Scientific Gleanings. 4*71 



his surface of the abnormal bodies moving in the solar sys- 

 tem, which appear to us as luminous meteors and shooting stars. 

 And he conceives that he has shown that there is in those bodies 

 an aboundable supply to keep up the heat of the sun; and that, 

 by the effects of them, the sun may have gone on radiating heat 

 for thousands and thousands of years without the smallest diminu- 

 tion. And this, again, is the result of profound and complex 

 mathematical calculations, — so wide is the domain of mathema- 

 tical reasoning, and so necessary is it in any line of speculation in 

 which we are to convert our ignorance into knowledge. I may 

 mention, as a public example of this, a case which is far removed 

 from the vastness of astronomical phenomena, — a case of the 

 manipulation of mathematical law upon a scale of the smallest 

 dimensions, and in the work of a humble insect. I speak of the 

 form of the cells of bees: a mathematical problem which already 

 attracted the attention of the ancient Greeks, and which has been 

 the subject of mathematical investigation by several of the most 

 eminent mathematicians of modern times, — the most eminent, for 

 being a problem involving the properties of space of these dimen- 

 sions, it requires admirable powers of mathematical conception 

 Upon this subject two communications are promised to the pre- 

 sent Meeting, to be laid either before this Section or the Section 

 of Natural History. And in order further to exemplify the advan- 

 tages derived from the action of the British Association, I may 

 mention another report upon a very different subject, Mr. Cayley's 

 "Report on the Progress of Theoretical Dynamics." The gene- 

 rality, multiplicity, and complexity of the recent labours of analysts 

 in this department of mathematics have been so great that ordi- 

 nary mathematicians cannot hope to follow them by reading the 

 original memoirs; and I am greatly obliged, as one of them, to 

 Mr. Cayley for enabling us compendiously and easily to under- 

 stand what has been done and how it has been done. Perhaps, 

 after all, his report is not so very unlike that of Prof. Powell 

 " On Luminous Meteors, — for the original researches of the great 

 analysts who have treated this subject, though bright and objects 

 of wonder, are so far above our head and so difficult to under- 

 stand, that they are not unlike the things tabulated in the other 

 report. And now, having explained that we must often be neces- 

 sarily difficult to follow in this Section, I must ask the ladies and 

 gentlemen here present, as the Spectator has his readers, to be- 

 lieve that, if at any time we are very dull, we have a design in it. 

 [To be continued) 



