404 Simple Contrivance for a Planetary Movement. 



IV. 



ConJlru3ion of a Wheel adapted to exprefs by its Rotation the unequal angular Motion 



of the Planets. By M. Roemer. 



To Mr. NICHOLSON. 

 SIR, 



A. 



^S you have profeflcd it to be part of your plan to infert all difcoverles in your 

 Journal without regard to date, provided they poflefs fufficient merit, and are not fuffi- 

 .ciently known in this country, I take the liberty of recommending to your notice an 

 invention of Angular ingenuity, upwards of a century old, but fo little known, that the 

 (in my opinion inferior, though happy) contrivance of Defaguliers was offered to the 

 public forty years afterwards, and ftill continues in ufe. 



I am, SIR, ' 



Your's, &c. 



R. B. 



If it be defired • to move a wheel of 24 teeth by a pinion of fix, in fuch a manner that 

 in certain parts of its revolutions it (hall move fo fwiftly as if it had but 12 teeth, and in 

 other parts as flowly as if it had 48 teeth, the method of accomplifhing this is as follows : 



1. Defcribe the right angled parallelogram L M N O, Fig. i, Plate XVII. having its 

 fide N O equal to the diameters of the great wheel and the pinion taken together, and its 

 breadth L N equal to their thicknefs, which laft muft be greater, the more confiderable the 

 inequality of the intended movement. 



Divide N Oin Q, in fuch a manner that.Q^O may be to Q^N as 6 to 48, that is to 

 fay, reciprocally as the velocity of the pinion to the greateft velocity of the wheel. 



Divide alfo L M in P, in the proportion of 6 to I2> or reciprocally as the velocity of 

 the pinion tb the fmalleft velocity of the wheel. Then draw P Q^ and as many lines S R, 

 parallel to L M, as there are teeth intended in the great whed, upon which write the de- 

 gree of velocity they exprefs, which are in the inverted ratio of their lengths. 



2. Let two truncated cones be made in the lathe; one equal to what might be formed 

 by the revolution of the trapezium L P Q^M round L N as an axis, and the , other 

 equal to what might be formed by the revolution of the trapezium P Q^M O round 

 the axis MO. 



• In what follows I tranflate and take the figure from the Machines et Inventions approwvees par 

 tAcademie Royale des Sciences for 1699, page 89.— -B. 



