Observations on Mr. Newton’s Articles on Algebra. 179 
which dissolves the chloride of silver, while the alloy of osmium 
and iridium remains pure. This may be again calcined with the 
mixture of nitre and potash, to decompose it completely. 
24. Into the solution of iridium, which is of a very deep red- 
dish-brown colour, muriate. of ammonia is to be poured,.and the 
liquid is to be evaporated to dryness, at a gentle heat. The re- 
siduum is to be then treated with alcohol very highly rectified, 
which takes up the excess of sal ammoniac, and occasionally a 
little muriate of iron; because the alloy sometimes contains a 
little of this metal. When the alcohol is no longer coloured, the 
ammonio-muriate of iridium remains pure. It is necessary merely 
to calcine it strongly in a crucible to have pure iridium. This 
metal, being more infusible than rhodium, can be melted only 
in very small quantities by the oxygen on charcoal, or hydrogen 
blow-pipe. 
XL. - Observations on Mr. Nuwton’s Articles on Algebra, 
published in our January and February Numbers. By 
A CoRRESPONDENT. 
To Dr. Tilloch. 
Sir, — Havine read in the Philosophical Magazine for January 
and February last, two letters on algebraic Addition and Sub- 
traction, I beg leave to offer a few remarks on the subject. 
The writer of the letters here referred to observes, that 
“the operations of addition should be restricted to quan- 
tities, whether like or unlike, which have like signs; and that 
that part of addition which consists in collecting quautities, 
whether like or unlike, which have unlike signs, should be classed 
under the rule for the subtraction of simple quantities.” Thus, 
to find the sum (n—m) of n and —™m, is, according to the ob- 
servation above quoted, called an example under the rule of sub- 
traction. In order to judge of the propriety or impropriety of 
classing such an example under such a rule, we must consider 
whether the nature of the proposition contained in the example 
corresponds with the definition of the rule under which such ex- 
ample is placed; for it is not the manner of working the ex- 
ample, but thé thing therein proposed to be done, that must point 
out the rule to which it (the example) belongs. Now as subtrac- 
tion consists not in finding the sums but the differences of quan- 
tities, it is speaking quite contrary to the definition of the term 
(subtraction) to call that an example under subtraction, in which 
(example) it proposed merely to collect quantities together, be 
the nature of those quantities what it may. Hence the above 
Z2 example 
