ON THE CALCULATION OP MATHEMATICAL TABLES. 59 



In Region II, b, = ^, b,=^-^^^\ 



„, , 4 sin489 sinJ21 sinns , , o^ 4 sin451 sini69 sinns 

 ^ ' sini54 sml54 



2fe2-fci ^tan439 tan421. 



62 + 26, 



tan 39=al 1-90836 92094 tani39=al 1-95418 46047 



tan 21=al i-58417 74241 tan»21 = al 1-79208 87121 



^^2-6| ^g^l i-74627 33168 



62 + 26, 



sin 39=al 1-79887 18039 (sin 39)i=al i-89943 59019 



sin 21=al i-55432 91618 (sin 21)4=al i-77716 45809 



sin 18=al 1-48998 23641 sinn8 = 2"-979 96 47282 



2-65656 52110 

 sin 54=al 1-90795 76446 (sin 54)?= i-93096 82334 



al 2-72559 69776 

 4=al 0-60205 99920 

 262-6, =ali-82765 69696 

 x/K' = al 1-92474 25010 

 2F(36}-E(18)=ari-25239 94706=0-17881 81556 



|||i=|l|l = al i.74627 88168 



F(36) + 2E(18)=al 1-50612 61624=0-32082 06813 

 E(18)= 0-09252 54012 

 F(36)= 0-13566 92789 



Thus Eegion II gives B(18), D(8), E(18), A(36), C(36), F(36) ; and 

 the remaining six values will be given in Region I or III. 



In Region I, 6i = ?^M, bi = ^^, and we have to verify that 



F(18)=0-08047 39933 

 E(36) =0-14308 64509 



F(18)=al 2-90565 55525 E(36)=al 1-15557 89315 



J^,=al 0-07525 74989 -?^=al 0-07525 74989 



6, =al 2-98091 30514 62=al 1-28085 60108 



= 0-09570 02454 = 0-17015 94254 



26i= 0-19140 48908 26,= 0-34081 88508 



262-6,= 0-24461 86054 62 + 26,= 0-86156 43162 



