]4 RELATIONS PERTAINING SIMPLY [BoOK I. 



first and second quadrants, the lower in the third and fourth), wherefore, either 

 M, or its value increased or diminished by any estimate whatever, can be taken 

 for the first value of E. It is hardly necessary to observe, that the first calcu 

 lation, when it is commenced with a value having no pretension to accuracy, does 

 not require to be strictly exact, and that the smaller tables * are abundantly suffi 

 cient. Moreover, for the sake of convenience, the values selected for e should be 

 such that their sines can be taken from the tables without interpolation ; as, for 

 example, values to minutes or exact tens of seconds, according as the tables 

 used proceed by differences of minutes or tens of seconds. Every one will be 

 able to determine without assistance the modifications these precepts undergo if 

 the angles are expressed according to the new decimal division. 



13. 



Example. Let the eccentricity be the same as in article 10. M=33228 

 54&quot;.77. There the log e in seconds is 4.7041513, therefore e = 50600 = 14 3 20&quot;. 

 Now since E here must be less than M, let us in the first calculation put e 326, 

 then we have by the smaller tables 



log sin 9.7475GW, Change for V ... 19, whence A = 0.32. 



log c in seconds . . 4.70415 



4.45171; 



hence esiner -28295&quot;= 751 35&quot;. Change of logarithm for a unit of the table which is here 



Jtf-L. e gin . 324 3720 equal to 10 seconds ... 16; whence/* =1.6. 



differing from .... 1 22 40 = 4960&quot;. Hence, 



fl 39 



~ X 4960&quot; = 1240&quot; = 20 40&quot;. 



l.zo 



Wherefore, the corrected value of ^becomes 32437 20&quot; 20 40&quot;= 32416 40&quot;, 

 with which we repeat the calculation, making use of larger tables. 



log sine .... 9.766305Sw I = 29.25 



loge 4.7041513 



4.4704571 n fi = U7 



* S ich as those which the ill istrious LALANDE furnished. 



