1886.] Estimation of Micro-organisms in the Atmosphere. 443 



off DO equal to twice AD, from D erect a perpendicular, and with 

 radius AC = 3DA cut off DP ; AC and AP are sides of the lozenge 

 ACEP, which fulfils the required conditions. It is manifest that 

 from this lozenge the remaining two lozenges and also the six 

 trapeziums can be immediately constructed. 



The triangular pyramid which terminates the lee's cell may be in- 

 scribed in a sphere whose diameter is three times the side of one of the 

 edges of the pyramid. The base of this pyramid is an equilateral 

 triangle, the side of which is h\/3, and whose circumscribing circle 

 has 2h for its diameter. This diameter is a chord of the spherical 

 segment whose versed sine is x. Hence, if D is the diameter of the 

 sphere in which 2h is a chord, xD = h 2 -\-x 2 , but alsa h=-2*/2x, and 

 s=z3x, whence 



D=9x=3s. 



We have also D = > 2h. 



2V2 



Hence the sphere contains within it all that part of the bee's cell 

 bounded by the three lozenges, together with as much of the hexa- 

 gonal prism as may be measured by twice the side of a lozenge on 

 the shorter edge of the prism. 



This result, together with the extremely simple mode now given 

 for constructing the figure, divests the problem of the complexity 

 and difficulty with which it was formerly sometimes regarded, and it- 

 may also possibly enable the naturalist to more readily explain th% 

 action of the bees in moulding the cells of the honeycomb to their 

 observed shapes. 



II. "A New Method for the Quantitative Estimation of the 

 Micro-organisms present in the Atmosphere." By Percy 

 F. Frankland, Ph.D., B.Sc., F.I.C., F.C.S., Assoc. Roy. 

 Sch. Mines. Communicated by Professor Frankland, 

 D.C.L., F.R.S. Received November 15, 1886. 



(Abstract.) 



The author commences by giving a sketch of some of the more 

 important methods which have been devised for the bacterioscopic 

 examination of air. In these he includes the experiments of Pasteur, 

 who was the first to show that the air at different places varied in 

 the number of micro-organisms which it contained, and of Tyndall,. 

 who proved that the microbes suspended in the air become rapidly 

 deposited in the absence of any disturbing influence. He further 



2 h 2 



