1 80 On prime and ultimate Ratios. 



banum, tacamahaca, resin of common jalap, Venice tur- 

 pentine, oil of turpentine, and several other resinous and 

 gummo-resinous substances, gave the same results with 

 those obtained from the scammonies, sandarach, and o!i- 

 banum. From these facts we may infer that it is still dif- 

 ficult to resolve this question : Is it to the presence of an 

 acid in the resins, that we ought to ascribe the reddening of 

 turnsole ? 



► If the acids alone had the property of reddening the blue 

 vegetable colours, we should not hesitate in recognising the 

 existence of this property in the resins, although experiments 

 have not yet proved it. As to the infusion of violets, over 

 which the resins have no action, this property is found in 

 the sublimated benzoic acid, which strongly reddens turn- 

 sole tincture, and which does not change the colour of vio- 

 'lets. Has this acid, notwithstanding its solubility in water, 

 any analogv to the resins ? We shall abstain from deciding 

 on this subject, although we are induced to believe that this 

 substance is a compound of a vegetable acid, and a small 

 quantity of resin, which perhaps gives it the concrete state: 

 lastly, as all the vegetable acids are soluble in water, it is 

 still difficult to ascribe to the presence of an acid, the pro- 

 perty which resins have of reddening turnsole. It seems 

 probable therefore, until some new experiments prove the 

 contrary, that we may regard it as being one of the cha- 

 racters of the resins to redden the blue colour of turnsole. 



XXXIV. On prime and ultimate Ratios; with their Appli- 

 cation to the first Principles of the Jluxionary Calculus. 

 By Mr. Mark at. 



JLyatio denotes the relation which two quantities bear to 

 each other. 



The two quantities must be of the same kind, otherwise 

 no comparison can be made between them. 



The measure of a ratio is obtained by considering what 

 part, or parts, one te. in of the ratio is of the other. Thus, 



let a and b denote the tertns of a ratio, or let y express 



any ratio; then, its measure is had by considering what 

 part, or parts, a is of b, ' 



Let us denote a by 6, and b by 2, then, -|= f, or 3 is the 

 measure of the ratio £ . 



If a=2 and Z/=6, then, ■§.=-] ; or -J- is the measure of 

 the ratio of, |-; and so on for other quantities. 



The 



