Hoyal Society. 385 



in fluxions, — nz z = -^ — ^^s 



-3n-i . y!i±3fyy±rt . 



and z z — — —^3 > 



^ , — Al -3«-i. }^y+V!ry+fVy. 



therefore, az —J \ z x = — ^^3 > 



and its fluent is — — 5 — — "T ^ 



no' na 



30/ + 84^ + 7Qr _ a% —f\-y.ZOax, +24afz +l6f 

 105 "~ "~ lOona' 



" tTI^ 2 n ^ 2n 



_1 a— /x r 30a +24nfz + ififz 



105na^ 



„ |A 2 72 2 2n 



fl-Jz r X 30a + 24afz + l6f z 



•^ ^ , which was to be 



found. 



J. A. 



LVIII. Proceedings of Learned Societies. 



KOYAL SOCIETY. 



April 30. A LETTER to the President from Capt.Maun- 

 sell was read, describing the peculiar appearance of three 

 coronae or suns which he observed at Plymouth, some time 

 since. The author had often seen two coronie, but never 

 before three j the rainbow colours which formed these solar 

 circles were in the inverse order in which they usually ap- 

 pear. 



May 7. A very long paper, communicated by Mr. 

 Brown of the Linnean Society, from Dr. Allman, on the 

 figures of the tubes and pores of plants, was read. Dr. 

 Allman having been led to investigate the cells and tubes 

 of plants during a course of botanical lectures, observed 

 that they might all be reduced to some regular geometrical 

 figure. He then proceeded to demonstrate mathematically 

 thtit the various tubes of plants necessarily assume octahe- 

 dral, dodecahedral, or other geometric figures, either sim- 

 ple or combined. In the conclusion of this paper, which 

 does not admit of analysis. Dr. A. acknowledged the merit 

 of the labours of Mirbcl and Decandolle on this branch of 



vegetable 



