13 



TALMUD. 



TANGENT. 



Greek aymbolum (aun&oKov') was in some cases a species of tally, which 

 was used between contracting parties ; being broken in two, and one- 

 half given to each. Upon tablets of wood called axones the Athenians 

 inscribed the laws of Solon ; and the ancient Britons used to cut their 

 alphabet with a knife upon a stick, which, thus inscribed, was called 

 Coelbren y Beirdd, " the billet of signs of the bards," or the Bardic 

 alphabet. These sticks were commonly squared, but were sometimes 

 three-sided ; each side, in either case, containing one line of writing. 

 Another illustration, of later date, is the clog-almanac, described by 

 Dr. Plot, in 1086, as then common in Staffordshire. Such calendars, 



il. d. i. i. d. s. d. d. d. 



i i j i i i i i e 6 



s. d. d. d. 



i 6 i i; 



which had the various days marked by notches of different forms and 

 sizes, were sometimes made small enough to carry in the pocket, and 

 sometimes larger, for hanging up in the house. Similar calendars are 

 said to have been formerly used in Sweden. Perhaps the most curious 

 of these tallies is the Saxon Reive-Pole, which, down to a recent period, 

 was used in the Isle of Portland for collecting the yearly rent paid to 

 the crown as lord of the manor. This rent, which amounts to 141. Us. 3rf., 

 is collected by the reive, or steward, every Michaelmas ; the sum which 

 each person has to pay being scored upon a squared pole, a portion of 

 which is represented in the subjoined cut, with figures to mark the 

 . d. d. d. d. d. d. s. d. d. d. d. d. d. d. 



1 1 Jii 1 i 6 111 1 1 1 1 i i 1 1 1 1 J J 



~ 



Fig. 1. 



111111 



. . s. d. i. d. d. d. d. A. d. d. i. s. t. 3. 



Ill JiJ 6 J 1 (i 1 1 J 6111$ 1 1 1 1 1 



Saxon Reire-Pole used in the Isle of Portland. 



amount indicated by each notch. " The black circle at the top denotes 

 the pariah of Southwell, and that side of the pole contains the account 

 of the tax paid by the parishioners ; each person's account being 

 divided from that of his neighbour by the circular indentations between 

 each. In the present instance the first pays 24</., the second is. 2d., 



the next one farthing, and so on." The other side of the pole which is 

 represented in the cut is appropriated to the parish of Wakem, of 

 which the cross within a circle is the distinctive mark. 



The tallies used in the Exchequer (one of which is represented by 

 fy. 2) answered the purpose of receipts as well as simple records of 



Fig. 3. 



Exchequer Tally. 



matters of account. They consisted of squared rods of hazel or other 

 wood, upon one side of which was marked, by notches, the sum for 

 which the tally was an acknowledgment ; one kind of notch standing 

 for lOOCtf., another for lOOi, another for 201., and others for 20., Is., 

 Ac. On two other sides of the tally, opposite to each other, the 

 amount of the sum, the name of the payer, and the date of the trans- 

 action, were written by an officer called the writer of the tallies; and, 

 after thin was done, the stick was cleft longitudinally in such a manner 

 that each piece retained one of the written sides, and one-half of every 

 notch cut in the tally. One piece was then delivered to the person 

 who had paid in the money, for which it was a receipt or acquittance, 

 whilt; the other was preserved in the Exchequer. Madoz observes, 

 reflecting these*rude and primitive records, " The use of them was 

 very ancient ; coeval, for aught I know, with the Exchequer itself in 

 England." They were finally discontinued at the remodelling of the 

 Exchequer in 1834 ; and it is worthy of recollection that the fire by 

 which the Houses of Parliament were destroyed was supposed to have 

 originated in the over-heating of the Hues in which the discarded tallies 

 were being burnt. Clumsy as the contrivance may appear, tallies were 

 effectual in the prevention of forgery, since no ingenuity could produce 

 a false tally which should perfectly correspond with the counter-tally 

 preserved at the Exchequer ; and no alteration of the sum expressed 

 notches and the inscription could pass undetected when the two 

 parts of the stick were fitted together. The officers of the Exchequer, 

 >nly called tellers (talliers), as well as several other functionaries, 

 derived their name from the word tally. 



Tnlli/ Trade. The word tally has come to mean a counterpart, 

 although no cutting of a wooden tally is necessary. Thus, in the 

 tally-drapers' trade carried on at the present time in various parts of 

 tli^ kingdom, there are 10,000 or 12,000 persons employed in the dis- 

 :.>nof clothing or drapery which has cost them 7,000,OOOJ. or 

 8,000,0007. annually, and which is re-sold by them on the tally system. 

 Tliry receive weekly payments from their cxiatomers ; and these pay- 

 ments are recorded on a tally and a counter-tally ; these are books, one 

 of which is kept by the buyer and the other by the seller. Here the 

 tally is a record of payments, as in the olden days, but maintained in 

 a different form. There are tally-shops, also, where weekly payments 

 are taken for goods bought ; these differ from the tally-drapery trade 

 cliieUy in this that in the latter the goods are taken round by^the 

 tally-men, who keep no shops. 



TALMUD. [HEBREW LANGUAGE.] 



TAMARINDS, Medical Properties of. Of the two varieties of the 

 only species of this genus, the fruit is much larger in the East Indian 

 than the West Indian. The shell being removed, there remains the 

 flat square hard seeds, imbedded in a pulp, with membranous fibres 

 running through it. In the East Indies the pulp is dried, either in the 

 sun, and this is used for home consumption, or with salt added, and 

 in copper ovens, which kind is sent to Europe. (Crawfurd's 

 ' Indian Archipelago.') This sort, called natural tamarinds, is much 

 darker and drier than the West Indian, which are called prepared 



taina 



The We.-t Indian tamarinds reach maturity in June, July, and 

 August, when they are collected, and the shell being removed, they are 



put into jars, either with layers of sugar put between them, or boiling 

 syrup poured over them, which penetrates to the bottom. Prepared 

 tamarinds, therefore, contain much more saccharine matter than 

 the others. According to Vauquelin, prepared tamarinds contain per 

 cent, citric acid 9'40, tartaric acid 1'55, malic acid 0'45, bitartrate of 

 potash 3'25, sugar 12'5, gum 47, vegetable jelly (pecten) 6'25, paren- 

 chyma 34'35, water 27'55. This prepared pulp has a pleasant astrin- 

 gent taste, with a somewhat vinous odour. 



It presents an example of one of those natural combinations of 

 gummy, saccharine, and acid principles which are of such great utility 

 in hot climates. It is used not only in India, but in Africa, as a 

 cooling article of food, and the travellers across the deserts carry it 

 with them to quench their thirst. In Nubia it is allowed to stand in 

 the sun till a kind of fermentation takes place : it is then formed into 

 cakes, one of which dissolved in water forms a refreshing drink. In 

 India a kind of sherbet is made with it, and by the addition of sugar it 

 becomes a source whence vinegar is readily obtained. In the fevers and 

 bilious complaints, and even dysenteries of those climates, it proves 

 highly serviceable ; in small quantity it 'acts as an astringent, but in 

 larger it proves laxative. Boiling water poured over tamarinds yields 

 a drink which is very grateful in the inflammatory complaints of our 

 own country, particularly in the bilious fevers of autumn. An agree- 

 able whey may be made with it, by boiling two ounces of tamarind- 

 pulp with two pints of milk. Tamarinds may advantageously be added 

 to curries, which should always have a vegetable acid as an ingredient. 

 Tamarinds are frequently given along with senna, but they are said to 

 lessen its purgative property. They form an ingredient in the confeclio 

 teniuf and confectio cassia. 



In times of scarcity in India the seeds are eaten, being first toasted 

 and then soaked for a few hours in water, when the dark skin comes 

 easily off; they are then boiled or dried, and taste like common field- 



TANACETIN. A bitter and crystallisable substance found in the 

 flowers of the tansy (Tanacetum i-ulgare). 



TANGENT. In the article CONTACT we have given the first notion 

 on this subject, which we now resume in a somewhat more general 

 manner, annexing the usual details of formula;, but without proof. 



It is usual to apply the word tangent to the tangent straight line 

 only, on which see DIRECTION : generalising the definition, it will be 

 as follows : Of all curves of a given species, or contained under one 

 equation, that one (B) is the tangent to a given curve (A) at a given 

 poult, which passes through that given point, and is nearest to the 

 curve (A) : meaning that no curve of the given species can pass through 

 the given point, so as to pass between (B) and (A), immediately after 

 leaving the point at which the two latter intersect. 



To ascertain the degree of contact of two curves which meet in a 

 point, proceed as follows. Let y=tyx and y tyx be the equations of 

 the curves, and a the abscissa at the point of contact ; so that $a = <l/a. 

 At the point whose abscissa is a + h, the difference of the ordinates of 

 the curves is, by Taylor's theorem, 



