206 Transaction*. — Miscellaneous. 



Section 9° 0' - 10°. 

 sin 9° - 4- 0-15643, 44650, 4 



A sin 9° = + 0-00086, 18610, 01 



sin 9° 3' = + 0-15729, 63260, 4 



A 2 sin 9° = -- k . sin 9° 3' - 0-00000, 01197, 880 



A sin 9° 3' = A sin 9° + A 2 sin 9° = = + 0-00086, 17412. 13 

 A 3 sin 9° = - k . A sin 9° 3' - 0-00000, 00006, 5625 



&c. 



Sections of 1° each (0°-l° ; l°-2° ; &c.) are formed thus, 

 and the values found in 2 above are used to check each 

 terminal value. 



Thus for the section 9° 0' - 10° the sines are : — 

 ° ' Sines. 



9 0-15643, 44650, 4 



3 0-15729, 63260, 4 



6 0-15815, 80672, 5 



54 0-17192, 91003, 8 



57 0-17278, 87047, 7 



10 0-17364, 81776, 7 



10 0-17364, 81776, 67 check valae. 



4. Finally we have the case of a 10" table to seven deci- 

 mals. 



Tabular interval = A# = 10". Initial value, 9° 54'. 

 sin 10" = 000004, 84813, 68092, 4 



cos 10" = 0-99999, 99988, 24778, 473 



k = 000000, 00023, 50443, 053 



A sin 9° 54' == cos 9° 54' . sin 10" - J sin 9° 54' 

 = 0-00004, 77592, 458 



Section 9° 54' -9° 57'. 

 sin 9° 54' = + 0-17192, 91003 



A sin 9° 54' = + 0-00004, 77592, 458 



sin 9° 54' 10" = + 0-17197, 68595 



A 2 sin 9° 54' = - k . sin 9° 54' 10" = - 0-00000, 00004, 04221, 8 

 A sin 9° 54' 10" = + 0-00004, 7758s. 1 L6 



A sin 9° 54' = - k . A sin 9° 54' 10" = - 0-00000, 00000, 00112, 



254 &c. 



These leading differences are sufficient to determine the 

 sines to ten decimal places approximately ; and for this 

 particular section the value of sin 9° 57' is 0-17278, 87047, 6, 



