226 report — 1859. 



Again, since the normal to the mirror is inclined at an angle of 15° to the 

 incident ray, and since the sensitive cylinder is 5*965 feet, or 71*58 inches 

 distant from the mirror, it may be shown that the vertical space of one inch 

 traversed by the luminous dot upon the cylinder, represents an angular change 

 in the position of the magnet 



_ 1 



143-16 X cos 15° 5 

 hence the value of 1 inch in parts of force 



T' 2 cote 



T 2 143-16 cos 15°' 



The second method, by which the value of one inch in parts of force may be 

 determined, is that of deflections. Let a suitable apparatus (see Plate 3. figs. 

 5a, 5a) be contrived, by means of which a deflection magnet, m, may be 

 placed vertically with its centre at a given distance, r, from that of the ver- 

 tical-force magnet and in continuation of the magnetic axis of the latter 

 magnet, when horizontal. Let the change of position of the luminous dot 

 upon the cylinder be registered photographically as before; let this be 

 =n inches. 



Let the deflecting magnet be now placed with its centre at the distance r 

 from that of the declination magnet, and in continuation of the magnetic 

 axis of the latter magnet; also let the magnetic axis of the deflecting magnet 

 be perpendicular to the magnetic meridian ; and, finally, let the angle through 

 which the declination magnet is deflected be determined photographically. 

 Call this angle u ; then it may be shown that the value of one inch in parts of 

 force for the vertical-force magnet is found from the following expression: — 



tt i p . * tan w 



Value or one inch=— . 



n tan 



By the method of vibrations the value of one inch was determined on 

 February 27th, 1858, to be ='00221 in parts offeree, while by the method of 

 deflections (mean of three distances) its value was found to be = "00211 in 

 parts of force. There is thus a very satisfactory agreement between the 

 results of the two processes. 



On April 18th, 1860, the value of one inch was determined by the method 

 of deflections to be =-00249 in parts of force. There is thus a change 

 = •00038 which has taken place in the value of one inch during the course of 

 about two years. This has no doubt been occasioned by loss of magnetism 

 of the magnet widening the distance between the dots and rendering it 

 necessary to alter the balance of the magnet by means of the horizontal 

 screw from time to time. 



A proper method of interpolation will enable us to determine with suffi- 

 cient accuracy the value of 1 inch in parts of force for any period between 

 February 27th, 1858, and April 18th, 1860. 



It is perhaps a safe rule to determine the value of the scale coefficients of 

 bifilar and vertical-force magnetographs,by the method of deflections, once 

 a year. 



Monthly observations of dip are made at Kew, which, combined with the 

 monthly determinations of absolute horizontal force, will enable us to deter- 

 mine the absolute vertical force, and thus to eliminate from the vertical-force 

 curves the changes that have been occasioned by loss of magnetism from 

 time to time. 



Method of tabulating from the curves. — By pushing the dots of light 

 forward a little, two days' curves are recorded on each sheet of sensitive 



