xxiv Introduction to the Makerstoun Observations, 1844. 



ness oi' the suspension thread, it was vibrated with the vertical circle of the inclinometer 

 biihmced horizontally upon it ; the results are : 



Internal radius of ring = 0-39541 feet. External radius of ring = 0-43779 feet. 

 Weight of ring - 9G28-6 grains. 



Semiarcs of vibration, arc " ^ a = 12°, arc - ' a' = 7f, temperature of bar = 38° -0 Fahr. 

 Rate of chronometer, Dent, No. 1665, s = — 5^-0. 



Mean observed time of one vibration from 120 vibrations, T/ = 27^-8006. 

 Bitilar magnetometer, observed every 5™ during vibration ; mean during vibration cor- 

 rected for temperature = 569-3 sc. div. 



Deflecting bar with scale and lens suspended in brass stirrup * =0003966. 



As all the observations for the time of vibration of the deflecting bar had been 

 made previously with the bar suspended in a stirrup of silk fibres, in order to employ 

 the second formula for K, given above, depending on the dimensions and weight of 

 the bar, it was necessary in the present case, to determine the value of K for the 

 same mode of suspension. The two values of * given above for the bar suspended 

 in a brass and in a silk fibre stirrup, without the ring, give $ with brass stirrup 

 suspension, to * with silk stirrup suspension, as, 193 : 200, whence, from the value 

 of $ above for brass stirrup suspension and magnet with the ring, = 0-003966, we 

 find * for silk stirrup suspension and magnet with ring = 0-004109. 



Since J„ - 6, = - 15-4 sc. div., k = 0-000135, (^ - (, = + 0^-4, g = 0000288. 



The true time of one vibration with the ring (reduced to the value of X for T„) T, = 27^-8403. 



25. From the above, therefore, we find for the deflecting bar without ap- 

 pendages. 



Log Kg = 2-9091359 at the temperature of 38''-4 Fahr. 



The value of K used in the reductions in the present volume has been obtained 

 from Ko by the formula 



K = Ko{l + e(<„-38)}- 



where e is the dilatation of steel for 1° Fahr. = 0-0000068, and t„ is the temjjerature 

 of the bar during vibration. 



From the formula K = ^~-^' W, log K = 2-9096331. 



26. The following are the observations for the value of the induction coefficient 



— . Nov 15, 1847. A strong wooden beam having been fixed horizontally in the 



jirolongation of the magnetic axis of the bifilar magnet which lies at right angles 

 to the magnetic meridian, the deflecting bar was mounted in a wooden block having 

 a groove cut to contain the bar ; when the deflecting bar was in its place, it was in 

 the same horizontal plane with, its axis was at right angles to, and its centre was in 

 the prolongation of, the axis of the bifilar magnet. The block was fixed to the 



