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XXXVI. Intelligence and Miscellaneous Articles. 
NOTE ON “qr.” BY R. CHARTRES. 
iG could be easily shown that if two numbers are written down 
at random the probability that they will be prime to each 
other —— 
2 
T 
This affords a simple and interesting method of obtaining an 
approximate value of z. 
Having asked three friends to write down at random five pairs 
of numbers, I found in each case three pairs out of the five were 
prime to each other, giving == = or 7’ =10. 
T 
I did the same with fifty students with the following result :— 

6 sets of five pairs had only one pair prime to each other = 6 
9 3 . Fe two pairs - es = 18 
16 ee ss 2 three ,, : - = 48 
13 3” P) ° four ” oo) 33 aS 52 
6 39 99 *) five 39 39 3° == 30 
Total 50 154 
= 6. 4 q ; 
thus 3 = 950° a= 9-74, or r= 3°12. 
De Morgan obtained a very fair approximation by using Buffon’s 
Problem, that if a needle be allowed to fall on a plane ruled 
surface, the probability of the needle cutting one of the lines 
twice the length of the needle 
~ = times the distance between the lines © 
OBITUARY NOTICE: DR. WILLIAM FRANCIS. 

Dr. Witt1am Francis was born in London on the 16th of 
February, 1817. He was educated at University College School 
and St. Omer. He left St. Omer in 1834 and proceeded to 
Crefelt, but in the autumn of the same year went to Gera, where 
he remained for about two years. In 1836 he returned to England 
and spent a year at the London University (University College), 
afterwards devoting some time to learning the printing business 
under Mr. Richard Taylor, to whom he had been apprenticed some 
time previously. He then went to Berlin, and thence to Giessen, 
where he studied under Liebig, and did much original work, chiefly 
on the salts of molybdenum. He took his degree of Doctor of 
Philosophy at Giessen in 1842. 
He early developed a taste for Natural History, and during 
his stay at Gera he devoted much of his time to entomological study 
and pursuits. While in England, in 1837, “ fresh from the teach- 
ings of Ehrenberg, and profoundly influenced by the spirit of 
scientific research which then, as now, prevailed in Germany,” he 
“‘ suggested to Mr. Richard Taylor the establishment of a journal 
