Dr. Lamont on the most advantageous Form of Magnets. 375 



transformed into a mathematical line, i. e. into a so-called 

 linear magnet. 



The most advantageous form of a magnet, so far as the pro- 

 portion of the magnetism to the weight is considered, is there- 

 fore an imaginary one ; practically, however, there are two forms 

 which appear advantageous, namely the fiat, contracting to a 

 point from the middle, and the flat prismatic : and indeed in the 

 former form the proportion of the magnetism to the weight is 

 more advantageous by one-eighth part than in the latter; so 

 that it must always hold as a rule that the thickness and breadth 

 must be as far diminished as the other necessary conditions per- 

 mit. 



We should still have to investigate in what proportion in the 

 above-mentioned forms the magnetism stands to the moment of 

 inertia ; but I consider it superfluous to annex here the tabular 

 exhibitions relative to this, since without such it is easy to see 

 that the form which we have pronounced as disadvantageous in 

 reference to the weight, must also be disadvantageous as regards 

 the moment of inertia. But as respects the flat form contracting 

 to a point from the middle, and the flat prismatic form, which 

 have been noted above as the only appropriate forms, the weights 

 are, with equal length, and equal breadth in the middle, as 1 to 

 2, and the moments of inertia as 1 to 3"75, so that the form 

 contracting to a point must be recognized as by far the best. 



In regard to the preceding investigation, it ought yet to be 

 mentioned that it must prove always too much dependent on 

 circumstantial details, and too little satisfactory, as long as we 

 are not in a position to lay down the laws of the distribution of 

 the magnetism and of the dependence of the magnetic moment 

 upon the dimensions. In this latter point of view the labours 

 hitherto employed have had only very trifling success. From 

 numerous observations which I have made with the prismatic 

 bars, it results that with equal thickness the magnetic moments 

 are in the proportion of the square roots of the thickness ; never- 

 theless this law only obtains for greater transverse sections, and 

 is perfectly unavailable for smaller dimensions. I have now 

 made substitutions in the formula 



V 



,T + C 



where x is the variable dimension, and a, b, c constants ; and I 

 find that it very accurately corresponds with observation in small 

 as in great dimensions. Even when laminae are laid together, 

 this formula represents very well the result, as will be proved 

 by the following Table, in which the second series of experi- 



