82 THE 8AYRE OBSEKVATORY. 



We can now write for each observed latitude an equation of the form 



yV ( A </, — (M— M>) A.ifl = n), 



where A <p and A/', are corrections to the latitude! and the assumed screw value, if and 31' 

 being the micrometer readings, corrected, of course, for progressive errors. 



Fourteen sets of equations were formed for deriving corresponding values of A $ and 

 A*j5,the aim being to limit each series in respect to time, so that no considerable changes 

 in those quantities need be apprehended. 



The following example will illustrate the process: 



Qrmtp. 



Number. 



No. o/ Obs. 



i/p 



M—M'. 



n. 



v. 





1 



10 



i 



— 15.8 



— .4'.) 



— 00 





2 



10 



l 



+ 4.2 



+ .40 



— 20 





3 



9 



i 



— 14.2 



— .57 



+ 00 





4 



11 



t 



— 8.5 



— 87 



+ 27 



I 



5 



11 



l 



+ 8.8 



+ .82 



+ 01 



6 



10 



i 



+ 0.7 



+ .30 



— 01 





7 



10 



i 



— 10.1 



— .88 



+ 80 





8 



10 



i 



+ 0.4 



+ .42 



— 14 





9 



10 



I 



— B.8 



— .01 



— 10 





10 



'.) 



l 



+ 21.4 



I ■ .88 



- 02 





11 



6 



0.7 



— 0.4 



— .is 



— 08 





12 



5 



0.7 



— 5.1 



«>;> 



+ 07 





18 



4 



0.7 



+ 2.5 



+ .50 



— 48 





14 



:; 



0.6 



— 2.1 



— .08 



+ 08 



11 



15 



:; 



0.1! 



— o.;s 



— .o:'. 



+ 05 





16 



3 



0.0 



— 22.'.) 



— .54 



— 81 





17 



;s 



0.0 



— 11.7 



— .85 



— 00 





IS 



:; 



0.0 



+ 20.'.) 



+ .24 



+ 00 





1!) 



2 



0.5 



+ 10.0 



-f .01 



+ 01 



From these equations, 



a </> = + .0854 

 AJi? = + .0385 



No use is made of A <p in what follows. 



All observations on one pair during the time embraced have been combined into 

 one equation, the number being indicated in the third column. 



The following table gives the results derived from these fourteen sets of equations. 

 The adjusted value of Ai/.' is explained in what follows: 



