1822.] and Difference of two Arcs. 23 
sin. (A —+A)= sin. A = sin. A cos. 1 A — sin. i A cos. 
Fi, payee eats nv dfcheheihni ate)'sie) aka fatyaristla) sl'siaPbyete!aifelle: ahd jarelye trey syprereye GC) 
cos. (A —+A)=cos.4A=cos. Acos.tA+sin.bA......(f) 
From equation (e) we have sin. A (1 + cos. A) = sin. A 
- 1+ cos. A = 
cos. 1 A; therefore, cot. 1 A = rere From equation (f) 
we have cos. 1 A (l—cos. A) = sin. A sin } A; therefore, tan. 
1—cos. A 
2 A= sin. A 
tions, we obtain tan. 1A + cot. + A = 2 cosec. A; and cot.1 
A — tan. A = 2 cot. A. From whence cosec. A = cot. + 
cot. $A + tan. $A 
; by adding and subtracting the two last equa- 
me ms a. mh We aa Maral agli 
A—cot. A =tan.1 A + cot.A; and Sey A aay AT Bee 
cot. A + tan. A 2 
MGS ciara we POR “Me . 
We also have by the common property of sines and cosines 
cos. 1A + sin.21+ A = 1], and by equation (d) cos.2t A — sin.” 
1A = cos. A; by adding and subtracting the two last equa- 
2 
1—cos. A 
tions, we have sin. 4 A = \/ oo) atid *co8i4. oAviz 
1+ cos. A 
2 < 
~ Articte VII. 
On the Use of Tincture and Braxil Wood in distinguishing seve- 
ral Acids, and ona new Yellow Colour obtained from it. By M. 
P. A. de Bonsdorff.* 
Ir is well known that Brazil wood, when treated with an alka- 
line solution, yields a very fine violet colour. It is on account 
of this property that the tincture of Brazil wood, or paper 
coloured by it, is used in chemistry as a very delicate test of the 
alkalies.+ Besides this property, it possesses another which 
may prove interesting to the chemist; it may be seen by the 
experiments which | had occasion to make on this substance, 
and which are the subject of this memoir, that Brazil wood 
paper may be employed not merely as a delicate test of the 
presence of acids in general, but as a certain means of detect- 
ing several acids, and distinguishing them from each other. 
ith respect to the action of acids upon the red colour of 
Brazil wood paper, it is to be observed; first, that a concentrated 
* From the Annales de Chimie et de Physique. 
+ The chemists of France and England prefer reddened litmus or turmeric paper to 
detect an excess of alkali; but these reagents, and especially the latter, cannot be com~= 
pared as to sensibility with Brazil wood paper. 
