86 GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 



must always be small. If, however, all pretensions to great 

 accuracy of measurement are relinquished at the outset, by 

 making the magnetic needle play on a pivot, instead of sus- 

 pending it by a silk thread, the friction of the point renders 

 fineness of measurement quite illusory, and the former much 

 less advantageous plan is the only one that remains open ; the 

 endeavour must then be to adopt the arrangements and pro- 

 portions best suited to produce the greatest possible deflection. 

 This is the express object of the small size of the apparatus de- 

 scribed, and not merely to render it Ught and convenient of 

 transport. 



That the small size of the apparatus does actually allow of a 

 great amount of deflection is evident by the result ; for in the 

 experiments above mentioned all the measured angles exceeded 

 20° : it is easy to explain the reason. 



1. The distance of the deflecting bar from the needle must be 

 relativehj great, but need not be absolutely so : it must at least 

 be three or four times greater than the length of the deflecting 

 bar, or of the magnetic needle. 



2. By diminishing in proportion all the linear dimensions of 

 the apparatus (viz. the dimensions of the magnets, and their 

 distance apart), the angular magnitudes, of which the deflection 

 is one, remain unchanged ; therefore such proportional reduc- 

 tion in the size of the apparatus causes no loss in the amount of 

 the deflection to be measured. 



3. But if instead of diminishing in equal proportion all the li- 

 neal* dimensions of the apparatus, we diminish only the length of 

 the magnets and their distance apart, the breadth and thickness 

 of the deflecting bar being httle or not at all diminished, then 

 we even gain an increase in the angular magnitudes, and it only 

 remams to know how far this increase may be canned. 



The limit depends on a single circumstance, viz. on the 

 breadth and thickness of the deflecting bar, with a given length. 

 Experience has shown, that neither the breadth nor the thick- 

 ness of the bar ought to exceed the eighth part of its length. 

 It follows that the greatest deflection may be produced by a 

 magnet bar, of which the breadth and the thickness are equal, 

 and of which the length is eight times greater than either, and 

 acting upon a magnetic needle, placed at a distance equal to 

 three or four times the length of the bar ; the length of the 

 needle must not exceed that of the bar. 



