Royal Society ^ 79 



both cases being more considerable as the intensity of the needle is 

 weaker. Let Iq, Ii, l^i ^^' be the inclination observed with different 

 intensities ; To, T^, Tc2j &c. be the times of vibration, which increase 

 as the index increases ; a small correction is required, which can 

 be determined in the following manner. — Take either Iq or a some- 

 what less value (in round minutes) as being nearly correct, and let 



lo— Ii = Ali, ; Io-l2=Al2, &c., 



then Al = a;H-T2?/; 



X being the correction ; thus I found 



If I take 70° 55'*0 as nearly correct, I obtain the three following 

 equations ; 



0'-l=aj + (M67)-?^ ; 20'-2=^ + (l-738)22/ ; 281 -3= a? + (4-25)2^. 

 The three equations have not however the same weight, as the di- 

 rective force is less in proportion as T is larger; in order to give 

 them all the same weight I divide each by the coefficient oiy, and 

 thus obtain in logarithms 



8-86586=9-86586^+y ; 0-82525 =9*51 990 a? +y ; 

 M9239=8-74322a;+y. 



and hence :r=21'-8 ; and the true dip =70° S3'-2. 



I have here taken an imperfect needle, which I also observed" in 

 Azimuths of 30° to 30° ; in one position of the axles I obtained 70° 

 39'-5 ; +5'-9 ; and in a second 70°42'-5 ; +5'-4 ; mean 70°41'-0. On 

 a subsequent day I observed with a second needle and obtained 70° 

 43'*4 ; but an independent needle gave a dip 2'*6 greater, so that 

 the two determinations are 70° 42''1, 70° 42'*3, if we add to each 

 the half difference. 



In this method, in which no reversal is needed, the differences of 

 the partial determinations will appear somewhat large, but you must 

 not forget that instead of the ordinary eight observations only two 

 have been taken. 



I permit myself one additional remark. In observations on dif- 

 ferent azimuths, it is usual to take simply cot I. = cot I^ cos a; in 

 latitudes where the dips are so high as here and in England, this 

 equation may be employed without much error, as the force in 

 azimuths perpendicular to the meridian is little less than in the 

 meridian ; but it is quite otherwise in small dips. With the decrease 

 of force the possibility of error increases, and hence when the ob- 

 servations made in different azimuths are combined as by Kupffer, 

 they have not the same weight. In more exact determinations I 

 employ the following method. 



Let K be the total, H the horizontal, V the vertical force,fand a 

 the nearly known azimuth; then 



V 1 

 K cos I=H cos a ; K sin I=V ; tan I=iT • rTr~ ' 



xX COS ct 



