Appreciation of Ultra-visible Quantities. 425 



upon the methods employed in dynamical inquiries, as pointed 

 out in a Paper by the present author on t{ Texture in Media." 

 [Scientific Proceedings of the Royal Dublin Society, vol. vi. 

 p. 392 ; Phil. Mag. for June 1890, p. 467.] 



2. The direct bearing of the inquiry upon chemistry is 

 obvious. It is briefly referred to in the Scientific Transactions 

 of the R. D. Society, vol. iv. p. 608. In fact the record of 

 the chemist is not unlike what one often sees upon a tomb- 

 stone — " Born in such a year ; Died in such another ; " — 

 while the intervening life is passed over in silence. So the 

 chemist submits two or more substances to their mutual 

 influence, and finds that such and such substances emerge ; 

 but he takes little note of the eventful time during which all 

 the protracted contests of the reaction have taken place, which ; 

 if it has lasted for only the five-hundred- thousandth of one 

 second, has been as long in reference to the activities of the 

 molecules as a long life of 60 years would be in reference to 

 all the thoughts and actions of a man. 



3. The minimum visibile, as defined above, is between the 

 fourth and fifth of a micron, and a speck whose volume is the 

 cube of this may be regarded as the smallest organic speck 

 that the biologist can distinguish from other specks by the 

 highest powers of his microscope. Its volume is accordingly 

 about one-hundredth of a cubic micron — about the l/7000th 

 part of the volume of one blood-corpuscle. Now, liquid or 

 solid material, if resolved into its chemical elements, and if 

 these be brought into the gaseous state, will, at the tempera- 

 ture and pressure of the atmosphere, expand about 1000 times. 

 Hence the foregoing speck, if thus resolved into gas, would 

 occupy about ten cubic microns. But this volume of gas at 

 that temperature and pressure contains about a uno-ten 

 (10,000,000,000) of molecules, which for the most part will 

 consist each of two chemical atoms. Hence the number of 

 chemical atoms in our speck may be taken to be about two 

 uno-tens. Our speck, perhaps, consists of very complex 

 organic molecules ; but however complex each of these may 

 be their number must nevertheless be very great. For, let 

 us make the liberal allowance of 2000 chemical atoms for each 

 organic molecule, and the number of these very complex 

 molecules will be about ten millions. This is an army quite 

 large enough to admit of an immense amount of differentiation 

 within its ranks — of very active operations within and among 

 the complex molecules or between brigades of them — all of 

 which are ultra-visible events. These are facts which every 

 biologist should keep constantly before his mind when carry- 

 ing out his investigations and interpreting them, and especially 



