48 REPORT— 1873. 



to the unit arc, or arc equal in length to radius. The latter method is usually 

 described in English text-books under the title " Circular Measure ; " so that 

 in the descriptions in § 4 we have spoken indifferently of the length of the 

 arc of 0;°, the longitude of >t°, or the circular measure of .r°. The tables of 

 circular arcs usually give the circular measure of 1°, 2°,. . up to 90°, 180°, 

 or sometimes 360°, of 1', 2', . . . . GO', of 1", 2", .... GO", and very often of 

 1'", 2'",. . . .60'" also. By means of such a table any number of degrees, 

 minutes, &c. cau be readily expressed in circular measure. 



The following is a detailed list of the lengths of circular arcs contained in 

 ■works described in § 4 : — 



(To 44 places) Hobert and Ideler, 1799, G (centesimal division), 



(To 27 i^laces) Academie de Prusse, 177G [T. II.] ; Schulze, 1778 

 [T. VII.]; Lamdert, 1798, T. XXIII. 



(To 25 places) Callet, 1853 [T. V.] (sexagesimal and centesimal). 



(To 15 places) Hantschl, 1827, T. X. 



(To 12 places) Schmidt, 1821 [T. IV.]; Muller, 1844 [T. IV.]. 



(To 11 places) Vega, 1794, T. II.; Hulsse's Vega, 1840, T. II.; Kohler, 

 1848 [T. V.]. 



(To 10 places) Shortrede, 1849, T. III. ; Bruhxs, 1870. 



(To 8 places) Vega, 1797, T. III. ; Pearson, 1824 [T. III.]. 



(To 7 places) Dodson, 1747, T. XXV. ; Ursinus, 1827 [T. III.] ; Grtt- 

 soN, 1832, T. VI.; Trotter, 1841 [T. VII.] ; Shortrede (tables), 1844, 

 T. XXXVIII.; Warnstorff's ScntrjiAcuER, 1845 [T. II.]; Willicu, 1853, 

 T. D ; Bremiker's Vega, 1857, T. II. ; Hutton, 1858, T. XI. ; Dupuis, 

 1868, T. IX. ; Peters, 1871 [T. III.] 



(To 6 places) Bremiker, 1852, T. II. 



(To 5 places) Wackerbartu, 1867, T. IV. 



See also Vega, 1800, T. II.; Byrne, 1819 [T. II.]; *ScnLoMiLCH 

 [1865?]. 



Art. 12. Tables for the e.vpresslon of hours, minutes, S,-e. as decimals of a day, 

 and for the conversion of time into sjicice, and vice versa. 



The largest table we have seen to convert hours, minutes, &c. into decimals 

 of a day is Houel, 1866. Tables of this kind are not numerous. 



Three hundred and sixty degrees of space or arc are equivalent to twenty- 

 four hours of time ; so that 1" corresponds to 15°, 1'" to 15', and 1" to ] 5" ; 

 1" is therefore 4 thirds of time = 4' ; 36' ==2'" 24^ &c. Small tables to convert 

 space (arc, or longitude) into time arc not unfrequcntly given in collections 

 (generally nautical) of tables. A complete tabic of the kind gives the numbers 

 of hours and minutes corresponding to 1*^, 2°, . . . . 360° ; and the same figures 

 also denote the number of minutes and seconds, and seconds and thirds (of 



time) corresponding to 1', 2', 360', or 1", 2", 360" respectively. In 



this Report •■, ", % &c. arc used to denote hours, minutes, seconds, and thirds (of 

 time), and °, ', ", "' for degrees, minutes, &e. of space — a distinction which it 

 is often convenient to adopt. 



Littrow, 1837. T. I.-IV. (5 pp.) are small tables for the conversion of arc 

 into time &c. All the other tables, which occupy more than nine tenths of 

 the tract, are astronomical. 



Hoxiel, 1866 (Time Tables), T. II. To convert hours, minutes, and 

 seconds into the decimal of a day (pp. 15). Any number of hours, minutes, 

 and seconds (and fractions of a second, as proportional parts arc added) 



