Intelligence and Miscellaneous Articles. 407 



In Mr. A. Cohen's paper, p. 470, I fear that the author's " com- 

 plete sum " will rather confuse terms. His A B is the " complete 

 sum of O A and O B," while it is really less than either ; and the 

 angular opening of O A and O B is totally disregarded, the paren- 

 thesized (O A) and (O B) being a questionable caution-mark. 



It is much to be deplored that Mr. John Long's mode of raising 

 logarithms (Phil. Trans. 1714, ' Hutton's Tracts') has not been 

 generally adopted for teaching in schools. It rests simply on arith- 

 metical notions of progression. Thus log 10=1, log 100=2; let 



N=A.B.C.D.E.F.G, &c, and log A = -^-, log B == — , 



log C= y^» &c„ so that with his Table of the 10th, 100th, 1000th 



parts of 10, we find 10»-«=A,N-r A=B C D,&c. Tabular 10°'° 6 =B; 

 B . C . D, &c. -rB=C . D . E, &c, and thus we finally get 



•a + '05 + '000c-f"000d,&c.=logN 



without any previous algebraic knowledge being required. In countries 

 where the decimal division of coins, weights, and measures is in 

 use, this popular mode of teaching logarithms ought surely to be 

 a branch of primary education, as much as exchanges, equation of 

 payments, &c. 



London, Jan. 12, 1863. S. M. Drach. 



ON A PARTICULAR CASE OF THE FORMATION OF SOAP-BUBBLES. 

 BY M. FELIX PLATEAU. 



Being merely a student of the Faculty of Sciences, I should have 

 thought it premature to submit to the Academy the results of an 

 observation to which chance alone had led me ; but I have yielded 

 to the pressing wish of my father, who finds the observation curious 

 in itself, and important in its bearings on a meteorological question. 



I was emptying a dish containing some waste liquor which had 

 been used for cleaning metal plates, and I tried by darting it obliquely 

 in the air to spread it out as a sheet. I obtained a sheet, in fact, but 

 I was surprised to see it change into a bubble of 8 to 9 centims. in 

 diameter. 



I repeated the experiment several times, simply using soap- water, 

 and I soon succeeded in producing the effect with certainty ; but 

 almost always several bubbles were formed, sometimes as many as 

 fifteen. Their diameter, which might reach 8 to 9 centims. in the 

 largest, was less as they were more numerous. 



The conditions which appeared the best are as follows. A dish is 

 taken about 15 centims. in diameter; success may be obtained, 

 though less certainly, with vessels of other shapes and different 

 dimensions. There ought to be a large quantity of liquid ; it is pro- 

 jected at an angle of about 45 degrees, being turned rapidly on itself, 

 so as to produce the most extended surface possible . The liquid 

 which gave me the best results is a solution of 1 part of Marseilles 

 soap in 40 parts of water. In order the better to make out the mode 

 in which the phenomenon takes place, I observed it from an upper 



