Dderiiiinatioii of the Earth's Horizontal Magnetic Force. 395 



The case of the temperature terms is less satisfactory. Taking, for 

 example, the mean values of Table I, viz., 



q = 335 x 10-*, q = 14 x 1CT 7 , 



we have 



t' = 10° 20° 30° 



qt' + q'f- = 349 x lCT 3 726 x 10~ 5 1131 x 1CT 5 



Following exactly the same procedure as in the case of P/ ,_2 , we 

 thence conclude that the treatment applied to the temperature terms 

 will on the average begin to introduce error, supposing X = 0-18, 

 when t' reaches 20° C. 



When a magnet with large temperature coefficients is used in hot 

 weather at a place where X is large, the error due to the treatment of 

 the temperature terms becomes very sensible. Suppose, for instance, 



f = 6x 10-*, q = 22 x 1CT 7 , 



values exceeded in one actual case, then we have 



for t' = 35°, 



qt' + q'f 2 = 0-0237. 



This gives an error of approximately 0*0001 C.G.S. unit when 

 X = 0-36. 



Criticism from Physical Standpoint* 



§ 29. Under this heading I shall discuss certain grounds of uncer- 

 tainty which may affect the accuracy of the calculated values of the 

 horizontal force. The considerations are mainly, but not exclusively, 

 physical. 



An objection to both the fundamental formulae (7) and (8) is that they 

 represent all the quantities involved as constant, whereas in general 

 magnetic force and declination, temperature, and moment of magnet, 

 are constantly altering. 



In reality, however, the t appearing in (7) is the mean of two read- 

 ings of a thermometer adjacent to the collimator magnet, taken, the 

 one immediately before, the other immediately after, the vibration 

 experiment ; while the f appearing in (8) is the mean of eight thermo- 

 meter readings taken nearly simultaneously with the individual obser- 

 vations of the deflection angles. There is thus very fair provision for 

 changes of temperature so long as the temperature changes slowly and 

 continuously in one direction, provided the thermometers really record 

 the temperature of the magnet. In a fixed observatory these condi- 

 tions are probably as a rule fairly secured if the magnet and thermo- 

 meter be freely exposed to the air for five or ten minutes before the 

 experiment commences. 



* November 22. — Compare a paper by Wild (which I had overlooked), 'Terre- 

 strial Magnetism,' vol. 2, 1897, pp. 85—104. 



