Formula and Determination of Constants 25 



The value of one scale division, where the graduation is on a glass diaphragm in 

 the reading telescope, is quickly obtained by setting the successive scale marks 

 on a very distant object and reading the horizontal circle; thus, horizontal circle 

 readings are obtained for every fifth division, 0, 5, 10, 15, etc., to the 7/th division 

 and back in the reversed order, w 5, ... 10, 5, 0, the setting of the middle 

 division on the object being repeated so that successive values of ^n divisions in 

 arc may be obtained, thus (fn 0), {^n + 5) 5, etc. For instruments in which 

 the scale is mounted on the magnet, similar readings of the horizontal circle are 

 made by sighting on the successive scale divisions of the magnet, care being taken 

 to reverse the order of operation in the second half-set so as to eliminate, as far as 

 possible, diurnal variation effects. 



For the determination of the moment of inertia of the magnet and suspension, 

 a number of oscillation observations with and without the inertia bar are made, 

 thus a, ab, ab, a, a, ab, ab, a, a, etc., concluding with a, where c is a complete set of 

 oscillations without the inertia bar and ab a complete set with the inertia bar. 

 These observations are then grouped in pairs 1 and 2, 3 and 4, etc. If T is the 

 time of an oscillation without the bar, corrected for the rate of chronometer, 

 induction efTect, torsion effect, and to the temperature of its corresponding set 

 with the bar, and Ti is the mean time of the oscillation with the bar, corrected for 

 rate of chronometer, induction effect, and torsion effect, and if Ki is the computed 

 moment of inertia of the inertia bar reduced to the temperature for Ti, then the 

 moment of inertia of the system is: 



K = 



'T"2 2^2 



For the determination of the induction coefficient both Weber's and Lamont's 

 methods have been used. Plate 6, Fig. 1, shows the coil as used in the first method, 

 the observation being as follows: the instrument is oriented so that the coil may 

 be rotated in the plane of the magnetic prime vertical, connection being made 

 with a ballistic galvanometer of high sensitiveness; the empty coil is rotated through 

 180 in the vertical plane, this rotation being repeated at intervals agreeing with 

 the period of the galvanometer until the extreme deflection of the galvanometer, Oo, 

 expressed in arc, is determined. The magnet, the induction coefficient of which is 

 being determined, is then centered in the coil by some convenient arrangement, 

 e. g., a wood frame, and the coil rotated, the galvanometer read as before, thus 

 determining a deflection a; the coil is then placed in a vertical position and the small 

 auxiliary' magnet, the magnetic moment of which, nii, may be determined with 

 sufficient accuracy by the method of deflections, is brought rapidly from some 

 distance, mounted in the middle of the coil and then quickly withdrawn, this 

 operation being repeated until the extreme swing of the galvanometer is obtained, 

 the total deflection being Oi. The induction coefficient, h, may be reduced from the 

 data so obtained by the formula: 



, ^ mi(a gp) 

 2mZai 



/ 



