Formulae and Determination of Constants 23 



observation, reckoned from the North Pole, and s = ^{h -\- <f> -{- p). North 

 latitudes and north declinations of the Sun are to be given the plus sign; south 

 latitudes and south declinations will then have the minus sign. The determination 

 of the local apparent hour angle, t, results from the formula: 



tan U = s ec{s-p)sln(s-h) 

 cot ^A 

 Converting the derived value of t into time and applying E, the equation of time, 

 the local mean time of the observation set is obtained, whereas the mean standard 

 time results from the mean chronometer time corrected with the aid of the data 

 given in the chronometer record. From the difference between standard time 

 and local mean time, the difference in longitude, east or west, of the standard mer- 

 idian is finally found. As a check upon the computations the formula: 



sin A = sin / cos 5 sec h 

 is used; see specimen given bottom of p. 33. On p. 32 is shown the computation 

 of the Sun's declination and equation of time. 



Magnetic Work. 



Declination observations. For specimen of computations with the usual type 

 of magnetometer, in which the scale is on the diaphragm of the observing telescope, 

 see p. 37. For an instrument of the type in which the graduated scale is mounted 

 in the magnet, there is some slight modification in the computation ; the axis value 

 results directly from the mean of the scale readings, magnet erect and inverted; 

 the reduction to magnetic south meridian is, scale erect minus axis converted into 

 arc by means of the value of one division of the scale, the difference being applied 

 algebraically to the circle reading, that is to say, the respective circle and scale 

 graduations are such that for an erect reading of the magnet on the scale greater 

 than the axis value, the correction to the horizontal circle reading is positive, the 

 circle being graduated in a clockwise direction as seen from above. The compu- 

 tation of approximate values of the magnetic declination as obtained with the 

 compass attachment of the dip circle is shown on the specimen form, p. 40. 



Horizontal intensity observations. ^As shown on the specimen forms, pp. 34, 35, 

 the horizontal intensity is computed by means of the formulae: 



^ i^K H C 



mH = -^f^ = -. 



7^ m sin u 



T is the time of one oscillation corrected for rate of chronometer, torsion, tempera- 

 ture effects, amplitude, and induction; K is the moment of inertia of the oscillating 

 magnet and suspension, and m its magnetic moment; u is the mean deflection angle, 

 and C the constant, corrected for changes in length of brass deflection bar with 

 temperature, which involves the deflection distance r, induction coefficient ju, and 

 distribution coefficients P and Q, thus: 



C = 



'(.+??) 



