ready formed, nor does the substance from which the colour 

 is derived reside indiscriminately in all parts of the plant. It is indeed 

 only the ligneous or woody portion of the long fibrous routs of the 

 rubia that are valuable, and hence the various operations that are 

 performed upon them before being sent into commerce. These pre- 

 paratory processes consist iu, first, carefully drying the roots in a stove, 

 then thrashing with a flail, winnowing and sifting away the dust or 

 dried cellular matter, and finally, again drying, and, in nearly all cases, 

 powdering the resulting fibres. 



The ground madder thus prepared is called in France garance, but 

 occasionally it is sent out in the entire state, especially from Turkey 

 and the Levant, and is then called li:ari or aiuari (from >(df, the 

 modem Greek name for madder). 



Madder thus prepared has a reddish appearance, and contains three 

 distinct colouring principles, namely : 1. Alitarix ; 2. Purpurin ; and 

 3. Rabtadn. Of these, alizarin is the one of greatest importance. 

 Madder also contains. 4. Chluroyenin a green, pulverulent species of 

 extractive matter ; 5. Erythro;ym, a ferment ; and 6. Kubian, a body 

 of deep yellow colour, not, however, a colouring principle in the 

 practical sense of the term, but which, by the action of ferments, acids, 

 or alkalies, yields up large quantities of alizarin. 



1. Alizarin (C 2 ,H I0 0, + 6HO) Lizaric acid. This substance, though 

 chiefly resulting" from the decomposition of rubian during the dyeing 

 operations, has nevertheless been shown by Schunk to exist ready formed 

 in dried madder, and has probably been produced from the rubian 

 originally in the plant by the action of a ferment in the drying 

 operations. 



Alizarin was first discovered by Robiquet and Colin. It is identical 

 with Runge's Madder red. It may be extracted directly from the 

 root, but is best obtained from garancin, a substance prepared by 

 acting upon powdered madder, with strong hot sulphuric acid, by 

 which the earthy matter and a large quantity of valueless tissue U 

 rendered soluble, and is removed by well washing the residue with 

 water. The dried, insoluble portion constitutes the garancin ; it is 

 very largely used in print works, and it is from this that alizarin U 

 moat conveniently prepared. The garancin is boiled for some time 

 with a quantity of water, and the colouring matters precipitated from 

 the resulting liquor by sulphuric acid. The precipitate well washed 

 with cold water, dried, and submitted to sublimation, yields beautiful 

 orange coloured needles of alizarin. An impure alizarin was described 

 by Robiquet and Colin, under the name of culorin. 



Alizarin is tasteless and inodorous, neutral to test paper, almost 

 insoluble in cold water, more so in hot water, and freely taken up by 

 alcohol or ether. The alkalies dissolve it, forming a beautiful purple 

 solution, but acids reprecipitate it unchanged. It forms a splendid red 

 lake with alumina, and purple ones with lime, baryta, and oxide of 

 iron. Alizarin is converted into phthalic acid (alizaric acidi by ebul- 

 lition with dilute nitric acid, and since chloroxynaphthalic acid, a body 

 prepared from naphthalin, also yields phthalic acid under the same cir- 

 cumstances, it has been thought, that chloroxynaphthalic acid is simply 

 alizarin with an atom of hydrogen replaced by one of chlorine. Schunk, 

 however, does not think this to be the case, nor has gtrecker himself, 

 who was the first to throw out the hint, been able to replace the 

 chlorine in chloroxynaphthalic acid by hydrogen and thus convert it 

 into alizarin. Were this accomplished, naphthalin would no longer be a 

 waste product as it now is, but become of great value and importance. 



Alizarin plays the principal, and probably the only part, in the pro- 

 duction of madder colours. Schunk has, in fact, after a long courso 

 of experiments, been led to the conclusion, that the final result of 

 dyeing with madder and its preparations is simply the combination of 

 alizarin with the various mordants employed, and that consequently 

 if an economical method of preparing alizarin on a large scale could 

 be discovered, a great gain would result to the arts. 



2. Purpurin was the name given by Robiquet and Colin to the 

 colouring matter that remained dissolved in the alum liquor after the 

 preparation of alizarin. Dr. Debus has called it ojcyluaric add. It 

 dissolves in alkalies with a red colour, quite distinct from the purple 

 of an alkaline solution of alizarin, and moreover the resulting solution 

 decomposes when exposed to the air, which is not the case with a 

 similar solution of alizarin. Professor Stokes, who has examined the 

 optical properties of purpurin, also thinks it quite distinct from 

 alizarin ; nevertheless, these two bodies are shown, by other re-actions, 



