Royal Irish Academy. 395 



instrument are at 60 o, 9-10ths of a degree higher than the truth. 

 If such he the case, *5457, instead of being the force of vapour at 

 61°-63, is the force at 6T63 — 0*9 = 60°73 ; and to compare the 

 result of my experiments with the tables of Dalton and Kiimtz, it 

 is only necessary to extract from these the values of the force of 

 vapour corresponding to the temperature 60°* 73. 



My experiments. Dalton. Kamtz. 



60°-73 -5457 "5361 -5157 



Difference between Dalton's number and mine — "0096. 



Difference between Dalton's^ number and that of Kamtz . 4- *0184. 



The consideration, therefore, of the error of my thermometer, and 

 the allowance made for it, only strengthens the conclusion already 

 arrived at ; and I do not now feel any difficulty in giving it as my 

 deliberate opinion, that the table of the force of vapour given by 

 Kamtz is, within the atmospheric range of temperature, erroneous, 

 his values being all too low. 



June 14, 1841.— The Rev. H. Lloyd, V.P. read a "Note on the 

 mode of observing the vibrating Magnet, so as to eliminate the Effect 

 of the Vibration." 



The following modification of one of the methods proposed by 

 Gauss for the attainment of this end, appears to combine the greatest 

 number of advantages ; namely, to take three readings, at the times. 



t — T, t, t+T; 



t being the epoch for which the position of the magnet is desired, and 

 T its time for vibration*. In order to show that this method is ade- 

 quate, it is necessary to deduce the equation of motion of a vibrating 

 magnet in a retarding medium. 



Let X denote the horizontal part of the earth's magnetic force ; 

 q the quantity of free magnetism in the unit of volume of the sus- 

 pended magnet, at the distance r from the centre of rotation ; and 9 

 the deviation of the magnet from its mean position. The moment 

 of the force exerted by the earth on the element of the mass, dm, is 



X q r d m sin ; 

 and the sum of the moments of the forces exerted upon the entire 

 magnet is 



X jW/ sin ; 

 where jo, denotes the value of the integral fq r d m, taken between 

 the limits r — + I, 2 I being the length of the magnet. 



Again, the velocity being small, the resistance may be assumed to 

 be proportional to the velocity. Accordingly, if ca denote the angular 

 velocity, the retarding force due to resistance, upon any element of 

 the surface, d s, at the distance r from the centre of motion, is 



— Kdsrw; 

 and the entire EAoment of this force upon the whole magnet is 



Ku>fr*ds=-Kuj r r * dm ] 



* In practice, it is sufficient to take the nearest whole number of seconds 

 for the value of T. 



2D2 



