444 Mr. H. Wild on a Complete Theory 



vitation-couple. On the other hand, it amounted to only 0'3 

 per cent, in a bifilar of the Pawlowsk Observatory , this instru- 

 ment having cocoon fibres 1*2 metre long. From the consi- 

 deration of the conditions which determine the magnitude of 

 the torsion and gravitation-couples respectively, Prof. Wild 

 concludes that it is not probable that the proportion between 

 them can be reduced much below that which exists in the 

 last-mentioned instrument, namely 0*3 per cent., and hence 

 that the correction for torsion cannot be of negligible amount 

 in accurate observations. 



When this correction is applied, as well as that for induc- 

 tion, the author finds that the differences between the results 

 of calculation and experiment disappear, and that very nearly 

 identical values of the characteristic magnitude of the bifilar 

 magnetometer, namely the so-called " torsion-angle " z, are 

 obtained by both methods. The reader may be reminded that 

 this angle z is the angle which a vertical plane passing through 

 the upper ends of the suspending fibres makes with a vertical 

 plane through their lower ends when the magnet is perpendi- 

 cular to the magnetic meridian. If D be the moment of the 

 directive couple due to the suspension, H the earth's horizon- 

 tal intensity, and M the moment of the magnet, the angle z 

 is defined by the equation 



Dsin^=HM. 



Its magnitude may be found by direct experiment ; or it may 

 be calculated from the periods of vibration of the magnet 

 observed when its position of equilibrium is in the magnetic 

 meridian and its north-seeking pole is towards magnetic 

 north and its south-seeking towards magnetic south respec- 

 tively. If t-i and t 2 are the periods in the two cases, 



.2 f2 



singsct fr" \ 



c 2 + h 



The author observes, in the next place, that the direct de- 

 termination of z, together with the observation of the periods 

 hy hi h (the last being the period of vibration when the posi- 

 tion of equilibrium of the magnet is perpendicular to the me- 

 ridian), affords an excellent method for determining separately 

 the two induction-coefficients of the magnet, namely the coef- 

 ficient of increase and that of decrease of the magnetic mo- 

 ment. The advantages of this method are chiefly that it does 

 not depend upon the mutual action of two magnets, which 

 can be only approximately calculated, and that it requires the 

 use of only one instrument. He also remarks that these advan- 

 tages apply also to the method indicated by him in a previous 



