OF ARTS AND SCIENCES I FEBRUARY 8, 1870. 



213 



4- - tan 4 - tan 4 — !— - sin 4 / 



4 2 

 + &C 



As tan — tan ~*~ , in the case of the moon, is always between the 



limits ± — , the above series is, for this body, quite convergent. 



OX 



f — A 



cos 



I add the values of the function log 



cos 



+ A 



, computed for every 



degree from 0° to 35° of the argument A and for e = 23° 27' 20". 



A 



log 



e + A 







1 



2 



3 



4 



5 



6 



7 



8 



9 

 10 

 11 

 12 

 13 

 14 

 15 

 16 

 17 

 18 

 19 

 20 

 21 

 22 

 23 

 24 

 25 

 26 

 27 

 28 

 29 

 30 

 31 

 32 

 33 

 34 

 35 



.0000000 



.0015736 



.0031474 



.0047218 



.0062969 



.0078730 



.0094503 



.0110292 



.0126098 



.0141924 



.0157773 



.0173647 



.0189549 



.0205482 



.0221447 



.0237449 



.0253489 



.0269570 



.0285694 



.0301866 



.0318087 



.0334360 



.0350688 



.0367074 



.0383521 



.0400032 



.0416610 



.0433258 



.0449979 



.0466776 



.0483653 



.0500612 



.0517658 



.0534793 



.0552021 



0.0569346 



15736 

 15738 

 15744 

 15751 

 15761 

 15773 

 15789 

 15806 

 15826 

 15849 

 15874 

 15902 

 15933 

 15965 

 16002 

 16040 

 16081 

 16124 

 16172 

 16221 

 16273 

 16328 

 16386 

 16447 

 16511 

 16578 

 16648 

 16721 

 16797 

 16877 

 16959 

 17046 

 17135 

 17228 

 - 17325 



A s 



Change of this 



function for an inc. 



in e of 1" in units 



of the seventh 



decimal. 



