Intelligence and Miscellaneous Articles. 



671 



a random sampling from the Gaussian curve in 15 or 16 cases on 

 an average out of 10,000,000 trials. This result depends upon 

 the value of \ calculated for 11 groupings being 45-811. Dr. 

 Macdonell has just indicated that there is a regrettable slip in the 

 arithmetic. Taking 12 groupings, the value of •% should be 

 34*7485, or taking only 11 groupings, as Mr. Merriman does, the 

 value of x 2 i s 34*6269. In the first case the odds against Mr. 

 Merriman's data as a random sampling from a normal distribution 

 are 3667 to 1, and in the second case 6915 to 1. These odds, 

 while far less than those cited above, are, 1 consider, more than 

 sufficient to justify all my criticism of such treatment of the curve 



of eiTors * I am, Gentlemen, 



"Faithfully yours, 



Karl Pearson. 



AN ERROR IN DR. WILLOWS S PAPER " ON THE ABSORPTION 

 OF GAS IN A CROOKES TUBE." 



To the Editors of the Philosophical Magazine. 

 Gentlemen, — 

 It is doubtless difficult for anyone to preserve the historical 

 unities when he finds at the end of a long investigation that his 

 observations do not differ from those of previous observers. This 

 is probably why Dr. Willows quotes me as saying that the gases 

 in a vacuum-tube go out through the glass walls, and fails to state 

 that his conclusion that gases combine chemically with the glass 

 is simply a confirmation of my previous observations recorded in 

 the papers from which he incorrectly quotes. It was Tesla who 

 stated that the particles went out through the glass walls. I was 

 careful to state this in my papers mentioned by Dr. Willows. I 

 showed that the glass became discoloured, that when the surface- 

 colour due to metal had been dissolved there remained a purple 

 colour which was in the glass, and that this colour could be dis- 

 charged by heat, gas being evolved in the process, and that in the 

 gas 1 found the hydrogen spectrum. Perhaps the most interesting 

 observation in the papers mentioned in connexion with disap- 

 pearing gases was that there was no practical way of introducing 

 fresh gas which would enable the tube to go on giving a brilliant 

 -r-light with a reasonable amount of energy. I also showed that 

 we depend on gas amalgamated with the terminals to produce an 

 efficient cathode-stream and .r-light ; therefore when this supply is 

 becoming exhausted, simply introducing any of the common gases 

 will not restore the pristine brilliancy of the .r-light, that it is 

 necessary to restore the proper material to the terminals. 



1 am, Gentlemen, 



Yours faithfully, 



William Kollins. 

 ■ioO Marlborough Street, Boston, U.S.A. 

 May 7th, 1901. 



