344 
Proceedings of Royal Society of Edinburgh. [sess. 
Quaternion Notes. By the late Professor Tait. 
Communicated by Professor C. G. Knott. (With a Plate.) 
(Read June 16, 1902.) 
The following quaternion notes are interesting as the last piece 
of mathematical work written down by Professor Tait. During 
his last severe illness he referred several times to the importance of 
working out still further the theory of the linear vector function ; 
but he had not been able to put pen to paper for months previous 
to July 2, 1901, just two days before his death. On that date he 
wrote down the notes now printed, probably at intervals through- 
out the day. They would serve, in all likelihood, chiefly as nuclei 
round which his thoughts would circle ; and they will now serve 
to indicate in some measure the directions in which his thoughts 
were moving. The foolscap sheet on which the notes were written 
was handed to his eldest son, with the request that it should be 
preserved, as he believed it contained the germ of an important 
advance. A facsimile of this sheet, on a reduced scale, is repro- 
duced in the accompanying Plate. 
With the exception of one line, the notes have to do with the 
linear vector function. This one line 
p= +?M_iVaUp.T^ 
represents motion in which the acceleration consists of a resistance- 
retardation directly as the square of the speed, and a component 
perpendicular to the plane containing the radius vector and a given 
constant vector, with a value proportional to the speed and to the 
sine of the angle between the radius vector and the constant vector. 
Had the second term on the right contained Up instead of Up, we 
should have had the case of a rotating projectile moving through 
air, gravity being neglected. This possibly was the intention. I 
think it may be assumed that Professor Tait was for the time 
engrossed with a fresh consideration of his well known golf-ball 
problem. 
