ON SELF-RECORDING AIAGNETOGRAPHS- 225 



On December 2, 1859, a similar set of observations gave 



£=•01004. 

 These may be taken as the correct values of k at their respective dates', 

 but we wish to obtain the values of k for intermediate dates. In order to do 

 this, let us make use of the other formula, 



A = cot vlv. 

 On April 30, 1858, v was nearly=43° 13'; hence 



£ = cot 43° 13' X — ?— =-009078. 

 117-24 



On December 2, 1859, v=35° 56' ; hence 



£ = cot 35° 56'x— ^— = -011769. 

 117-24 



By the first or more correct formula we find the change that had taken place 

 in the value of A between the two dates to be -00204, while by the latter formula 

 the change is -002691. We cannot go far wrong in supposing that the real 

 change upon k is equal to that given by the formula (A=cot# S v) multiplied 



by the fraction -. Hence to find the real value of k for any value 



3 -002691 



of v, we have 



£ = -00204_ | cot ^ y _. 0090 ' ;8 } + . 00800 . 



•002691* x 



In these instruments it is of great importance to have magnets which lose 

 their magnetism very slowly ; for it is the loss of magnetism, rather than any 

 other cause, which renders it necessary to turn the torsion circle, and occa- 

 sions changes in the value of the scale coefficient. In connexion with this 

 magnetograph, it is necessary to make frequent observations of absolute hori- 

 zontal force, noting the precise times at which the observations are made. 

 Such observations will serve to eliminate from the results of the horizontal- 

 force magnetograph those changes which are occasioned by loss of magnetism 

 and stretching of the suspension thread. It is particularly desirable to make 

 absolute observations immediately before and after turning the torsion circle. 



3. Vertical-force Magnetograph. 



The temperature correction of this instrument, if fitted with a slip of brass, 

 as in the present instance, will have to be determined by the observations 

 themselves. It is well, however, as a measure of precaution, to determine 

 the temperature coefficient of the magnet before it is mounted. 



With regard to the value of one inch in parts of force, there are two methods 

 by which this may be determined, viz. the method of vibrations, and that of 

 deflections. 



With respect to the former of these — 



Let T denote the time of vibration of the magnet in a vertical plane ; 

 T' the time of vibration of the magnet in a horizontal plane* ; 

 the magnetic dip ; 



Y the vertical component of the earth's force ; 

 which suppose to become Y-f-ciY, occasioning a change in the angular posi- 

 tion of the magnet represented by h ; then it may be shown that 



_=_ coteae. 



* Suspended so as to have the same moment of inertia which it has in the vertical plane. 

 1859. Q 



