406 THE PRINCIPLES OF SCIENCE. [chap. 



by the power of the telescope and other conditions, so our 

 knowledge of the minute world has its limit in the powers 

 and optical conditions of the microscope. There was a 

 time when it would have been a reasonable induction that 

 vegetables are motionless, and animals alone endowed 

 with power of locomotion. We are astonished to dis- 

 cover by the microscope that minute plants are if any- 

 tliing more active than minute animals. We even find 

 that mineral substances seem to lose their inactive 

 character and dance about wdth incessant motion when 

 reduced to sufficiently minute pnrticles, at least when sus- 

 pended in a non-conducting medium.^ Microscopists will 

 meet a natural limit to observation when the minuteness 

 of the objects examined becomes comparable to the length 

 of light undulations, and the extreme difficulty already 

 encountered in determining the forms of minute marks on 

 Diatoms appears to be due to this cause. According to 

 Helmholtz the smallest distance which can be accurately 

 defined depends upon the interference of light passing 

 through the centres of the bright spaces. With a the- 

 oretically perfect microscope and a dry lense the smallest 

 visible object would not be less than one 8o,oootli part 

 of an inch in red liglit. 



Of the errors likely to arise in estimating quantities by 

 tlie senses I have already spoken, but there are some cases 

 in which we actually see things differently from what 

 they are. A jet of water appears to be a continuous 

 thread, when it is really a vi'ondert'ully organised siuicps- 

 sion of small and large drops, oscillating in form. The 

 drops fall so rapidly that their impressions upon the eye 

 run into each other, and in order to see the separate drops 

 we require some dtvice for giving an instantaneous view. 



One insuperable limit to our powt^rs of observation 

 arises from the impossibility of following and identifying 

 tlie ultimate atoms of matter. One atom of oxygen is 

 probably undistinguishable from another atom ; only by 



^ This curious pheiioiiienoii, wliiili I propose to call pede.ns, or the peddic 

 movnncnt, from TrnScw, to jimiji, is carcliilly described in my paper pulJlislitHl 

 in the Quartcrli/ Jour mil of Science for April, 1S7S, vol. viii. (N.S. ) 

 p. 167. See also Proceedings of the Literary and Pliilosopkieal Societij 

 of Manchester, 25th January, 1870, vol. ix. j). 78. Nature, 22nd Auf^ust, 

 1878, vol. xviii. p. 440, or the Quarterly Journal of Science, vol. viii. 

 (N.S.) p. 514. 



