428 Mr, C. Chambers on Magnetic Dip- Observations. [May 13, 



to investigate the effect of a hypothetical irregularity in the shape of the 

 axle of the needle, such that a section of the axle by a plane perpendicular 

 to its axis would be elliptical instead of circular in form. Another source 

 of error, which was brought to the notice of the Royal Society many years 

 ago in a paper published in the Proceedings, is the displacement of the 

 centre of gravity of the needle from the centre of the axle, combined with in- 

 equality in the magnetization of the needle when the poles are direct and re- 

 versed. Experience has led the author to the conclusion that the usual 

 method of magnetization, by a definite number of passes of the same pair of 

 bar-magnets, communicates magnetism to the needle very unequally when 

 the one end of the needle is made north and when the other end is made 

 north. Consequently it is advisable to investigate the effects of ellipticity 

 of the axle and of displacement of the centre of gravity at the same time, 

 which the author proceeds to do. 



As each of these errors depends upon two independent unknown quanti- 

 ties, suppose the excentricity and the azimuth of the major axis of the 

 elliptic section of the axle for the first, and the two coordinates of the 

 centre of gravity, referred to axes in the plane of motion of the needle and 

 passing through the centre of the axle, for the second, the equation con- 

 necting the true and apparent dip, in any one position of the needle and of 

 the face of the dip-circle, will involve four unknown quantities depending 

 on the above errors. If we suppose the instrumental errors small, so that 

 the apparent dip does not much differ from the true dip, these four unknown 

 quantities will appear as coefficients respectively of the sine and of the 

 cosine of twice the dip for the elliptic error, and of the sine and the cosine 

 of the dip for the error of excentricity of the centre of gravity, and will be 

 divided in each case by the magnetic moment of the needle. On taking 

 the mean of the apparent dips in the four usual positions of the needle and 

 of the dip-circle before the magnetism of the needle is reversed, two of the 

 terms, one for each error, disappear, and there results for the difference 

 between the true dip and the mean of the four apparent dips (0') an 

 equation of the form 



»'(A-B)=(fl')-e, • • • (i) 



where n' is the reciprocal of the magnetic moment of the needle, and A and 

 B are the constants depending on the errors of the pivot and of the centre of 

 gravity respectively. These two quantities are constant only for the same 

 place, the first involving as a factor the sine of twice the dip divided by 

 the total force, the second the cosine of the dip divided by the total force. 



Now let the poles be reversed in the usual way, and let n" be the reci- 

 procal of the magnetic moment, and (0") the mean apparent dip in the four 

 positions after remagnetization ; then 



n"(A+B) = (0")-0 (2) 



The equations (1), (2) contain three unknown quantities A, B, 0; but if 

 we repeat the observations with the difference that this time the needle is 



