Septembeh 14, 18S3.] 



SCIENCE. 



379 



laborer would be found, for the first class of states, 

 fully $25; for the second, nearly $25; for the third, 

 loss than $20; for the fourth, about $13.50. 



An application of the same test to the value of 

 annual production for each man engaged in agricul- 

 ture brings equally interesting results in the follow- 

 ing table: — 



The states with less than 30 per cent in farm-labor 

 realize nearly three times as much per man as those 

 which have over 70 per cent in farm-work. In other 

 words, one man in the first class realizes as much as 

 the three men who are competing with each other, 

 having little outlet for surplus production. Three 

 brothers in Alabama, laboring through the year, get 

 as much for their aggregate produce as one faimer 

 receives in Pennsylvania, simply bec.aui?e that farmer 

 has a brother engaged in manufacture and another in 

 mining. It is because in one case there is a market 

 for one product only, thousands of miles away: in 

 the other, there are markets at every door. 



It appears evident that the proportion between 

 agricultural and non-agricultural population is a 

 measure of the values of the land, of the production, 

 and of the labor of the farm. These values are rapid- 

 ly enhanced by the increase of non-.tgriculturists. 

 This is the lesson of the most authentic statistics of 

 our own and of other countries. 



A new system for the treatment of sewrer-gas. 



BY T. E. JEFFEKSON, HUDSON, WIS. 



In this paper, which was well illustrated by dia- 

 grams, special reference was made to a series of im- 

 portant inventions which of late have attracted much 

 attention both in this country and Europe. This 

 system chiefly consists in making sewers approxi- 

 mately air-tight by sealing the sewer inlets so as to 

 admit sewage, but exclude the air; making pipe con- 

 nections between sewers and buildings, and different 

 healing-apparatus arranged to admit the in-flow of 

 atmosphere and the products of combustion into the 

 sewer, and, at the same time, prevent the back-flow 

 of gas; when by the connection of a powerful suction 

 apparatus with the sewer, near its outlet, the removal 

 of sewer-gas and smoke from furnaces and fires, and 

 the thorough ventilation of buildings, is positively 

 elTected and regulated as desired. 



liy employing mechanical force for creating draught 

 for fires, the large percentage of heat heretofore re- 

 quired for this purpose is retained, effecting a corre- 

 sponding saving in the consumption of fuel. 



The main portion of these important discoveries, 

 including the removal of sewer-gas, and the positive 

 means of ventilating buildings and carrying the vi- 

 tiated atmosphere and poisonous vapors away from 

 contact with the inhabitants, was recently m.ide by 

 lion. John Comstock of Hudson, Wis., and first in- 

 troduced in one of the districts of the city of Paris, 

 France, dming the present year, wliere its great 

 utility and practical success are fully demonstrated. 



List of other papers. 

 The following jiapers were also read in this sec- 

 tion : Building associations, by Edijur Friahy ; and 

 Health foods, by T. S. llaiijU. 



WEEKLY SUMMARY OF TUE PROGRESS OF SCIENCE. 



MATHEMATICS. 

 HypereUiptic functions. — M. E. Wiltheiss starts 

 out from a memoir of Prof. Kronccker's which ap- 

 peared in the ifonatsberichte of the Berlin academy 

 for the year 1800, in which a method was developed 

 for obtaining the parameters r,* of those theta-func- 

 tions, which, for a certain definite transformation, 

 remain unaltered. Prof. Kronecker started out from 

 a purely algebraical stand-point, and solved the equa- 

 tions which connect the original and the transformed 

 parameters i.t and r'jji. Corresponding to the trans- 

 formation of the theta-functions, there is a transfor- 

 mation referring to the integrals belonging to these 

 functions. Noting this fact, the author of the present 

 paper has arrived at these singular values of the 7,i 

 in another manner, and his results bring into evidence 

 a certain proi)orty which is analogous to the complex 

 multiiilication of elliptic functions. The author con- 

 fines his attention solely to the theta-functions of two 

 variables. — {Math, nnn., xxi.) T. c. [214 



Curvature of surfaces. — M. Rud. Sturm has 

 given here a very interesting theorem analogous to 

 Gauss' well-known theorem concerning the measure 

 of curvature at a point on a surface. Gauss' theorem, 

 stated briefly, is, that if a curve p enclosing an area F 

 is drawn around a point T of a surface, and if a cor- 

 responding curve p' enclosing an area F" is traoed out 

 on a sphere of radius unity by the extremities of 

 radii drawn parallel to the normals to the given sur- 

 face at each point of p, then the limit value of the 

 ratios of F' and F will be equal to the inverse 

 product of the radii of curvature A',, 7{.., of the given 

 surface in the point P. JI. Sturm's theorem is, that 

 if the curve p is cut out of the given surface by a 

 sphere whose centre is at P, then the mean curvature, 



viz., i{jr + ,, ), is equal to the limit value of the 



ratios of the two perimeters p and p'. — {Math, onn., 

 xxi.) T. c. [215 



