478 



the theory of atoms by which these facts are explained is by no means 

 of importance to the present inquiry. It is by means of a series of 

 numbers computed according to the method of Richter, that this 

 scale is constructed so as to answer at one view the very numerous 

 questions that occur to an analytic chemist in the examination of 

 any saline compound. It is similar in principle to the common 

 sliding rule, and like that instrument has the usual Gunter's line of 

 numbers on the slider ; but upon a line adjacent to the slider are 

 marked certain points corresponding to those numbers which repre- 

 sent the various chemical elements, acids, alkalies, and other com- 

 pounds intended to be included in the present view. By motion of 

 the slider any one point of the line of numbers, as 100, may be made 

 to correspond with the point indicating any compound, as sulphate 

 of potash. By the position of the point for sulphuric acid, this salt 

 is seen to contain 46 of acid, and the other ingredient potash at the 

 same time corresponds with 54 on the slider. By the position of 

 the point for sulphate of barytes, it appears that 135 of this pre- 

 cipitate would be obtained from 100 of the salt, and in the same 

 manner that it would yield 176 of sulphate of lead, with a great 

 variety of similar answers respecting the equivalent quantities of 

 other compounds in which the same quantities of acid or neutralizing 

 base is contained. 



Since the line of numbers is so divided that a given space of every 

 part of it corresponds to numbers that bear a given ratio to each 

 other, and since the intervals on the adjacent column of equivalents 

 are all laid down according to certain given portions of the same 

 scale, they directly indicate by juxtaposition numbers that are in 

 the same proportion on any part of the scale that may be presented 

 to them, as will be very evident to those who are acquainted with 

 the common properties of other sliding rules. 



For the sake of those who may not be accustomed to the use of 

 the sliding rule, and for the purpose of recommending that valuable 

 instrument to more general use, the author enters rather more than 

 might otherwise be requisite into the elementary principles of logo- 

 metric division. 



Methods of clearing Equations of quadratic, cubic, quadrato- cubic, 

 and higher Surds. By William Allman, M.D. Communicated by 

 the Right Hon. Sir Joseph Banks, K.B. P.R.S. Read July 8, 

 1813. [Phil. Trans. 1814, p. 23.] 



In a paper communicated to the Royal Irish Academy by Dr. 

 Mooney, the method of exterminating any number of quadratic 

 surds is pointed out by successively squaring them when brought 

 alone to one side of the equation ; and the present is an extension 

 of the same method : first, to all surds whose indices are any integral 

 power of 2, as the fourth, eighth, sixteenth, thirty-second power, &c.; 

 and next to cubic surds, and to any number of surds whose common 

 indices are in any manner compounded of the factors 2 and 3 ; next 



