TRANSACTIONS OF THE SECTIONS. 15 



Tlie linear velocity of advance of a wave is expressed by mS, in wliicli S denotes 

 tlie imdistiirlied value of the bullciness. In all the various cases investigated the 

 limit towards which that linear velocity approximates when the disturbance dimi- 

 nishes indefinitely is the well-known value of the velocity of sound. 



On tlie Mechanical Tracinr/ of Curves. By W. H. L. Eussell, F.B.S. 



In this paper the author gave an accoimt of a machine which he has invented for 

 tracing the general equation of the nth. order by continued motion. 



On Professor Christian Wiener^ s Stereoscopic Representation of the Cubic 

 Eihosi-heptagram. By Professor Sylvestee, F.E.S. 



The author produced stereographic drawings sent over to him by Professor 

 Christian Wiener, of Karlsruhe, of tlie famous complex of 27 right lines lying 

 on a cubic surface discovered by Salmon and rediscovered by Steiner. Dr. 

 Wiener, at the request of Professor Clebsch, of Heidelberg, had actually built up a 

 suitable cubic surface, and marked the lines in colours upon it ; from this model 

 the stereograms produced had been photographed. 



On the Successive Involutes to a Circle. By Professor Sylvester, F.R.S. 



The author referred to his communication to the Section at the Meeting held last 

 year at Norwich, " On the General Theory of the Successive Involutes to a Circle 

 now called Cyclodes/' and went on to give an account of a particular kind of 

 cyclode which is the simplest of their respective orders, and from the lowering 

 of the degree which takes place in their arco-radial equation are termed reducible 

 cyclodes. He referred to his researches for determining their number and 

 groupings for any order of derivation, and to a new class of theorems in the 

 Partition of Numbers in which these researches have eventuated. 



A sketch of his conclusions is contained in a Number recently published of 

 the Proceedings of the London Mathematical Society, copies of which were 

 distributed among the Members of the Section present. 



ASTUOKOMT. 



On Secular Variations of Lunar Tints and Spots and Shadows on Plato. 

 By R. W. BiRT, F.E.A.S. 



One of the most promising lines of research having reference to the physical 

 aspect of the moon's surface consists in an examination from time to time of the 

 tints which characterize every portion of the visible disk. To take this in its en- 

 tirety would be a most enormous labour; the only way to deal with a subject of 

 this kind is to select a few of the most prominent objects which differ in brightness 

 and colour, and regularly observe them at stated intervals ; if even half a dozen 

 such objects were selected and observed on every occasion when the moon appeared 

 above the horizon, as the observations proceeded it would be found that not only a 

 large amount of labour must be expended before any valuable results could be ob- 

 tained, but the observations must be continued over a long period of years to eli- 

 minate the effects of those agencies which produce merely apparent changes. That 

 changes of tint and brilliancy occur on the moon's surface is very evident ; no lunar 

 observer is ignorant of the fact that many portions of the surface vary in tint during 

 the course of the luni-solar day ; the variation of brilliancy in many of the brio-hter 

 spots is still more marked during the same period, and these variations havelbeen 

 referred, probably with great truth, to the change of angle at which the sun's lio-ht 

 falls upon the objects, but up to this time we are really destitute of the "proof" 



