( 841 ) 



not disappear on shaking for a while, bnt if the liquid was allowed 

 to stand over night it became homogeneous, and on distillation in 

 vacuo yielded diisobutjlformamide. 



Formic esters of unsaturated glycols also seem to react readily 

 with amines, at least Mr. W. van Dorssen, who is engaged iji the 

 Utrecht laboratory upon the study of the 3.4-dihydroxy-J.5-liexadiene 



CH., = CH — CH.Oll 



OH, = CH — CH.OH 

 obtained, on mixing 1 gram of the diformate of this glycol with 1.3 

 gram of benzylamine, a rise in temperature from IS'' to 65^, and after 

 distilling otf the glycol could readily isolate benzylformamide ni. p. 61°. 



Mathematics. — "A local probability problem''. By Prof. J. C. 

 Kluyver. 



The following problem was lately (Nature, July 27) proposed by 

 Prof. Pearson : 



"A man starts from a point 0, and walks / ^^ards in a straight 

 line ; he then turns through any angle whatever, and walks another 

 / yards in a second sti-aight line. He repeats this process n times. 

 I require the probability that after these n stretches he is at a distance 

 between r and ;* -f- dr from his starting point 0." ^) 



I find that the general solution of this problem depends upon 

 the theory of Bessel's functions, especially that in some particular 

 cases it leads to the evaluation of certain definite integrals, involving 

 these functions. 



Let OAA^A^A^ . . . An-\ be 

 the broken line, the n stretches 

 of which need not be all of the 

 same length. Then the shape of 

 the figure, not its orientation in 

 the plane, is wholly determined 

 by the lengths a,a^,a^, . . , rt„_i 

 of the stretches, and by the 

 magnitudes of the angles 

 ^y^i, • • > <Pn—2 , formed at the 

 origin of each stretch a/c by 

 the stretch itself and by the 

 radius vector Sfc—i . 



1) Recently (Nature, August 10) Prof. Pearson stated, that the solution for n 

 very large was already virtually contained in a memoir on sound by Lord Rayleigh. 



