Determination of the Earth's Horizontal Magnetic Force. 39D 



If F alters owing to change of temperature in the collimator magnet, 

 its increment SF and the increments 8\f/, 8u in \p and u are connected by 

 the relation 



(F + SF)/X = sin (u + Sw)/cos + 8f). 



But S\p and 8u are equal and so, supposing SF/F small, we have 



SF/F = (cot % + tan f)$U. 



The assumption, tacitly made in practice, that the magnetic axes are 

 perpendicular is legitimate only when we may neglect 



tan xp/cot u. 



The size of the error varies with the moment of the deflecting 

 magnet, and also with the secular change of declination. A slight 

 change is, I think, desirable either in the experimental arrangements or 

 in the calculation.* 



§ 36. A more strictly physical objection to the temperature experi- 

 ment is that in it the changes of temperature are very sudden, whereas 

 in actual use they are gradual. I am not aware of any experiments 

 bearing directly on the question whether a change of from 15° C. to 

 40° C, occupying only a minute or two, has the same temporary effect on 

 a magnet as an equal change occupying as many hours. Theoretically 

 it would be very desirable to make the changes of temperature slow, 

 but in practice this is troublesome, owing to the disturbing influence of 

 changes in declination and horizontal force. A change of 18° C. in the 

 temperature of a collimator magnet at Kew seldom alters the azimuth 

 of the deflected magnet by more than 10', so that it is important to 

 avoid the risk of sensible disturbances so far as possible, even though 

 corrections are applied from the magnetic curves. 



Another objection is that sudden changes of temperature are apt, 

 like mechanical shocks, to permanently diminish the magnetic moment. 

 It is clear that unless such permanent loss is small, satisfactory values of 

 q and q' are unlikely to result from a calculation which assumes that 

 the temperature effects are purely temporary. 



In the normal temperature experiment at Kew the cycle "hot," 

 " mean," " cold " is repeated three times, and the arithmetic mean of 

 the three readings of the deflected magnet's azimuth, answering, say, to 

 the three " hots " is attributed to the temperature which is the arithmetic 

 mean of the three observed temperatures. This method probably 

 eliminates to a considerable extent the influence of permanent changes, 

 supposing them to exist, but it also renders their detection somewhat 

 difficult. To investigate the matter I took a number of temperature 

 experiments, and employing the values found for q and q calculated 



* November. 7. — Since this was written the small necessary change in the appa- 

 ratus has been effected. 



