Experimental Mathematics. 395 



This paper is intended to give a general view of the phe- 

 nomena connected with ionization by spraying. It is clear 

 that much more remains to be done in obtaining more accurate 

 relative values, and in determining the sizes and velocities 

 and rates of recombination of the ions from various liquids. 

 The effect of using various gases in place of air has also to 

 be determined. Perhaps other workers may find the field 

 interesting and help to throw light on the subject. If large 

 inert ions may in some cases be stored without entire loss for 

 more than an hour in a closed vessel, it is passible that they 

 may exist for a long period in the opan air. Thus the " gros " 

 ions, found by Langevin, may have an important influence in 

 meteorological phenomena. 



It is important to use liquids free from impurities, and I 

 am grateful to Professor H. Walker for his kindness in pro- 

 viding me with such. I have to thank both him and Dr. D. 

 Mcintosh for advice in matters relating to chemistry. 



XXXV. Experimental Mathematics. 

 By E. A. N. Pochin, B.A* 



MATHEMATICS is an experimental science, just as 

 much as Chemistry or Physics.'' 



This very suggestive statement was made, about a year ago, 

 by a friend who held that everything on earth was done the 

 wrong way, and the teaching of mathematics in particular. 



Being greatly struck by so original a view, I resolved to 

 give it a trial, and selected e for my purpose, as being the 

 first thing to which I could not attach some visible, material 

 meaning. The method of investigation I now place before 

 you, in the hope that it will be of interest, not only in itself, 

 but especially as affording a graphical treatment of logarithms, 

 which may be of use to those engaged i n teaching. 



Here is an instrument, for drawing logarithmic spirals, 

 which is shown diagrammatically in fig. 1. It consists of a 

 metal boss, with a compass-point at its centre 0, and has a 

 smooth steel rod AB sliding freely through it. To one end 

 of this rod is connected a sharp-edged roller D, running in a 

 carriage C, and capable of being clamped at any desired 

 angle with AB by means of a milled nut. Two small guides 

 are added, to keep the carriage upright. By way of illus- 

 tration, I will clamp the roller at 45° to the rod, place it at 

 unit distance — say one inch — from the compass point 0, and 

 pressing it firmly into the paper, push it forward, thus 

 describing the curve which will form the main subject of 

 * Communicated by the Physical Society : read March 22, 1907. 



