954 JMh le cerf on ct new-invented 
of feven is to raife 5 1° 25 ^ and fome feconds; one of 
eight is to raife 45 0 ; one of ten is to raife 36°: finally, 
one of twelve mull inconteftably raife 30° per tooth, 
fince 1 2 x 30 = 360. 
§ 5. Amidft various methods that have been ufed for 
the folution of this important problem, I fhall mention 
only the moft firnple one which may be underftood by 
thofe who have the very firft principles of arithmetic. 
§ 6.1 let in motion two wheels, each of twelve teeth. 
By making one wheel turn the other, it is evident that 
thefe two diameters muft be perfectly equal between 
themfelves, allowing for the neceffary fhake between the 
teeth 
(a ) This fhake is very inconfiderable, efpecially when the pinion and the teeth 
of the wheel are properly opened; for,according to my experiments, the deduction 
to be made on this account is reduced to the 96th part of the circumference of a 
pinion 
6 doit lever 6o° par aile, parce que 6 x 60= 360; un de 7 doit lever 51 0 25*-' et 
quelques fecondes; un de 8, 45 0 ; celui de iOj 36°; enfin un pignon de I2> 
doit inconteflablement lever 30° par aile, puifque 12 x 30 — 360. 
§ 5. Entre diverfes regies que Pon a employees pour refoudre cet important 
probieme; on fera mention feulement dela plus firnple et qui fe trouvera a la 
portee de ceux quiauront les premieres notions des elemens de Parithmetique. 
§ 6. Si je fais fon&ionner par engrenage deux mobiles du rneme nombre, que 
}e fuppofe de 12 dents chacun, il eft elair que ces deux diametres doivent etre 
parfaitement egaux entreux (au lochement pres qu’ exige tout engrenage libre*). 
'* Lochement qui fe reduit a ties peu de chofe, fur tout quand le pignons et la denture font 
vuid6s a leur point, car fuivant l’experience que j’en ai faite, cette confederation fe reduit a. 
ivuie rigeur a yn 96® dcla circonference d’un pignon ds 1?, qui produit la fomme d’une S« de 
