(2.4.6)'^.3.5.7 



12 049 407 . . / . A 



142 Mr Sang on the Friction of Timr-Keepers 



Or, 



r;A=A+^sin A(sm-) 



+ ;; sm A (sill— ) 



(2.4)2.3.5 ^ 2 / 



23031 . ./.Ax" 

 A(sm-) 



__._ A (sin— \ 

 (2.4.(J.8)'^.3. 5.7.9 ^ 2 / 



13 793 405 025 . ./.Ax™ 



r+ ? sin A ( sm — I + «^tc 



^ (2.4.6.8.10)2.3.5.7.9.11 ^ 2/ ' 



Here the order of the denominators is sufficiently obvious. 

 That of the numerators can be exhibited thus : Let A, B, C, 

 D, E, etc. represent the successive numerators, tli«n 



A = 1 



B = A. 4=^ + 3' 



C = B. 63 + (3.5)? 



D = C. 8» + (3.5.7)^ 



E = D. 10^ + (.3.5.7.9)3 , etc . 



By means of which formulae, logarithms of the coefficients 

 have been computed. 



At the first glance, however, it will be apparent that the va- 

 lue of •i^A given in terms of the radius will be exceedingly in- 

 convenient for computation, since it would be necessary to con- 

 vert the arcs also into decimal parts of the same unit. It would 

 be more convenient to take some small arc, as one minute, for the 

 unit ; in this case, all the coefficients would need to be multi- 

 plied by the constant ^^, or their logarithms to be increased 

 by the logarithm of that fraction. The formula then becomes 



1O80O 1 . ^ / . A V « ^ 

 ^'A = A' + ^ sm A (sm - ) + etc ; 



and its application is given by the equation 



A'— A' 



= T V sec ?- 



■^'A — ■v/^'A 



the accents denoting that the quantities are taken in minutes of 

 a degree. 



The computation of a table of the values of ^/A being very 

 laborious, the operations have not yet been revised. In this 

 case it is deemed advisable to postpone their publication until 

 the revision is completed. 



60. North BRincT, \ 

 . 22rf.Va.v 183.->. i 



