OF THE MAGNETIC DECLINATION. 9 



Owing probably to tlie several accidental changes in the suspension of the bar, 

 and consequent uncertainty in the precise amount of scale correction, the mean 

 readings of each year, when compared with one another, exhibit differences not 

 actually due to inequalities occasioned by declination changes. This question, 

 however, does not directly bear upon the present investigation, which mainly 

 depends on differences of readings, and it is proper to remark that the observed 

 increase, giving the weight one-half to the mean of 1840 and of 1845, is under the 

 supposition of a uniform annual change between these years, equal to 4'.50. From 

 Mr. Schott's investigation^ of the secular change of the declination at Philadelphia, 

 supported by observations between the years 1701 and 1855, the annual increase 

 between the years 1840 and 1845 is 4'.98, a result which accords tolerably well 

 with actual observations. According to his formula, the declination on the first of 

 January, 1843, the mean epoch of the present series was 3° 32' west, with a probable 

 error of +_ 10', which corresponds to the scale reading 560.31, deduced by taking 

 into account the weights of the annual means. 



We now proceed to the investigation of the inequality in the diurnal variation, 

 changing the preceding formulae for greater convenience into the following : — 



ForlS-lO A=+2'.S15sin (IS^'n + 36° 35') + 2'.078 sin (30°n+ 217° 33') + 0'. 743 sin (45°n4-68° 50') 



" 1S41 A=+2.214s(n (15 n + 30 05 ) 4-1.984 sm (30 n + 212 38 ) -f 0.716 sm (45 n + 50 14) 



" 1842 A = -f 2.240sm (15 n + 33 49)-f-1.908 sin (30 J!-f-217 12 ) -|- 0.663 sin (45 n + 64 42 ) 



" 1843 A =-)- 2.015 sm (15 n+36 00 ) -f- 1.775 sm (30 n + 218 05) + 0.820 sm (45 n + 68 18) 



" 1S44 A = + 2.032 sin (15 n+34 35 ) + 1.754 sin (30 n + 222 23) + 0.816 sin (45 n-|-68 53) 



" 1845 A = +2.060 sin (15 n + 35 33 ) + 2.206 sin (30 n + 225 35 ) + 0.900 sin (45 n + 61 20) 



Where A = the regular solar-diurnal variation. 

 n = the number qf hours after midnight. 



To show the agreement between these expressions and the corresponding observed 

 quantities, and to exhibit to the eye the character of the diurnal variation, the 

 results have been, thrown into curves. The observed bi-hourly means are repre- 

 sented in Fig. 2 (p. 11) by dots, and in no instance do they differ from the com- 

 puted values by as much as 0''.8 or 0'.3. As a specimen of the representation, 1 

 add the results for the year 1845: — 



The average probable error of any single representation by the formula is +0>l-.22 or+O'.lO. 



By means of the preceding formulae the following values were computed: 1. The 

 time when the north end of the magnet reached its extreme eastern position, or, in 

 other words, the epoch of tlie eastern elongation. 2. Tlie corresponding maximum 

 scale reading, or, more properly, the corresponding minimum of western declination. 

 3. The time of the occurrence of the western elongation ; and 4. The corresponding 



' Report on the progress of the U. S. Coast Survey for 1855, Appendix, No. 48, and an Appendix 

 (p. 11) of the report for 1859. 

 2 



