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 suspending 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 proportions best suited to produce the greatest possible deflection. This is the express object of the small size of the apparatus described, and not merely to render it light 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 relatively 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 reduction 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 linear 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 little or not at all diminished, then we even gain an increase in the angular magnitudes, and it only remains to know how far this increase may be carried.
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 thickness 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.
