358 Wm. A. Norton on the Variations 



in which the dotted lines represent the actual variations of the 

 vertical force, and the full lines the variations as deduced from 

 the theory that they are proportional to the variations of the dif- 

 ference of temperature. On examining these figures it will be 

 seen that there is some cause in operation, making the vertical 

 force to decrease more rapidly in the afternoon until 8 p. m., 

 than the difference of temperature, and to decrease less rapidly 

 or to increase from 8 p. m. to midnight. It will be seen also 

 that in the Spring the vertical force increases less rapidly than the 

 difference of temperature during the latter part of the night, and 

 more rapidly during the forenoon ; and that during the latter half 

 of the year the reverse is true. It is observable also that these 



discrepancies are greatest in amount during the first half of the 



year; that they lie continually in the same direction during the 

 first half of the year, and also continually in the same direction 

 during the other half of the year. As to their origin, they may 

 be purely accidental, for the locality, or for the time; or they 

 may arise from the fact that the variations of the difference of 

 temperature between Washington and Philadelphia do not repre- 

 sent with exactness the variations of the vertical force, since 

 these depend upon the variations of the differences o( tempera- 

 ture of all points of the earth's surface, situated within a certain 

 distance of the station of the needle. It would, at all events, be 

 premature to enquire after some secondary physical cause tending 

 to produce these effects, after so partial an examination of the 

 facts. 



The curves shown by the full lines in figs. 21 to 24, were 

 constructed upon different scales, obtained by assuming that, for 

 each quarter of the year, the variation of the differences of tem- 

 perature from h to 12 h be represented by the line which repre- 

 sents in figs. 13 to 16, the variation of the vertical force during 

 the same interval. The coincidence of the full and dotted lines 

 at h and 12 h is a necessary consequence of this assumption. 



Diurnal Variations of the Declination. 



The general theory is, that the needle is nearly perpendicular 

 to the isogeothermal line — that is, that the mean position of the 

 needle is at right angles to the ideal line passing through those 

 places which have the same mean annual temperature. But, in 

 general, the true and mean temperature are different to a certain 

 depth in the ground. There is a stratum of about 60 feet in 

 depth which slowly varies in temperature from one season to 

 another, and a portion of this stratum, of the depth of some three 

 feet, which varies in temperature during the day. If we consider 

 the action of this latter stratum by itself, agreeably to our gene- 

 ral theory, its tendency at any moment will be to place the needle 

 at right angles to the line connecting the points where the aver- 





