168 Professor Forbes's Experiments on 



ing six months down to May 1833, during which the needle 

 was in a state of almost perfect repose. 



20. The mode of allowing for this is the following. All 

 determinations of intensity are relative, referring to some in- 

 tensity as a standard ; but I have taken the horizontal inten- 

 sity at Paris as unity (which is to that at the magnetic equator 

 as 4,788 to 10,000 according to Humboldt)*. Hence, since 

 the squares of the times of 100 vibrations are inversely as the 

 magnetic forces, the terrestrial horizontal intensity at a station 

 A is to that at Paris, or 1, as the square of the time observed 

 at Paris (which time we may call T P ) is to the square of the 

 time observed at station A (or T A ). Hence, 



Intensity at K = t~\ 



If the magnetism of the needle change, we must therefore 

 find by interpolation the time of vibration at Paris for the 

 particular epoch of observation. 



21. In the case of Needle No. 1, the magnetism being sta- 

 tionary, the time of 100 vibrations has been assumed from an 

 observation made (in M. Arago's Cabinet Magnetique), 11th 

 June 1833, as equal to 



247 sec 70; its log. 2*39392 



22. In the case of the " Flat" needle, a subsidiary table has 

 been calculated of the times for Paris, cor responding to the epochs 

 when observations were made elsewhere, which appear amongst 

 the details to be given in the sequel. On the 11th June 1833, 



the log. time of 100 vibrations at Paris was 252 159 



If, for the period from June 1832 to May 1833, we 



deduct -006 184 (by Art. 18) and for the month of 

 May 1833, *00040 being the rate of change for the 

 current period (Art. 18), we have a change for one 

 year, subtractive, *00724 



T F , or Time at Paris, June 11, 1832, Log. 2*51435 

 Adding -001 per month as] , ^^ 



proposedmArU9,weshall ^.n 2 . 51635 



have nearly these values | s ? t#n > .2-51735 



(neglecting trifling quanti- { Q * L „. ^^^ 



ties) as approximations to N » 2.519*5 



the value of Log. T P J WOV - 4 S ^5193^ 



* Deduced from the measure of total intensity 1-3482 at Paris, given in 

 the Memoires (TArceuil, torn. i. multiplied bv the cosine of the dip, there 

 alto given (69° 12'). 



