124, euRious property op single repetends. 



Fig. 2, the extremity of the leaf stalk, at p p, PI, III, fig. 

 $, undivided. 



Fig. 3, horizontal section of the stem of the sensitiye 

 plant. 



Fig. 4, part of a case full of the spiral wire much more 

 magnified than in fig. 8 of PI. III. In many plants it is 

 much thicker, but always loose : that is, it is formed exactly 

 like this, but doubled, or trebled, I imagine to preserve it 

 from the effect the moisture of the nourishing vessels might 

 have on it. 



Fig. 5, the spiral wire still more magnified. 



VI. 



A curious Properly nf Singh Repetends. In a Letter from 

 W. Saint, Esq. 



Cromer, Norfolk, Aug. 10th. 1809. 

 To Mr. NICflOLSON. 



SIR, 



multiples. 



Single repe- /i Friend of mine, some time since, in the process of aa 

 tends dm- arithmetical operation, observed, that any repetend digit, as 

 number^ex- 311111 &c, or 777777 &c, would divide by the odd num- 

 cept 5 and its b ers 3 } y ? g f anc J j [ ; an d supposing it probable, that such 

 repetends would divide by any odd number, 5 and its mul- 

 tiples excepted, he had die patience to try all such divisors 

 from 1 to 151, and found them to succeed, by taking a suf- 

 ficient number of digits for the dividend, which, he observ- 

 ed, never excee de d the number denoted by the divisor. This 

 property of numbers my friend submitted to me for demon- 

 stration, and as it is certainly a very curious one, I thought 

 it probable, that it might not be unacceptable to many of 

 your readers. I have accordingly sent it herewith, in the 

 form of a proposition, accompanied with a demonstration. 

 I am, Sir, 

 Your obliged and humble servant, 

 W. SAINT. 

 Proposition* 



