1883.] On Curves circumscribing Rotating Polygons. 319 



or by careful considerations of the conditions of weather and of soil 

 temperature under which each individual set is made. 



As regards hygrometry the data at present obtained relate solely to 

 9 a.m. and to the heights of 4 and 170 feet respectively. The mean 

 relative humidity at these points for nine months of 1882, is given 

 in the following table, which shows that the differences, though some- 

 what larger in summer than at other periods, are not generally of 

 importance. 





Relative humidity. 













4 feet. 



170 feet. 



Difference. 





Per cent. 



Per cent. 



Per cent. 





84 



80 



-4 





75 



77 



+ 2 





79 



78 



— I 





73 



78 



+ 5 





78 



83 



+ 5 





85 



88 



+ 3 





90 



93 



+ 3 





87 



90 



+ 3 





96 



98 



+ 2 





83 



85 



+ 2 



V. " On Curves circumscribing Rotating Polygons with re- 

 ference to the Shape of Drilled Holes." By A. MALLOCK. 

 Communicated by Lord Rayleigh, M.A., F.R.S. Received 

 June 11, 1883. 



It is well known that drills and other tools of the same class which 

 are guided by their cutting edges tend to, or at any rate can produce 

 holes which are not circular in section, and further, that if the tool 

 have n equidistant edges, the hole which it produces, if not circular 

 in section, will have n + \ sides or similar arcs,* but the exact shape 

 of these holes and the limits to their possible departure from circularity 

 have not as far as I am aware been hitherto examined. 



The problem consists in finding all the figures which will circum- 



* These sides are in general very much curved, and in fact are not distinguishable 

 without measurement when n is greater than 3 ; but when n = 2 the departure from 

 the circular form is often very wide. A good instance of this may be seen in the 

 holes bored in rock for blasting. These holes are made by an iron bar with a chisel- 

 shaped end, and the section of the holes is a triangle with the corners rounded off. 

 -Pig. 7. 



