224 report — 1859. 



radius, which is occasioned on v by the moveable dot traversing the sensitive 

 paper one inch ; k the scale coefficient, or value of one iuch in parts of 

 force; then £=cot« S». 



By this formula, k, or the scale coefficient, may be determined when v is 

 known. Let us determine v accurately when the magnet is mounted, that is, 

 let us find accurately the angle which the plane of the upper extremities of 

 the wire makes with that of the lower for a certain distance between the 

 fixed and the moveable dot of light upon the cylinder, then we can always 

 find the value of v. Loss of magnetism in the magnet may have widened the 

 distance between the dots on the cylinder since we first determined v*, but 

 knowing the angular value of one inch we can make allowance for this, and 

 thereby determine the present value of v, which will be somewhat less than 

 the first. The loss of magnetism may even have obliged us to turn the torsion 

 circle, in order to bring the dots of light nearer to one another, and of course 

 an accurate account must be taken of this, and allowance made for it in cal- 

 culating for the future the values of v. 



Taking these circumstances into account, viz. the amount of change of the 

 torsion circle, and the distance between the dots, v may always be determined, 

 and, consequently, by the above formula, the scale coefficient may be known. 



But as there is some doubt of the rigorous truth of the conditions which 

 the above formula assumes, another method of determining the scale coefficient 

 has been proposed which does not seem open to any such objection. 



Let a deflection bar be arranged as in Plate 3. fig. 4 a, 4 a, so as to support 

 a magnet horizontally placed, with its axis in the magnetic meridian, and so 

 that if prolonged it would pass through the centre of the bifilar magnet. 



Let the centre of the two magnets be at the distance r from one another. 

 The presence of the deflecting magnet will of course have changed the posi- 

 tion of the moveable dot upon the cylinder. Bring the bifilar magnet speedily 

 to rest, and allow the deflecting magnet to remain in its position for about 

 five minutes : this time will sufficiently enable us to procure a photographic 

 impression of the position of the bifilar magnet when deflected ; and having 

 its position before and after, we shall thus be enabled to estimate the amount 

 of deflection. Let this be n inches. 



Take the same deflecting magnet and place it in a similar position with 

 respect to the declination magnet, and also at the distances. Here it is 

 obvious that the axis of the deflecting magnet is at right angles to the 

 magnetic meridian. Determine photographically, as before, the angle of de- 

 flection which it has caused ; let this be u ; then k, or the value of one inch 



in parts of force for the bifilar magnetograph= . 



Example. On April 30, 1858, the deflecting magnet having been applied as 

 above to the bifilar magnetograph, the deflection produced was=2*887 in. 



The same magnet being applied in a similar manner, and at the same di- 

 stance, to the declination magnet, the deflection was =3*560 inches =78' 58". 



Hence ft- "^^=-00796. 



A similar observation having been performed at the distances 2*5 and 3*0 

 feet, we find as a mean result on that date, 



k =-00800. 



* In the declination magnetograph a decrease of distance between the dots denotes an in- 

 crease of westerly declination, while in the bifilar and vertical-force magnetographs it denotes 

 an increase of horizontal and vertical force respectively. 



