308 The Eev. T. E. Robinson's Experimental Researches on the 



Time = 7" . . . i = 66165 . . . -Fkept at 3-5938 



7 658-34 



7 648-10 



9 647-44 



8 644-58 



From all this it follows that the values given in this Table can be offered only 

 as a first approximation, but I hope a close one. The negative values imply that 

 the polarity is reversed. 



The sixth column contains the factor which gives the change of L due to a 

 small variation of F. It is the coefficient of the first power of the variable in 

 the formula for interpolation when the distances of the values from which it is 

 derived are unequal ; and besides its use in correction of results when there are 

 small diiferences of power, it is given here, because it must be, nearly, what I 

 call it at the head of the column, the first differential coefficient of L in respect 

 of F, and as such may be useful in testing the hypotheses which we form respect- 

 ing the functional relation of these quantities. Into this inquuy, I have stated 

 that I do not intend to enter, and I will at present merely direct attention to the 

 entire want of proportionality between L and F. 



Ascending from No. 26 we find that a current = 0-04 produces a power of 

 10 lbs. ; the addition of a second 0-04 adds 40; of a third, the same ; after which 

 the rate of increase goes on decreasing. No. 13 shows that a unit current will 

 excite an L of 500 lbs., and No. 1 that one nearly sevenfold will add to this only 

 its half. The result is even more striking if we consider column 6. Were L 

 as F, the numbers there should be constant ; whereas they decrease from 1028 

 to 20 ; and were the series continued upwards, must vanish at a certain value 

 of i not very much greater than 800. This leads us to the remarkable con- 

 clusion that L cannot exceed a certain magnitude A, however intense the 

 exciting power may be,* and as a necessary inference, that the separation of 

 magnetic polarities has a limit. For if we revert to the conditions of an excited 

 electro-magnet, which I have noticed at the commencement of this memoir, it 

 is clear that at the surface of contact of the keeper we must have 



= aH + bD - cM - eC. 



* This has been announced by Mr. Joide (PhiL Mag.) ; it was, however, recognised by me long 

 before I knew of his paper. 



