TWENTY-THIBD ANNUAL MEETING. 67 



of the generated content ABC will be aBC+ 6^C+ cAB; and the moments of the 

 generated powers A^, A^, A^, A*, A?, A% A*, A"S A~^ A-% will be 2aA, 3aA-, iaA^, 

 laA-i, %aA^, ^aA--', ^aA'^^, — aA^^, — 2aA-^, — \aA-1 respectively; and in general, 



n-m 



that the moment of any power A'", will be — aA '»■ . Also, that the moment of the 



HI 



generated quantity A^B will be 2aAB-\-bA'^; the moment of the generated quantity 

 A3B^C- will be ^aA-B^C- +4.bA^B-'C'^ + 2cA^B^C; and so on.'" 



We shall now illustrate Newton's method by the notation in common use: 



Let it be required to find the increment of the 

 rectangle ACNK. Let AC=a;; CN=i/; BC = — ^dx; 

 GDr= + Ux; MO = NP= — ^c?{/; NG=-EF= + Jdy. 

 Now, let xy represent the value of the rectangle 

 when it has reached ACNK. First, giving to x and 

 y the increments -\-\dx and +^dy., respectively, 

 and then the decrements — ^d-v and — \dy., we shall 

 have: 



(a), {x -\- \dx) {y + idy)^xy + iydx + ixdy + dx.dy. 



(6). {x — idx) {y — idy)=xy — hydx — hxdy -{-dx.dy. 



Subtract (b) from (a), and there will remain the absolute increase of the rectangle, 

 £. e., ydx-\-xdy. In a similar manner, it can be easily shown that the increment of 

 the volume xyz is xy.dz + xz.dy + yz.dx. Newton's method, therefore, is vastly 

 superior to the others, in that it disposes of dx.dy, dx.dz, dy dz, dx.dy.dz, dx-, dy\ 

 etc., by a mathematical demonstration that is rigorously exact. That is to say, when 

 those higher differentials are used in connection with differentials of the first order. 



AN ELECTRICAL HYGROMETER. 



[Abstract.] 

 BY LUOIEN I. BLAKE, LAWKENOE. 



An hygroscopic substance, as chloride of zinc, is made the electrolyte in a gal- 

 vanic cell. Variations in the amount of moisture in the atmosphere will alter the 

 amount of this electrolyte and consequently the internal resistance of this cell. The 

 cell itself is conveniently made by a strip of zinc and one of copper bridged by a 

 piece of filter paper soaked in ZuCL. By connecting the poles through a sensitive 

 galvanometer the deflections may be used as an indication of the amount of moist- 

 ure present in the air. After five hours the polarization is about 20 per cent., 

 hence it is practically nil during the time of an observation. Comparisons have 

 been made for about a week with a Regnault's hygrometer. While the deflections 

 followed the Regnault's with regularity, as yet the law connecting the amount of 

 moisture and the deflections of the galvanometer has not been fully established. It 

 is believed the instrument may be employed for a simple, inexpensive, and fairly 

 accurate method of hygrometric observations. 



FACIAL EXPRESSION AND ITS PSYCHOLOGY. 



BT A. H. THOMPSON, TOPEKA, KANSAS. 



The human face is said to be the mirror of the soul, because it reflects not only 

 the static intelligence and refinement of the mind, but also betrays its transient 

 emotions and passing impulses. The face is the servant of the emotions. It mir- 



