General Equation of Differences of the Second Order. 115 



T=C 2 ;<r& + HC<7, 

 V=Q*iak-H.C<n 

 from which 



and from the tangent-galvanometer we have 



_ tang 

 H'~ il ' 



^ Interchanging the two instruments and repeating the expe- 

 riment, we obtain two similar equations with H and H 7 inter- 

 changed. From which 



1 



(7 = 



2CC' 



^v / (T-T')(T''--T ,/ ') tan 6 . tan ff, 



where every thing is known, the values of C and C ; being 

 determinable by the dynamometer from the same readings. 

 a being once known, the horizontal intensity of a magnetic field 

 is determinable by simply setting up the dynamometer so that 

 the axis of its movable coil is at right angles to the meridian, 

 as described above, and then sending the same current through 

 it successively in both directions, the equation being 



A somewhat different use of the dynamometer for the same 

 purpose is given by Kohlrausch in his ' Physical Measure- 

 ments,' p. 180. 



In conclusion I wish to thank Prof. Foster for his kind- 

 ness in allowing me to test my instrument in the Physical 

 Laboratory at University College. My thanks are also due to 

 Mr. W. S. Grant for many valuable hints on the construction 

 of the instrument. 



XIV. On the General Equation of Differences of the Second 

 Order. By Thomas Muir, M.A., F.R.S.E* 



1. " TNDBR the above title, in the i Quarterly Journal of 

 vJ Mathematics/ xiv. pp. 23-25, there is a paper by 

 Professor Cayley, the object of which is to find from the 

 equation 



* Communicated by the Author. 

 12 



