- " a vi ima*mg ui wuicil me tabular 



orm ought to be frequently used, are in most instances altogether free 

 from them : and as to indexes, the art of making them seems to be 

 ; very few books, except those on law, have anything deserving 

 the name. The reason is obvious enough : where proper information 

 ot given, the table shows the spot where it ought to be, vacant 

 and a good index points out not only what u in the work 'but also 

 that which a not. For instance, to take a table which we should only 

 hare inserted in this article in mere illustration, the ' Numerorum 

 Hysteria,' of Peter Bungus (2nd ed. Bergomi, 1591) is a table of 

 numbers. The argument is the number sought, the tabular result is a 

 list of the hyper-arithmetical properties of the number. Thus, turning 

 166, we find all the modes of interpretation which a zealous 

 adherent of Rome could give, including Martin Luther, who satisfies 

 the equation, both in Latin and Hebrew, as perfectly as the average 

 run of solutions. But 6(57 is not in the table ; so that we see it has 

 no mystery about it. 



When the matter sought for is found by one argument only the 

 table is said to be of single entry ; when by two, of doMe entry. 

 Thus the common multiplication table is one of double entry ; and 

 so is any chronological table which consists of more than one column. 



of o 



due to the mathmat 

 works of the^rV 

 if he do not 

 in works of 



.n incor- 

 amount 



> same bad consequence, whether it be 

 the type-founder. This is not true of 

 there be the fault of the reader 



r 



* P> ' hether of the author or P ri " ter J 



' 



reasoning : 



ere sli^, .,u^ uljct wl tiie autnor or printer : but 

 reference all the parties to the result are of equal 



>f the old numerical type, namely, that in which all 

 m ..ss , i, ,>.s ' -ti t a head or a tai!. and in which the thick- 



reZimended b7rlT * ? ne part to another > was ad P ted and 



hadprevTouslv h theAst ral Society at the end of 1842; but it 



e^T^l*^^:* >* detail of the Cavendish 



re^ * 10 ^ 



d oes n T^ 

 * Ot 



The e writer' ^ f rmS , ne V Iume " f the Memoirs"^" 



T -tTT 6 ' Wh< ^ first Sl 'gg ested the revival of the old 

 ; to be employed in Taylor and Walton's five-figure 

 ^ neir reprint of Barlow's tables, and in his own work on 

 ic, before any one else had used it), is decidedly of opinion 

 change is yet wanting, the substitution of dull and 



that one 



rathei 



use 



I .- I 1_ ,. * ww^ittug, tue BUUSUIUUOE 



wh h /T" f the bright and 8hiniD g material n 

 ', which dazzles the eye too much. Tables should not b 



ow in general 



-e*"~* * "*- ""*.** wiioiov.1 vi muie Luau one column - -v~ mu^u. j. auies auoum not be hot-pressed 



A table is, of course, used after the manner of a dictionary ; and the ', 1 eren ^J?** 1 at alL The mischiefs of pressure are two-fold : 



"">" surface thereby created makes the page a kind of 

 aright image in one place, whereas rough paper 



chief phue attending the use is the constant turning of the leaves, 

 ;hia gives may be lessened by cutting off successive 

 length, on the right-hand marging, as is done in the indexes to ledgers, 

 and in other works of reference. We have tried this on a table of 

 logarithms (of the Useful Knowledge Society, 1839) taking the common 

 logarithms, and making the cuttings so as to show a little bit of every 



, ..., f . . 



alternate leaf. Enough of the leaf a shown to enter four figures of the contrast, over and above what is necessary to perfect 



the primitive with which it begins in black ink, and four figures of the I y ' m m J u us to it : jet upou snow would in time destroy the 



-ongest ees. Of l 



first, the 

 mirror, which 



o i !the a i t e; S f t ! l r hg ^ eqUa l! yin a1 ' direoti <>s; secondly, the^her side 

 .shows through much more after pressure than before. It 

 i mistake to suppose that great blackness in the ink, combined 

 Teat whiteness m the paper, is favourable to the reader. Every 

 increase of the contrast, over and above what is necessary to perfect 



-e -- u,ui vo uj. vuo i ft f 4 f\ f ,, J I uMt-jr >wu.u 111 kUUO IfmuTUy tU 



logarithm in red ink. The saving of trouble is so decided that no i res ' Of aU the things which are meant to be read ; 



person who has experienced it will ever again allow a table ichirh he ^. t . m n ^ m '! n t a !, Zn i F*on on white marble in a bright light' i 

 to be without thi: 



. . _ contrivance. So soon as th 



advantage is understood, tables will have the proper references printe< 

 on the proper parts of the margin, the binder being left to cut awa 

 the supervening strips. The same object might be gained by pro 

 truding slips of vellum pasted down the margin, if the boards of th 

 book were made to extend beyond the margin sufficiently to protec 

 the slips ; this also we have tried with good effect. We can assure 

 those who are constantly in the habit of using logarithms that they ma 

 make this hint give a greater facilitation than has ever been propose 

 since the time when Briggs brought forward his modification of Napier 

 system. 



I lematical tables maybe divided into conclusive and tufoiV/nn/ 

 conclusive, such as the table of squares, in which the tabular result ii 

 the object of the reference ; subsidiary, such as the table of logarithms 

 in which the tabular result only facilitates the object. Conclusiv 

 tables can be easily used by those who want them but seldom : sub- 

 sidiary tables are not much used, except by those who want them more 

 frequently. The reason is that a subsidiary table which is not often 

 wanted has its modta operandi forgotten between uses ; or at least the 

 possessor feels a want of practice, and a necessity for referring to th. 

 directions, to be sure of his result. The best thing to be done, when 

 a person first takes to a new subsidiary table, is for himself to write 

 in the book hit <nrn account of the method of using it, so soon as he 

 has learnt it, with some examples. This reference he will find, on 

 future occasions, to be more suggestive to his memory than anything 

 which the writer of the book has said or could have said. 



The method of printing mathematical tables is usually defined so 

 closely by the nature of the subject, that no remark is necessary except 

 on the tyi>e. The numeral characters, up to about the year 1785, used 

 to be smaller in the body than those now constructed, with distinguish- 

 ing heads and tails. Dr. Mutton, we believe, first employed the 

 character in which all the numerals are of the same depth, the heads or 

 tails being compressed into the body. This very disadvantageous 

 change was adopted by the type-founders, but for a long time only in 

 England : the consequence was that the superior legibility of the ancient 

 and of the modern continental tables was matter of common remark 

 among those who had to use them. Another circumstance which con- 

 tributed to this result was the introduction of numerals with thick and 

 thin parts, the superior elegance of which was supposed to be a recom- 

 mendation. The consequence was, that in many English tables it was 

 difficult to distinguish 3 from 8, and 9 or 6 from 0. Of late years 

 however, many works have been published which have used the old 

 type, >>oth as to heads and tails and uniform thickness ; * and their 



* In the new series ol the ' Nautical Almanac,' the heads and tails first 

 re.appcared, but the swelling of the type was not rejected. The works in which 

 the old legibility wa first completely restored were, so far as we know, the 

 tables of logarithms (four and five figures), and the reprint of Barlow's Tables 

 (Taylor and Wilton), the six-figure logarithms (Longman), and Lieut. Upper's 

 ' Klement.4 of Navigation.' Thus it stood when the ' Penny Cyclopaedia ' was 

 published. The legible figures are now common enough in England : but 

 Germany is infested with the illegible ones. The swelling type has been 



ABT8 AND SCI. DtV. VOL. VII. 



about the most difficult: one would suppose, to look at our" specimens 

 pensive printing, that such an inscription was the model which 

 itended to imitate, and if possible to surpass. We are satisfied 

 any trials and comparisons, that a dull paper, of a whitish- 

 brown character too thick to be seen through, and an ink which is 

 11-brown black, as it were the very deepest shade of the colour 

 he paper itself, are the things which are permanently agreeable to 

 it eyes. Those who try it should remember that the first pae 

 read is not so good a test as the hundredth. 



One of the most legible books we know of is the trade edition of 

 bbon s Decline and Fall,' &c., iu twelve volumes octavo, London, 

 it is considered by the booksellers themselves to be very 

 idly executed. But printers and publishers are too much in the 

 habit of forgetting that a book is a book and not a line engraving. 

 hey look at the page as a whole, and if the individual lines stand out 

 and make their separate existences too perceptible, they pronounce it 

 ugly. Accordingly, the uglier they hold it to be, the more legible the 

 ider will pronounce it. We have seen more than one printer and 

 publisher hold a page at such a distance from his eye as made it impos- 

 sible for him to read it, as a means of judging of the general effect. 

 burely a printed page is meant to be a congeries of particular effects, 

 each as distinct from the other as possible. 



We regret to see that, just as we have nearly abandoned the use of 

 the thick even-sized figures, the Germans are taking strongly to them 

 Most of the modern German tables have these illegible characteristics 



Since the invention of logarithms, the appetite for tables has not 



grown with the progress of mathematics. Calculation by logarithms 



so convenient for ordinary purposes, that many persons who are 



even well versed in mathematics are not aware how much assistance 



;hey might derive in particular cases from the various tables which 



lave been published. The list which we mean to give does not nrofess 



to be a bibliography of tables, but will nevertheless give information 



i the subject to all who are not particularly given to mathematical 



nbhography. 



We may divide mathematical tables into general and special; the 

 irst consisting of purely arithmetical and trigonometrical tables, and 

 also tables of logarithms. The special tables are those which are used 

 n the higher parts of mathematics, in commerce, navigation, astro- 

 nomy, meteorology, &c. M'e may further divide tables into tables of 

 acts and tables of mathematical results. All sciences have their 

 tables of facts ; thus the raw observations of astronomy, magnetism, 



ejected in the ' Nautical Almanac,' which is now as legible a tabular work 'as 

 xists, as to both print and paper. 



* So we said in the ' Penny Cyclopedia ' : we now incline to think that the 

 rintrr it the most important of all. One of his errors may be equal to many of 

 ic author's. For instance, in Chcrnac's table a line Ml out, probably just 

 efore press : it was put in again at the lop of its compartment instead of at 

 ic bottom. The consequences were 26 gro-s errors, of a far worse kind than 

 ic author could have made, unless he had tried. liurkhardt found but 10, 

 csides this pet, in the whole book ; and of these one was only 23 x 19 instead 

 f 19 X 23, and two others were clearly due to the printer at press. Chernac's 

 ork has 1020 large quarto pages full of figures, or lines of eijuil importance 



3 u 



