134 



Prof. H. Hennessy. Problems in [Feb. 24, 



February 24, 1887. 



Professor STOKES, D.C.L., President, in the Chair. 



The Presents received were laid on the table, and thanks ordered 

 for them. 



The following Papers were read : — 



I. " Problems in Mechanism regarding Trains of Pulleys and 

 Drums of Least Weight for a given Velocity Ratio." By 

 Henry Hennessy, F.R.S., Professor of Applied Mathe- 

 matics and Mechanism in the Royal College of Science, 

 Dublin. Received February 7, 1887. 



Eighty years have elapsed since Dr. Thomas Young* published a- 

 theorem which has since found a place in most of the scientific 

 treatises on mechanism. This theorem states that in order to obtain a 

 given value or velocity ratio by a train of toothed wheels and pinions 

 of which all the pairs are equal, the ratio of the number of teeth in 

 each wheel to the number in each pinion should be as 359 to 100, 

 when the total number of teeth in the train is the least possible. The 

 late Professor Willis has remarked that the rule deduced from this 

 theorem seemed not to have much practical utility, but he illustrates 

 his remarks by referring to the trains of wheels and pinions em- 

 ployed in clockwork. As trains of wheels, pulleys, and drums, are 

 largely employed in many machines whose arrangements greatly differ 

 from clockwork, and especially in the processes of textile manu- 

 facture, it may be interesting to examine whether there are not other 

 conditions, besides the number of teeth, which may be economised in 

 the transformation of a movement of rotation from a moderate rate 

 of velocity to a very high rate of velocity. f As the number of teeth 

 on a wheel or pinion is proportional to the circumference of the pitch- 



* ' Natural Philosophy,' vol. 2, p. 56. 4to. 1807. The preface to this volume 

 is dated March, 1807. 



f In some spinning machines it is said that the spindles rotate with velocities 

 of from 6000 to 7000 turns per minute, and high velocities are also often required 

 for reels, bobbins, and fliers. Between these rapidly rotating parts of the machines 

 and the prime mover, trains of pulleys, drums, or wheels are usually interposed, the 

 value of each such train depending on the required increase of velocity. — [Feb. 21, 

 1887.] 



