118 



ON POLYGONAL NUMBERS. 



the coal and ore are landed from the chaiu at the pit head, 

 moving on four small iron w'leels. 



7in. Baskets on which the coal and ore are raised from the 

 pits. 



0. The hook which goes into the staple of the basket to 

 draw it forward when lowering on to the tacking. 



After the basket is lowered, the tacking is drawn forward 

 by two girls to the edge of tht frame, which is laid level 

 with the ground on its outside, and near to which the coal 

 and ore are loaded into waggons, and afterward drawn upon 

 iron rail-ways to the furnaces, forges, &c. 



Fig. 3. A section of a part of the barrel and tire, show- 

 ing the manner the links of the chain lie on it, on a scale of 

 3 inches to the foot. 



Fig. 4. A section of the pulley, with a link of the chain 

 lying in it. 



In a large machine the barrel is fixed 24 or 25 yards from 

 the pit. 



VI. 



Refnarks on Mr. Gough's Essay on Polygonal Numbers : by 

 P. Barlow, Esq. 



To the Editor of the Philosophical Journal, 



SIR, 



On Format's ^^ J'^"'" number for July, the first article is an essay by 

 proposition on John Gough, Esq., in which he has attempted the demon- 

 nunfb stration of a very curious and general j^roperty of numbers; 



but as it appeals to want that perspicuity and simplicity, 

 which are the distinguishing beauty of mathematical rea- 

 soning, I have drawn together the following observations 

 upon it ; which, if you think proper to insert them, will 

 give your readers an opportunity of judging of its merits, 

 more particularly than they may have hitherto done. It will 



also 



