COMPARISON OF NOTATIONS 129 



method owes so much to you. But before venturing to publish under such auspices 

 I must wait for your own opinion on my investigation itself which I think you 

 may find interesting (though cumbrous) as I see on comparing the two it differs 

 so much from yours ...... 



I am delighted that you intend to publish soon, and as I have already said 

 you may make any mention you choose of our correspondence. 



The next day, Jan. 8, 1859, Tait continued in a letter which he called 

 PS. to 20 : 



Having posted 20 this morning, and having a respite of a couple of hours while 

 3 men are at work preparing our ozone with an electrical machine, I have compared 

 our methods of deducing the equation to the wave. 



Your <j>~* ( ) is the same as my ( _ ), or, as your 8/3 is my CT, and your u my 



= , all our equations can be at once compared by putting 



<fji~ l 8p = or 

 (where each member represents the whole elastic force called into play), 



Your symbol has over mine the great advantage of being separable from the 

 subject, so that you can write 



o = Sfj,~ l ($-* - /*-V/*- 1 . 



Having thus (as I hope) sufficiently allowed the superiority of your notation, 

 I may be permitted to remark that I think mine has one advantage as I have 

 applied it, namely, that of introducing directly the half of your operator <f>~ 1 , or what 

 might be written $~*( ) which will be what I denote by 



(__) or -aiSi( )-bjSj( )-&c. 



I have not time to examine the point, but I fancy that the introduction of 

 <~i into your process would make it even simpler than it is. 



As to the real question at issue I consider myself not to have used your 

 function <f>, as though my notation can be interpreted into something of the same 

 kind it wants the peculiar advantage of concentration which yours possesses, and 

 which forms one distinctive feature of your XV. 



Tait developed this new notation in his letters 22 and 23. Hamilton 

 did not immediately reply to this suggestion, other questions which will 

 be referred to in due course having absorbed his attention. On February 

 5, however, he remarked in [76] of Letter xiv : 



" But let me first get off my hands a remark about the new Form which you 

 suggest for the equation of the Wave Surface. I read it as 



T. 17 



