VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 6l 



call rotten. From this it appears that the property of becoming magnetic in 

 brass by hammering, is rather owing to some particular configuration of its 

 parts, than to the admixture of any iron; which is confirmed still further by 

 observing, that Dutch plate-brass (which is made not by melting the copper, but 

 by keeping it in a strong degree of heat while surrounded by lapis calaminaris) 

 also possesses that property; at least all the pieces of it which I have tried, have 

 that property. 



Further dissertations on this matter may be consulted in the latter part of 

 Cavallo's Treatise on Magnetism. 



ir. On Infinite Series. By Edw. Waring, M. D., F.R.S. p. 81. 



In the paper, before printed in these Transactions, on Summation of Series, 

 is given a method of finding the sum of a series, whose general term - is a de- 

 terminate algebraical function of the quantity z, the distance from the first term 

 of the series, which always terminates when the sum of the series can be ex- 

 pressed in finite terms. The terms of every infinite series must necessarily be 

 given by a function of z, or by quantities which can be reduced to a function of 

 z. Dr. W. here pursues the same intricate subject at considerable length, as in 

 his former papers printed in these Abridgments, and in his separate works. 



In the 2d part of this paper he observes that the doctrine of proportional parts 

 was probably very early known in the aera of science; for when men could not 

 find the exact value of a quantity, they were induced to find near approximations 

 by trials, and thence by proportion an approximation still nearer: which method 

 is commonly denominated the rule of false. This was often found to deviate 

 considerably from the exact value; and the same operation was repeated, which 

 frequently produced a nearer approximate value, and so on. This method of 

 approximations, the most general yet known, has been used in resolving pro- 

 blems by several of the most eminent mathematicians in different ages, and in 

 this particularly by M. Euler. 



The following observation, he believes, was first published in theMeditationes, 

 in the year 1770, viz. that the convergency of the approximate values, found by 

 the rule of false and method of infinite scries, generally depended on this, viz. 

 Iiow much nearer the approximate assumed is to one value of the quantity sought, 

 possible or impossible, than to any other, and not to the quantity itself: hence, 

 when two or more (n) values of the quantity sought are nearly equal, it is neces- 

 sary to recur to more difficult rules, viz. to 3 or more trials; as, for example, 

 let 2 roots be nearly equal, and write a, a -j- tt, and a + ^, for the unknown quan- 

 tity in the given equation made = 0, and let the quantities resulting be a, b, and 

 c, then will more near approximations to the two roots nearly equal of the given 

 equation be a + the two roots {pc) of the quadratic 



