PETER GUTHRIE TAIT 



give an estimate of the respective probabilities of either player winning. The 

 number of possible draws is obtained from the same fundamental equation, the 

 limiting conditions being P(x, y) = i when x=y, P(x,y)=o when x>y, 

 whether x is positive or negative. The values are represented by the 

 following scheme. 



Thus when the one player is 2 up and 4 to play, the game may be drawn 

 in 10 different ways, and hence the number of distinct ways in which such a 

 game may end is 26 + 5 + 10 = 41 . These schemes were expressed by Tait in 

 a formula based upon the expansion of the expression (a + i + i/a) raised to 

 the power y. 



In a brief paper on a Fundamental Principle in Statics, communicated to 

 the Royal Society on Dec. 21, 1874, Tait compared in a remarkably simple 

 manner the gravitational attraction between the two hemispheres of the earth 

 and the tendency to split across the diametral plane separating these in con- 

 sequence of the earth's rotation. He thus proved that it was gravitation and 

 not cohesion which kept the material of the earth together. A planet of the 

 earth's mean density and of tensile strength equal to that of steel would 

 be held together as much by cohesion as by gravitation if its radius were 

 409 miles. I believe this must be the result referred to by Kelvin in a short 

 letter to Tait, which was written from White's workshop in Glasgow, but of 

 which the date unfortunately had been torn off. It runs 



Dear T' 



I thought as much. It is not the thing I object to but your PFian way 

 of doing it. However enough of that. 



I still think your planet the greatest step in dynamics made in the second half 

 of the i Qth century 



I am up to see new electrometers but find them too unfinished. 



Yours 



T. 



