40 ON MAGNITUDE [ch. 



same scale the minute iiltramicroscopic particles of colloid gold 

 would be represented by the finest dots which we could make 

 visible to the naked eye upon the paper. 



A bacillus of ordinary, typical size is, say, 1 /a in length. The 

 length (or height) of a man is about a milhon and three-quarter 

 times as great, i.e. 1-75 metres, or 1-75 x 10® /x; and the mass of 

 the man is in the neighbourhood of five million, million, million 

 (5 X 10^^) times greater than that of the bacillus. If we ask 

 whether there may not exist organisms as much less than the 

 bacillus as the bacillus is less than the dimensions of a man, it 

 is very easy to see that this is quite impossible, for we are rapidly 

 approaching a point where the question of molecular dimensions, 

 and of the ultimate divisibility of matter, begins to call for our 

 attention, and to obtrude itself as a crucial factor in the case. 



Clerk Maxwell dealt with this matter in his article ''Atom*,' 

 and, in somewhat greater detail, Errera discusses the question on 

 the following lines f. The weight of a hydrogen molecule is, 

 according to the physical chemists, somewhere about 8*6 x 2 x 10-^^ 

 milligrammes ; and that of any other element, whose molecular 

 weight is M, is given by the equation 



(M) = 8-6 X ilf x 10-22. 

 Accordingly, the weight of the atom of sulphur may be taken as 

 8-6 X 32 X 10-22 jj^gni. = 275 x IO-22 mgm. 



The analysis of ordinary bacteria shews them to consist ± of 

 about 85 % of water, and 15 % of solids; while the solid residue 

 of vegetable protoplasm contains about one part in a thousand 

 of sulphur. We may assume, therefore, that the living protoplasm 

 contains about 



Tooo ^ Too — -L'J A iU 



parts of sulphur, taking the total weight as = 1. 



But our little micrococcus, of 0-15 /x in diameter, would, if it 



were spherical, have a volume of 



77 



7, X 0-15^ u., = 18 X 10-^ cubic microns: 







* Encyclopaedia Britannica, 9th edit., vol. ill, p. 42, 1875. v 



t Sur la limite de petitesse des organismes, Bull. Soc. R. des Sc med. et nat. 

 de Bruxelhs, Jan. 1903 ; Rec. d'oeuvres (Physiol, generale), p. 325. 

 { Cf. A. Fischer, Vorlesungen fiber Bakterien, 1897, p. 50. 



