428 Intelligence and Miscellaneous Articles. 



while n is fixed at the fairly high value of 500,000, r is taken 

 so small as half a millimetre. 



I wish to add that the value of B/ for alternating currents 

 of any periodicity is really due to Lord Bayleigh, who first 

 fully worked out this question. This acknowledgment, I find 

 to-day on looking up the passage referred to by Mr. Boynton, 

 we have inadvertently omitted. The particular Bessel Func- 

 tion method adopted in the book for obtaining the formula? is 

 the only thing to which we have any claim. 



I remain, Gentlemen, 

 University College of N. Wales, Your obedient Servant, 



Bangor, Sept. 1, 1890. ANDREW GRAY. 



XLIV. intelligence and Miscellaneous Articles. 



A NEW COMBINATION OF WHEEL-GEARING. 

 BY J. J. TAUDIN CHABOT. 

 TF we try to construct a skew-gearing (endless screw) with a 

 J- velocity-ratio of 1:1, we find that the two wheels become 

 identical. These, repeated to any desired extent, are the elements 

 of the model to be here discussed. The structure of the model 

 may be described as follows : — The axes of rotation of the wheels 

 coincide with the oc, y, z and <j), x> ^ axes °f two equidistant 

 systems of rectangular coordinates projecting into each other ; 

 on two of the axes of each of the two systems of coordinates there 

 occur alternately a wheel and a zero-point (point of intersection 

 with the other two axes of the same system); while on the third 

 axis of each system there occur in order a wheel, a zero-point, a 

 space without a wheel, a zero-point, a wheel, and so on in endless 

 repetition. These two last-mentioned axes cross each other at 

 right angles. 



Properties of the Model. 



I. When all the wheels rotate gearing into each other, a negative 

 or positive acceleration of the rotation of one of them causes the 

 rotatory motion — whether of this wheel only or of the wheels 

 directly or even indirectly in gear with it — to be partially trans- 

 formed into a motion of translation. The wheel moves in one 

 direction or the other along its axis of rotation until the accele- 

 ration ceases, or is replaced by one of opposite sign. In the 

 former case the wheel continues to rotate in its new position ; in 

 the latter it returns by a reversed motion of translation to its 

 original place (or goes beyond it, as the case may be). 



II. If translatory motion is continuously maintained, the wheel 

 may pass out of gear with the adjacent wheels, and may even 

 gear in with an independent set of wheels. 



III. The disturbances described under heads I. and II. extend 

 uniformly in all directions throughout a sphere of finite dimensions. 

 The working (regular rotation) of the wheels which at any instant 

 lie outside the sphere of disturbance remains unaffected, even if 

 they belong to the same model. — Communicated by the AutJior, 



