On the obtaining of an Electric Spark/rom aNaturalMagnet.359 



portional to the taxes, of the several boroughs. This new prin- 

 ciple is extensive enough, and may be sufficient ; but as the 

 numbers of each list may be infinitely varied, at the same time 

 that their proportionality is preserved, it is puzzling how to 

 choose ; as we have no clew to guide us. 



Let us try to throw some light on this matter. Find a mul- 

 tiplier 7)1 equal to the number of houses that produce £\ of 

 taxes on an average of all the boroughs ; that is, let 



Number of Ho uses of all the Boroughs 



Amount of Taxes of all the Boroughs in Pounds ' 

 then the importance of a borough may, with sufficient exact- 

 ness, be represented by {/i + m xt), h being the number of its 

 houses, and t pounds its taxes. If this formula be computed 

 for every borough, the results, or any set of numbers propor- 

 tional to the results, will be the scale demanded. 



To point out the reason of this rule, it is to be observed 

 that if the same taxes were levied on every house, we should 

 have mt = h, and the scale would be proportional to the 

 number of the houses of the several boroughs, as ought to 

 be the case : but the taxes varying with the quality of the 

 houses, according as / is less or greater than the average 

 taxes belonging to the number of the houses of a borough, m t 

 will be less or greater than h ; so that a borough will be de- 

 pressed a little on the scale by low taxes, and elevated a little 

 by high taxes. Whether the depression and elevation be ex- 

 actly according to the rules of distributive justice, there is no 

 means of inquiring; they are proportional to the defect and 

 excess of the taxes which the boroughs actually pay below 

 and above the sum which the number of their houses would 

 pay at tlie average rate of all the boroughs, which seems suffi- 

 cient for the practical purposes of Government. 



Be it now observed, that the above simple calculation, which, 

 it may be presumed, is level to every capacity, will bring out 

 the very same scale as Lieutenant Drummond's rules : so 

 that it may be doubted whether the results obtained by that 

 gentleman, when made intelligible, and stript of the covering 

 of functions and variations, can be practically improved. 



April 1832. 



LL On the obtaining of an Electric Spark from a Nattiral 

 Magnet. By James D. Fokbe.s, Esq.^ F.R.S.E., F.G.S., 

 Hon.M.Y.P.S. 



To the Editors of the Philosophical Magazine and Annals. 

 Gentlemen, 

 TF not too late for that purpose, you will oblige me by 

 * making public in the Philosophical Magazine and Annals 



for 



