360 yi?i entirely iieiv Method of extracting 



The Editors of the Connoisiance des Terns say, p. 372, that 

 all the faults imputed to them are unimportant, and efisy to he 

 noticed. M. de Zach asks them, if, when in the estimate of di- 

 stances thev make a mistake of seven degrees, such an error is 

 of no importance ? " If (he adds) the astronomers of Paris have 

 so easy a method of reconciling errors, they would deserve well 

 of science and humanity by communicating the discovery to 

 other nations. But, in the mean time, how nuich reason have I 

 to complain on account of those poor navigators who are gone 

 on long voyages with the Connoissancc des Terns of 1820 for 

 their guide ! May God help them 1" 



LVllI. ^n entirely New Method of exlractifig the Cube Root 

 in Numbers, By Mr. Petkr Nichoj,son. 



To Mr. Tillocli. 



Sir, — xIaving published a work entitled "Analytical and 

 Arithmetical Essays, containing the Demonstrations and Rules for 

 extracting the Roots of Equations of all Degrees," I beg leave, 

 for the promotion of the mathematical sciences, to introduce to 

 the readers of your excellent work thePhilosophical Magazine an 

 entirely new method of extracting the cube root in numbers. — 

 which method 1 consider to be one of the greatest improvements 

 the science of Arithmetic has received for many years, — and I 

 flatter myself that it will also be thought so by others who are 

 capable of appreciating its value. I am, sir. 



Your most obedient servant, 

 London, Nov. 13, 1820. • PetER NiCHOLSON. 



To extract the Cube Root of any Number. 



Divide the number into as many periods of three figures each 

 fvom right to left as possible. Find the nearest cube to the re- 

 maining figure or figures on the left, and subtract that cube 

 from the 'number formed by these remaining figures ; then the 

 root of the cube is the first figure of the root to be extracted. 



Call the triple root now found the first coefficient, the triple 

 square of this root the second coefficient, and the difference be- 

 tween the cube and the number to be extracted the absolute 

 number ; then write these numbers separately in one line. 



1. Divide the remainder by the second coefficient without the 

 last figure only to one place of figures in the quotient. 



2. Under the first coefficient, construct a column of three 

 numbers, so that the right hand figure may advance one place 

 to the right hand of the units place of the coefficient. Under 



^ the 



