363 On the improved Dividing Engine. 



D, two stakes a b . well fixed in the ground, in order that 

 they may not shake. Afterwards take with a string the 

 distance from the point D to the point A, or from the point 

 C to B ; double this string and knot it firmly, so that, by 

 placing between the two ends at the exiremity a tracing 

 Slick, it points precisely at the point A, and the stakes C 

 and D are embraced by this siring. 



Then guide the tracing stick, with the siring well 

 stretched but moving freely, from the |)oint A to the point 

 O, and successively to E, F, G, B, H, and finally to A. 



The triangles DC O, DCE, DCF, D C G,' represent 

 the various movements of the string turning upon the two 

 centres of the oval to the points D and C. 



We may always strike an oval, whatever may be the 

 length of the great and small diameter, by taking the dif- 

 ference which is between them, and by sharing out this dif- 

 ference so as that the half of the length which exceeds the 

 great diameter may be subtracted from each extremity of 

 the line A B, or from the greatest diameter. 



Let us suppose, fur instance, that the line AB of the 

 great diameter is 20 metres long, and that the line FH of 

 the small diameter is twelve metres long, it is evident that 

 the great diameter will exceed the small by eight metres, 

 the half of which is four metres. We must therefore place 

 a stake four metres from the point A, i.e. towards C, and 

 another at a similar distance towards D. 



It is right to observe, that the oval will be so much the 

 longer, the nearer the stakes approach the points B and A ; 

 in the contrary case, the oval will more nearly approach the 

 form of the circle. 



LXVI. Comm7inication froip, Mr. J. Allan respecting Ms 

 improved Dividing Engine, for which he received the 

 Gold Medal of the Society of Arts, &c. 



To Mr. Titloch, 



Sir, In compliance with a wish expressed by many, I have 

 long had an inclination to communicate, through the me- 

 dium of your journal, an account of the causes and circum- 

 stances that led me to contrive a self- correcting mathema- 

 tical dividing engine; but the difficulties which individuals 

 unused to literary composition experience in attempts to 

 convey mechanical ideas, and a diffidence in my own powers, 

 operated so powerfully on my mind, that I doubt whether 

 I should yel have ventured, did I not feel my?elf called upon 

 hy a second illiberal attack from an anonymous writer in 



an 



