37 
of Edinburgh, Session 1872-73. 
In's tastes were for mathematics and physics. lie was employed by 
Government to make a reduction of important magnetic observa- 
tions carried on by two Government ships in the Antarctic regions. 
He was employed at the suggestion of Sir Edward Sabine and Pro- 
fessor Airy, both of whom were well acquainted with his mathe- 
matical powers. The chief value of his services lay in his correct- 
ing the effect on the magnetic observations due to the iron in the 
ships. He afterwards, under the sanction of Government, drew up 
and published an “Admiralty Manual for the Deviation of the Com- 
pass,” a work greatly appreciated, and which has been republished 
in various languages. Mr Smith received from the Eoyal Society 
of London one of its Royal Medals; from the Emperor of Russia, a 
beautiful compass set with diamonds; and from our own Govern- 
ment, a gift of L.2000, in acknowledgment of his important 
scientific services. The three individuals to whom I have now re- 
ferred were each, in their different vocations, distinguished by high 
character, superior talents, and useful lives; and I am sure that all 
present will approve of the tribute of respect to their memory, 
which in name of the Council I have now, however imperfectly, 
attempted to offer. 
The following Communications were read : — 
1. On a Question of Arrangement and Probabilities. 
By Professor Tait. 
Many of the common illustrations of probabilities are taken 
from games in which each hand, or trick, must necessarily be won 
by one player, and lost by the other. It becomes an interesting 
question to inquire what modification is introduced if we contem- 
plate the possibility of a hand, or trick, being drawn — i.e. not won 
or lost by either player. The only difficulty lies in taking account 
of the limiting conditions. 
In the game of golf, for instance, where each hole separately 
may be won, halved, or lost, we have the following question. 
When a player is x holes “up,” and y “to plajq” in how many 
ways may he win ? 
