338 PHILOSOPHICAL TRANSACTIONS. [aNNO 1753. 



XII. A Second Letter of the Rev. William Henry, D. D. concerning the Copper 



Springs in the County of JVichlow in Ireland, p. 94. 



This is only a confirmation of the former account of procuring copper by 

 means of iron bars laid in the stream of copper-water. He further remarks, that 

 to prevent any dirt or mud from being carried out of the mines, by the streams, 

 which are let into the pits, where the iron bars are deposited, the stream, as it 

 issues out of the level, is collected into a large deep basin, where all the dirt sub- 

 sides ; and the clear water only is from the surface of the basin let out into 

 the pits. 



XIII. The Construction of the Logarithmic Lines on the Gunters Scale. By 



Mr. John Robertson, F.R.S. p. 96. 



The Gunter s scale (so called from its inventor Mr. Exlmund Gunter, astro- 

 nomy professor in Gresham-college, from March 6, 1619, till his death, Dec. 

 10, 1626,) is an instrument almost universally known, and amply described by 

 many writers ; therefore Mr. R. only shows on what principles the divisions of 

 the logarithmic sines, tangents, and versed sines, are usually protracted. 



The line of numbers on these scales consists of 2 equal lengths, commonly 

 called 2 radii ; the first containing the logarithms of numbers from 10 to 

 100; and in the second are inserted those between 100 and 1000, or such of 

 them as can conveniently be introduced. These divisions are taken from a 

 scale of equal parts ; such, that 1 00 make the length of one radius ; and from 

 this scale, the divisions for the sines, tangents, and versed sines, are also 

 taken. Now, from this construction of the line of numbers, it is plain that, as 

 the numbers in one radius exceed those in the other, by one place in the scale 

 of numeration ; therefore the difl^erence of their indices must also be unity ; so 

 that such numbers only, whose index differs by 1, can be estimated in a length 

 of 2 radii : but in a length of 3 radii, numbers, whose indices differ by 2, may 

 be read ; and a difference of 3 may be reckoned in a length of 4 radii, &c. The 

 tables of logarithmic sines, tangents, secants, and versed sines, are generally 

 computed for a circle, whose radius is 10,000,000. 



As the length of the Gunter s scale admits of no more than 2 radii, or of such 

 numbers only whose index differs by unity ; therefore, within this lengtli, no 

 more of the sines, tangents, or versed sines, can be introduced, than those 

 whose index differs by unity : and as not only the greatest number among the 

 sines and tangents, but also those more generally wanted, have the indices 9 and 

 8 differing by unity ; therefore all the sines from 90° to o" 34', and all the tan- 

 gents from 45° to 0° 34', are those only which are put on these scales ; the divi- 

 sions answering to the lesser sines and tangents being omitted for want of room. 



