43 S On the Benefit that may he expected. 



ma nc 



For v as -~ , therefore —. a= — „ or ma : ml : : ?zc : fti : 

 d' mb nd ' 



where m or n may be either whole numbers or fractions. 



Article XII. — If there be four quantities, such that 



a : b 1 1 c : d y and four others, such that c : d : : e :f, then 



will a : b : : e :f. 



For, since -7- = - ■ = - , therefore a : b : : e : f. 

 o d J J 



The above articles contain nearly all that is necessary to 

 fee understood concerning proportional quantities ; and by 

 students who know how to manage a simple equation in al- 

 gebra, they will be read without much difficulty in a very 

 short time. Not being ineumbered with equimultiples, the 

 demonstrations are general, and will serve equally for either 

 commensurable or uncommensurable quantities. Very little 

 indeed of what I here send you can be said to be entirely 

 new: it is presumed, however, that the principles on which 

 the above demonstrations are founded, are laid down with 

 more clearness and precision than in any author who has 

 written on this subject. By inserting them in your valuable 

 Miscellany, you will very much oblige your very humble 

 servant, Wm. Maruat. 



Boston, 

 May 18, 1809. 



LXXVI. A few Hints concerning the Benefit that may he 

 t xpectpd from the Nature of Coal Gas* 



To Mn. Tilloch,-— Sir, 

 X hk gas which is obtained when coal is distil red in close 



Is having lately attracted the attention of the public, 

 chiefly on account of its application for the production 

 of artificial light, has encouraged me to lay before your 

 readers a few observations concerning this subject, which 

 bids fair to be ranked among the most beneficial applica- 

 tions of chemical science to the useful purposes of so- 

 ciety. I will leave it to your judgement to abridge of these 

 lines, or to cancel, whatever you deem unworthy of notice, 

 to make room in your journal for more valuable subject* 



yot 



