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to unity , and in the identity of its series of bisections , when started from the different recurring points . Beginning at 8 , we have 4 , 2 , 1 , ^ , &c . ; but 10 soon brings in . fractions—10 v 5 , 2 % , l-i , - £ , and the series passes over unity altogether , though it is the base of all systems . The fourth of a shilling , of i eightpeace would be twopence , and . not twopence ; halfpenny , as in a decimal coinage ; and the eighth would be a penny , and not a . penny farthing . The same advantage attends all higher numbers *
Again : 64 , which in form and importance would stand in the place of 100 in our present notation , divides into 32 , 16 , 8 , 4 , 2 r 1 , without a fraction—the same series as before —only beginning from a higher point ; but 100 gives 50 , 25 , \ 2 \ , 6 ± , 3 £ , 1 ^ , %% , &c ., a series everywhere encumbered with fractions , different from that which : starts from 10 , and passing over unity again , but at a new distance from it . So also 512 , which would take the place and figures of our present 1000 , bisects to the same effect again—256 , 128 , 64 , 32 , 16 , &c—while 1000 gives 500 , 230 , 125 , " 62 £ , 31 ^ , 15 f , 7 * f , 3 ff , lf ^ iff , &c . —still a different series—and so on .
Any preference , however , for the octenary system on this ground , must depend on the comparative frequency with which we use halves , quarters , eighths , &c . rather than : other subdivisions . If we divided by 3 oftener than by 2 , it would be more convenient to use 9 for the recurring number than either 8 or 10 . There are however but few advantages in 10 , since it divides without fractions only by 2 and 5 . There is another advantage in 8 , which is not so obvious , nor indeed would it so often come into play . Sixty-four is both a square , that of 8 , and a cube , that of 4 ; from which it follows that all numbers of the moderate
extent most frequently occurring in practice would have their cube and square roots extracted approximately with a facility the existing , system does not afford . Divide the number hy 64 : the square root of the quotient ( known almost on inspection ) , multiplied by 8 gives the square root of the original number ; and the cube root of the same quotient multiplied by 4 gives the cube root of that original number . Thus 273 divided by 64 gives 4 * 26 , say 4 £ , whose square root is roughly 2- ^ , which , multiplied by 8 , gives 16 ^ for the square root of 273 , true in the first decimal ; and for the cube
root , 1-6 multiplied by 4 gives 6 * 4 , true in the same degree . The operation would really be much more simple than it here appears ; for in the notation of the octenary system the division by 64 would be done by merely pointing off the two last figures , and all the requisite numbers for use on inspection would not be nearly so many as those of our present multiplication table . By these means approximate results could always be obtained for common purposes with very little trouble ——an advantage the decenary system does not afford to nearly the same degree—for while no doubt 10 is the square root of 100 , the cube root is 4 with a tail of decimals .
We presume , however , that it is uselesB to say anything of these or other advantages of the ootenary scale : for it would seem that men of all races have counted on their thumbs Hindoos , Arabs , Komans , Celts , Saxons , Barbarian , Scythian , Greek , and Jew , all have the decimal or semi-decimal ay stem . Cuabxes XII . of Sweden , indeed , is said to have intended a reform in this universal mistake , and it was a project worthy of his iron will . Rut will , ! however iron , is not everything in influencing mankind ; and Chahuss ' s success "would hardly have been equal to that to bo won . by * the-amenities of cheerful perauoskm , and the . example of , successful use .
Taking it for granted that we have not the courage or the perseverance ^ requisite for changing the practice of the whole , world in this apparently simple matter , we sit down with the belief that the decenary system will hold . its ground . amongst us until a period of time far beyond our present provisions . But then , let us . at least be- reasonable in . using , it . "We are going to reform the : system of our money to suit : that of our arithmetic : but if we . go so far we ought to go farther , or our
money will halt and stumble with our weights and measures . The work is only half done if , while we make one factor decimal , we leave the other in the state of 16 ths , 8 fchs ,. 3 rds , &c . &e . Try 71 b . lloz . by 6 £ , and the result , a little over 4 shillings , is come at only by five or six lines of figures , and everi then with tolerable accuracy only by the help of decimals . The same- quantity very nearly would have been expressed by 7 ' 7 ths , and the money by G' 25 ; the result , 4 . 8 ' 1 pence , is obtained in two or at : most three lines . The
same contrast in . favour of decimals , throughout i at ally occurs perpetually in the detail of daily transactions . The contemplated reform then , we trust , will be completed by making the foot , the pound avoirdupois ,-and the gallon , the units of our weights and measureSj to be used decimally both upwards and downwards . One hundredth of a foot , or 001 , would give a little less than an eighth of an inch .. ; 10 , 000 feet , something less than 2 miles .
The ten-thousandth of a pound avoirdupois , or 00001 , expresses -J ~ £ of a grain ; and 2000 pounds -nearly a ton . The gallon requires no illustration . These figures show that our most common , popular , and best-ascertained measures , supply units which admit of convenient—expression for all quantities , both small and great , with very little aid from , other terms .
It is true that with this system we have not a complete and scientific connexion amongst our weights and measures like that of the French , in which the unit-basis of the weights is derived from that of the unit-basis measure of water : but we should have that identity of division which affords by far the greater part of the advantage . In deducing the weight of substances from their bulks , through their specific gravities , the French system affords that facility by design , which we get only by the accident of a cubic foot of water weighing about 1000 ounces . We shall lose this
accidental coincidence if we part with the ouace ; but we shall gain much more in other ways ; and a second column to our tables will at once repair even this small loss . The value of the proposed change will much depend on its completeness . If our money only is made to conform to our arithmetic we shall scarcely gain enough to compensate us for the disturbance of our habits : if we
carry the reform into every kind of quantity we use , we shall soon forget the inconvenience of the change in the magnitude and frequency of its advantages . If we had courage and patience enough to adopt the octenary system in arithmetic , money , weights , and measures , we should probably be followed in time by all other civilised nations . But in such a course there is this as well as
other difficulties : a government may decree weights and measures , but the people will make an , arithmetic for themselves ;—tho government in this as in everything els © has to take for granted in fundamental matters what the people spontaneously do for them > selves . Whether then by defect of courage , or by tho circumatancea of the case , we are bound to the decenary Byptemy , which men have ovory where adopted ; and . beings bound to it , let us have it , complete *;
THE CHURCH AND FREE WORSHIP . As , an Englishman you would certainly say , that in this free ,, religious ,- ; Protestant , ri ghtof-private-judgment . country 5 no kind of obstacles would . be placed in the waj of public religious , worship . You would say , we pride ourselves on the number of our churches , ou the ; number of our : chapels , on one gregarious religion . We think it a good thing—and a thing to be encouraged—public worship
and ouj ? Exeter-Hall Jjebbmiahs leading the way , we all weep when some sturdil y-statistical Horace Mann- shouts aloud " Give ear , O Protestant England , ! there are five millions who attend no place of worship at all . " W hen this is the case , and we turn up our eyes and mourn over it , like hypocrites as we are some of us , it never could be supposed that there is actually an < Act of Parliament prohibiting unlicensed public worship !
But it is so . People in England pray publicly by permission , confess their sins by permission ; they are authorised to do it , and must not do it unauthorised . Tavern ^ pawnshops , and churches all alike exist by virtue of tickets of leave from the State . Such is the law . By an act of George III ., any person assembling above twenty persons over and above his servants in any house not registered , for purposes of public worshipan elastic phrase that applies to the singing of a hymn as well as to the celebration of the whole service—is liable to a fine of 202 . for every offence . What is the consequence ? Thousands of persons , from the peer , nay , from the minister of State to the
labourer and the City missionary , break the law every week , almost every day . "While some consent , while to some it is convenient , to register their place of worship , in thousands of cases it is neither agreeable nor convenient . For instance : there is Sir George Gbet—he does not like to register his residence as a place of public worship , yet he violates the law every Sunday we are told on high authority . There is Lord
Panmure ; he does the same . Nay , when the Queen was present at the opening of the Exhibition by prayer in 1851 , her Majesty asr sisted at the infraction of this law , so natural to a free religious people . Seeing this , feeling for his ragged schools , and city missions , and " mother meetings , " and complicated benevolent apparatus for saving the souls of the poor and benighted wayfarers of life , my Lord Shaftesbuim comes down to Parlun
ment and asks the House , of Lords , and especially the bench of Bishops , to repeal the prohibitive and penal clauses of the Conventicle Act ; in other words , to establish for tho British people what it baa not got—the liborty of praying in concert . He did not contemplate opposition—short-sighted man ! Ho oxpected , no doubt , that every trues Protestant and sincere Christian would eagerly embrace , if not him , at least his proposal . Yaiu expectation ; how can , how dare , a divinely-instituted Church , with divinely-appointed Bishops , claiming to bo the National Church , permit other worship than that ordained in its di « vinely-conatituted rubrics , without confessing
a weakness incompatible with its pretensions , and displaying a greater love for tho purple and line linen than tho gospel of salvation which it assumes to monopolize ? Jlowdares , wo say , a State Church consent to the liberty of praying ? It Aaxo-not . Every now aud then comes up a question which is as a test applied to liliia Hinguixtt mechanism of property and religion , cullett the Church of England : tests which it cannot bear with safety . Liberty of . worfcthij ) ia one of these . Grant liberty of worship O J 3 i » lu > ps and , Laymen of the , dhurch of EugW ! aJict you pass a decreowhick sUakoa ^ youivautliowCy
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Leader (1850-1860), June 16, 1855, page 566, in the Nineteenth-Century Serials Edition (2008; 2018) ncse.ac.uk/periodicals/l/issues/vm2-ncseproduct2095/page/14/
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