ON MATHEMATICAL TABLES. 79 



(To 5 places) De Phasse, 1814 [T. II.] (?) ; Gaxbeaith and Haughton, 

 1800 [T. I.] ; Wackerbakth, 1867, T. V. 



See also Teotter, 1841 [T. I.]; Schlomilch [1865?]; Raxkine, 1860, 

 T. 3 ; and Pineio, 1871 (§ 3, art. 13). 



Art, 21. InteriJolation Tables. 



AH the tables of proportional parts (described in § 3, art. 2) are 

 interpolation tables in one, and that the most usual, sense ; and similarly^ 

 multiplication and product tables may be so regarded (see § 3, art. 2). We 

 may, however, especially refer to Scheon, 1860, as its printed title describes 

 it as an interpolation table — a designation not common. The only separate 

 table we have seen for facilitating interpolations, when the second, third, &c. 

 differences are included, is "Woolhottse, noticed below. We may also refer 

 to Godwaed's tables (title in § 5), but they seem of such special application 

 that we have not thought it necessary to describe their contents. 



Woolhouse, 1865. Papers extracted from vols, xi, and xii. of thd 

 * Assurance Magazine.' There are 9 pp. of interpolation tables (viz. pp. 

 14-22) . The work contains a clear explanation of methods of interpolation, 

 with developments. 



The following are references to tables described in § 4, 



Binomial-theorem coefficients. — Schulze, 1778 [T. XIII.] ; Yega, 1797, 

 Vol. II. [T. VI.]; Barlow, 1814, T. VII.; Hantschl, 1827, T. IX.; 

 Hulsse's Vega, 1840, T. XIII. ; Kohlee, 1848, T. X. ; Parkhuest, 187i; 

 T. XXXII. See also Rouse (§ 3, art. 25). 



Other interpolation coefficients. — Petees, 1871 [T. IV.], I. and II. 



Coefficients of series terms. — Vega, 1797, Vol. II. [T. VI.] ; Lambert, 1798, 

 T. XLIV. ; Hulsse's Vega, 1840, T. VIII. ; Kohler, 1848, T. XI. 



Art. 22. Mensuration Tables. 



We have made no special search for tables on mensuration (such as areas 

 of circles of given radius, volumes of cones of given base and altitude, &c.), 

 and have only included those that have fallen in our way in the course of 

 seeking for more strictly mathematical tables during the preparation of this 

 Report. As, however, for several reasons it seems desirable that a complete 

 list of such tables should be formed, we shall endeavour to render this 

 Article as nearly perfect as we can in the supplement. One reason, how- 

 ever, wh)^ such tables are not of very high mathematical value is that the 

 measures are generally expressed in more or less arbitrary units, such as yards, 

 feet, inches, &c., or metres &c. 



We may especially refer to the large table of circular segments in Sharp, 

 1717 (§ 4). 



Sir Jonas Moore (1660?). The table is a very small one, and 

 scarcely occupies a third of a folio page. It gives the periphery of an 

 ellipse for one axis as argument (the other axis being supposed equal to, 

 unity) to 4 places, with differences ; the range of the argument is from -00, 

 to 1-00 at intervals of -01. Thus, to find the perimeter of an ellipse, axes 1 

 and -78, we enter the table at 78 and find 2-8038. If oue axis is not equal 

 to iinity, a simple proportion of course gives the perimeter. After working^ 

 out four examples, the author proceeds : " I have made above 45,000 arith*- 

 metieal operations for this table, and am now well pleased it is finished.. 



