ON THE MAGNETIC VERTICAL FORCE. 



69 



variation of the inclination and total force, the former expressed in seconds, the 

 latter in parts of the total force. The letter M, heading columns 2, 3, and 5, sig- 

 nifies units of the sixth place of decimals or millionth parts of the force. 



Table X.- 



-Ltjnar-Diurnal Variation of thi 



Inclination and Total Force. 



(t's 



aY 



aX 





A'p 



hour angle. 



Y 



X 



a9 



t 





M. 



M. 



// 



M. 



tJ. C. 



+ 3.3 



+11.0 



—0.5 



+ 4.0 



1 



+10.9 



+18.2 



—0.4 



+11.6 



2 



+24.7 



+32.8 



—0.5 



+ 25.4 



3 



+ 5.0 



+40.1 



—2.1 



+ 8.3 



4 



—12.5 



+ 7.3 



—1.2 



—10.6 



5 



+ 6.6 



+25.5 



—1.1 



+ 8.4 



6 



—13.9 



0.0 



—0.9 



—12.6 



7 



—14.8 



+ 3.6 



—1.1 



—13.0 



8 



+ 5.0 



—21.9 



+1.6 



+ 2.4 



9 



+ 2.3 



—14.6 



+1.0 



+ 0.7 



10 



+1H.5 



— 7.3 



+1.4 



+14.2 



11 



-17.5 



+ 3.6 



—1.3 



-15.4 



L. C. 



—11.6 



+25.5 



—2.2 



— 8.1 



1 



— 7.6 



+ 7.3 



—0.9 



— 6.2 



2 



—17.2 



+14.6 



—1.9 



—14.1 



3 



— 9.9 



—11.0 



+0.1 



— 9.9 



4 



—13.2 



+ 3.6 



—1.0 



—11.5 



5 



— 4.3 



—25.5 



+1.3 



— 6.3 



6 



— 1.7 



—47.4 



+2.8 



— 6.1 



7 



— 5.6 



—21.9 



+1.0 



— 7.2 



8 



+ 1.6 



—18.2 



+1.2 



— 0.3 



9 



+ 7.3 



—36.5 



+2.7 



+ 3.1 



10 



— 1.7 



— 3.6 



+0.2 



— 1.9 



11 



+13.9 



+ 7.3 



+0.4 



+13.3 



The numbers in column 2 are deduced from observations between 1841 and 1845, 

 those in column 3 from observations between 1840 and 1845, the difference, how- 

 ever, is immaterial as far as it refers to the dip and total force, the lunar variations 

 being nearly the same for a few adjacent years. The total number of observations 

 employed in the combination is 41558. 



The lunar-diurnal variation in the dip is well represented by the formula, 

 dn = — 0".06 + 0".86 sin (6 + 156°) + 1".30 sin (20 + 206°) 

 the corresponding curve, as weU as the observed values, are exhibited in the follow- 

 ing diagram. The heavy smooth curve is the Philadelphia computed variation, the 

 dotted curve the Toronto variation, inserted here for comparison. The correspond- 

 ence between these curves is certainly remarkably close considering the minuteness 

 of the lunar effect and the somewhat long process of deducing it. 



