in the Magnetic Forces of the Earth. 3(53 



foregoing results have been obtained by taking it for granted that 

 the changes of the molecular magnetic intensity are the same at 

 the same hour of local time all around the station of the needle 

 as at the station itself; which is doubtless not strictly true. 



It remains for us now to enquire into the amount of the actual 

 daily angular movement of the line of equal magnetic action, 

 and into the intensity of the disturbing force necessary to the 

 production of the amount of movement of the needle which 

 actually occurs. Let us, in the first place, regard this line as 

 identical with the true isothermal line, and suppose B to be a 

 place situated on this line at 5 a. m.* (or thereabouts), and one 

 hour, say, to the east of the station A. By 9 a. m. the rise of 

 temperature at B will be as much as 2°, on the average, greater 

 than at A, and therefore the isothermal line through A will now 

 pass through a point (C), to the north of B, where the tempera- 

 ture is 2° less than at B. In the present discussion the station 

 A is Philadelphia, and it appears from an examination of the dif- 

 ferences of temperature at various hours during the day, between 

 Washington and Philadelphia, used in the discussion of the verti- 

 cal force, that the difference of latitude of B and C is about equal 

 to the difference of latitude of Washington and Philadelphia, or 

 about 1°, Taking this result and conceiving the isothermal line 

 to be an arc of a great circle, we find, by an easy calculation, 

 the displacement of this line from 5 a. m. to 9 a. m. to be about 

 3$°. The actual isothermal line, at 9 a. m., will really lie a little 

 to the north (as far as C) of the great circle taken for it, since the 

 variation of temperature about 9 a. m. is nearly uniform. This 

 an gle (3f °) is, however, only a part of the daily angular movement 

 of the isothermal line toward the north, to the east of A, since, as 

 we have already seen (p. 361), this movement begins about 7 p. m. 

 and continues until 8 or 9 a. m. The whole movement cannot 

 be less than 5°. This calculation proceeds upon the supposition 

 that the daily variation of temperature at B is the same as at A, 

 but as a matter of fact the change is somewhat greater for A than 

 for B: since, as we have seen, the difference of temperature of 

 Washington and Philadelphia increases during the forenoon, and 

 A is south and west of B. This will have the effect to diminish 

 the rise of the line of equal magnetic force, from 5 a. m. to 9 

 ***, (possibly to 2°); but, as the fall of temperature will be 

 more rapid after 4 p. m., at A than at B, the westerly movement 

 W *U begin earlier in the evening and attain to a greater amount 

 by 5 a. m. than upon the supposition made above. We may lay 

 ]t down then as highly probable that the displacement of the line 

 in question cannot be less than 3°. 



The 



needle. 



