W. I'\ SllKI'l'ARD 181 



.r='01, '02 ... worc obtaiiied by quailraturc*, .■uiil t.hose of : by iiiterpolatioii. Fdi- tlie rcinuiiider 

 of the twü tables, the values of z wero found iVoni thoso of log,,, 2, which are easdy calculated, and 

 thence the vahie.s of ^(1+«) were obtained by miadratui-o. For checkiiig tbe table of i(l+a), 

 values were directly calcidated at intervalst: and liotb t,d)Ie.s were furthi-i- checkcd by the 

 cakidations requirod where a fhial figuro was doubtful. 



l'"or constructing Tables III. and I\'., the vahie.s were iirst ulitained appro.Kiuiatcly tu .suven 

 place.s : and the tables were then e.xtended, by a method explained el.sewhere J. The extension gave 

 s to nine and .r to eleven place.s. The table was eheeked by direct cakiilition for h = 'I, "2, '3.... 



* See Piüc. of Luntl. Math. Svc. Vol. xxxi. pp. 179—482. 



t Some use was also made of Burgess's table» {Truns. Roy. Soc. Edin., Vol. xxxix., Pt. 2, No. 0), in 

 which a is given (to alargenumber of figures) in terms off = x/V2. But they were only useil inciclfntally 

 aud the two sets of tables may be regarded as independeiitly calculated. 



J Prof. 0/ Loiul. Math. Soc. Vol. xxxi. pp. 123, 43',l. 



TABLES I. AND II. Area und Ordinate in terms of Äbscissa. 



Note. 



For values of the abscLssa x from '00 to 4'.50, the vahies of the arca ^ (1 + a) 

 and of the ordinate z are given to 7 deciinal places (pp. 182-7). For values of x 

 from 4'50 to 6'00, the values of | (1 + a) and of 2 are given to teu decinial places 

 (p. 188), but the initial figures are omitted. Hence, in using this latter portion 

 of the tables the figures in the column for ^(1+a) must have OODÖO prefixod, 

 aud those in the column for z must have sufficient zeros prefixed to bring up 

 the total of decimal figures to ten. For exaniple, against ic = 5"7ö we have 99955 

 and 264. but we niu.st read h {l + a) = •9991)91)9955 and s = •0000000204. 



