

round the Needle of a Galvanometer" 37 



paper Professor Holman endeavoured to show that the state- 

 ment put forward by Messrs. Ayrton, Mather, and Sumpner 

 (Phil. Mag. July 1890) as to the extent of the waste space 

 round the needle of a galvanometer, a statement which, as 

 he said, I had adopted in my book on l Absolute Measurements 

 in Electricity and Magnetism,' was vitiated by neglect of the 

 non-uniformity of the field produced at the needle by the 

 current in a turn of wire of the coil ; and that, when this was 

 taken account of, the true extent of such space was found to 

 be comparatively trifling. 



At first sight Professor Holman's contention, based on a 

 calculation of the turning moment exerted on each element of 

 the magnet by the field at the element, seemed plausible ; 

 but on more closely examining the matter, I have found that 

 no correction whatever of the statement is required, and that 

 Professor Holman has, by omitting a term in the expression 

 for the total turning motive due to the forces on an element 

 of the needle, been led to an erroneous result. 



In trying to show what the omission made by Professor 

 Holman is, I shall not directly use the hypothesis of imaginary 

 magnetic matter, but shall regard each element of length of the 

 needle, supposed straight, infinitely thin, and uniformly mag- 

 netized in the direction of its length, as made up of a very 

 large number of uniformly distributed molecular magnets, 

 each practically infinitely small in every respect in comparison 

 with the element of the magnet used in integrating up the 

 action of the external field on its parts, and all perfectly 

 aligned along the axis of the needle. This seems a preferable 

 mode of regarding the magnet in the circumstances, as it has 

 regard to the physical facts of the case and avoids the appear- 

 ance of begging the question involved in arranging beforehand 

 a series of equal and opposite surface distributions on those 

 faces of adjacent slices which are in contact, and then showing, 

 what is obvious, that no magnetic matter exists for force to 

 act upon except on the end-faces of the needle. As a matter 

 of fact, however, the results of the two processes are equivalent. 



Let, then, the magnet be suspended horizontally so as to 

 be free to turn round a vertical through its middle point ; 

 let F (Professor Holman's/cos 6) be the magnetic force per- 

 pendicular to the magnet's length at a point of the magnet 

 distant s from the centre. Consider an element of the magnet 

 of length ds having its centre at the point s ; let the couple 

 exerted on the element of the magnet when placed at right 

 angles to the lines of force in a uniform field of intensity 

 unity be mds, so that the magnetic moment of the aggregate 

 of molecular magnets in unit length is m. If we take F as 



