112 On Chemical Equivalents. 



the mechanical addition and subtraction of ratios here performed 

 byjuxtaposition, correspond in effect to the multiplication and 

 division of the luimbers, by which those ratios are expressed in 

 common arithmetical notation. 



In his Essay on the Cause of Chemical Proportions, Berzelius 

 proposed a system of signs, to denote atomical combinations, 

 which it mav l-e proper briefly to explain. This sign is the initial 

 letter, and by itself always expresses one atom, volume, or prime 

 of the substance. When it is necessarylo indicate several volumes 

 or primes, it is done by prefixing the number: for example, the 

 cuprous oxide, or protoxide of copper, is composed of a prime of 

 oxygen and a prime of metal ; its sign is therefore C?i4-0. The 

 cupric oxide, or deutoxide of copper, is composed of 1 prime me- 

 tal, and 2 primes oxygen; therefore its sign is C?/ + 20. In 

 like manner, the sign for sulphuric acid is S + 30j for carbonic 

 acid, C + 20; for water, 2^+0, &c. 



When we express a compound prime of the first order, or 

 binary, we throw away the +, and place the number of primes 

 above the letter, as the index or exponent is placed in arithmetic. 

 For example, Cu04-S0*= suljjhate of copper; CnO' + 2SO^ = 

 bi-deutosu!phate of copper, or persulphate. These formulae have 

 this advantage, that if we take away the oxygen, we see at once 

 the ratio between the radicals. As to the primes of the second 

 order, or ternary compounds, it is but rarely of any advantage to 

 express them by fornmlae, as one prime ; but if we wish to ex- 

 press them in tliat way, we may do it by using the parenthesis, 

 as is done in algebraic formuhe : for example, according to Ber- 

 zelius, alum is composed of 3 primes of sulphate of alumina, and 

 1 of sulphate of potash. Its symbol is 3(A1 0M-2S0^) + (Po^ + 

 2S0'). The prime of ammonia is 3HN ; viz. 3 primes hydro- 

 gen + 1 nitrogen. We shall use these abbreviations in our table 

 of equivalent primes, at the end of the volume. 



To reduce analytical results, as usually given for 100 parts, 

 to the equivalent prime ratios, or, in hypothetical language, to 

 the atomic ))roportions, is now a problem of perpetual recurrence, 

 with which students are perplexed, as no rule has been given for 

 its ready solution. Though numerous examples of its solution 

 occur in this Dictionary, we shall here explain it in detail. 



As in all reasoning we must proceed from what is known or 

 determinate, to what is unknown or indeterminate, so in every 

 analysis, there must be one ingredient whose prime equivalent is 

 well ascertained. This is employed as the common measure, 

 and the proportions of the rest are compared to it. Let us take, 

 for instance. Sir H. Davy's analysis of fluate of lime, to deter- 

 mine the unkho.vn number, that should denote the prime of flu- 

 oric acid. We know, first of all, that 2 primes of oxygen = 2, 



combine 



