210 Mr. J. R. Ashworth. Methods of making Magnets 



higher roots is given. The earlier roots are examined numerical!}', 

 and tabnlated for four different depths of the ocean for the types 

 involving tesseral harmonics of rank 1 and 2, these types presenting 

 special interest in connection with the dinrnal and semi-diurnal 

 forced tides respectively. 



The types of free oscillation are found to "be of two classes, dis- 

 tinguishable by their limiting forms when the rotation-period is 

 indefinitely prolonged. In the former class the motion remains oscil- 

 latory when the period of rotation becomes infinitely long, while in 

 the latter the " speed " of the oscillation always bears a finite 

 ratio to the angular velocity of rotation, so that the oscillation will 

 be replaced by a steady motion when the angular velocity of rotation 

 is reduced to zero. 



In dealing with the forced oscillations, the theorem of Laplace 

 that in an ocean of uniform depth there will be no dinrnal rise and 

 fall at the surface is obtained and generalised as follows : — In an 

 ocean of uniform depth the tides due to a disturbing potential of 

 degree 5 + 1 and rank s will involve no rise and fall at the surface if 

 the period of the disturbing force be ^(s + l) sidereal days. 



A theorem given by Professor Darwin with reference to the 

 expression of the semi-diurnal tides in finite terms, as also Laplace's 

 solution of the problem of the diurnal tides in an ocean of variable 

 depth, is found to admit of similar generalisation. 



The general problem of the forced tides due to any disturbing 

 force derivable from a potential function in the cases where infinite 

 series are required for the solution is treated analytically, and is 

 further illustrated by numerical examples typical of the leading 

 tidal constituents which occur on the earth, the results where 

 possible being compared with those obtained by other methods. 



u On Methods of making Magnets independent of Changes of 

 Temperature; and some Experiments upon Abnormal 

 or Negative Temperature Coefficients in Magnets." By 

 J. Reginald Ashworth, B.Sc. Communicated by Arthur 

 Schuster, F.R.S. Received October 29, — Read December 

 9, 1897. 



The present investigation, which has been carried out in the 

 Physical Laboratory of the Owens College, Manchester, was under- 

 taken at Professor Schuster's suggestion with the object of ascertain- 

 ing what kinds of iron and steel are least liable to a change of 

 magnetic intensity under moderate fluctuations of temperature. 



Specimens of steels containing severally tungsten, manganese, 

 cobalt, and nickel, also cast irons, of different blends of pig irons, and 



