258 



SCIENCE 



[Vol. LVI, No. 1444 



Periodic spasms of the larynx and incessant 

 vomiting continued for the next eight days. 

 The generalized fibrillations gradually dimin- 

 ished in intensity but the clonic jerkings of 

 the temporal muscles persisted together with 

 anorexia and a marked depression. The gastric 

 juice which was vomited up contained appre- 

 ciable free and total acidity. Throughout this 

 period intravenous injection of Ringer's and 

 enemata were freely given. On May 20 the 

 animal seemed decidedly better. Thereafter the 

 condition gradually improved. At the time of 

 writing (May 30) the animal is again free 

 from all s3rHiptoms of tetany. All treatment 

 was discontinued 14 days after the reappear- 

 ance of the tetany. 



In many respects the tetany appearing dur- 

 ing the oestrus cycle of this animal was more 

 severe than the tetany seen the first month 

 following the parathyroidectomy. 



We are in no position to explain the re- 

 occurrence of the tetany with all its severity 

 during the oestrus cycle months after the ab- 

 sense of any sign suggestive of tetany. The 

 facts however seem to show that the tetany ap- 

 pearing in partially strumectomized women 

 during menstruation is due primarily to hypo- 

 function or absence of the parathyroids. As 

 in previous work we observed during the tetany 

 seizures signs pointing to a paresis of the sjrm- 

 pathetic nervous system (enophthalmos), 

 pseudoptosis, paretic nictitating membrane, 

 bradycardia, conjunctival injection, general 

 vasodilation, and a sluggish atonic gastero- 

 intestituil tract. The latter condition (paralytic 

 ileus) would favor the production of toxic 

 products by bacterial action; the splanchnic 

 dilatation (paresis of vasoconstrictor control) 

 would permit of so rapid an absorption of 

 these poisonous products that the liver would 

 be functionally inadequate to neutralize them 

 because of the speed of their delivery (ali- 

 mentary toxemia). As in Eck fistula animals 

 parathyroidectomized animals suffer from an 

 intestinal toxemia. On this hypothesis the 

 reported Ca deficiency in parathyroidectomized 

 animals might well be an effect of the tetany 

 condition rather tlian its cause. 



Aeno B. Luckhaedt 

 J. Blumensoxjck 



Unfversitt of Chicago 



THE ALGEBRAIC METHOD OF BALANCING 

 A CHEMICAL EQUATION 



A CHEMICAL equation is said to be "balanced" 

 when, for each element involved, the number of 

 gram atoms in the left member of the equation 

 is equal to the number of gram atoms in the 

 right member. Given, then, the initial and 

 final substances concerned in a chemical reac- 

 tion, say 



aAg^AsO^ + jgZn -f XH^SO^ = 



SAsH^ + sAg -|-!;ZnSO^ -f 7iH,0 



"balancing" the equation consists in finding a 



set of values for a, j3, X, etc., such that the 



above named condition is fulfilled. 



There are several methods of balancing a 

 chemical equation. With simple equations the 

 necessary coefiieients are at once evident, or 

 become so on brief application of the expedient 

 of trial and error. In more complicated equa- 

 tions, however, the method of trial and error 

 becomes tedious and other methods are con- 

 venient. In an oxidation-reduction reaction, 

 consideration of the valence changes will usu- 

 ally give enough data to enable one to arrive 

 at a solution of the problem, but this method 

 is limited, even in application to such equa- 

 tions. 



The algebraic method of balancing an equa- 

 tion is of general application and will be found 

 time saving in dealing with complex equations. 

 This method is outlined in a few of the text- 

 books, but is not in general use. 



THE ALGEBRAIC METHOD 



The ordinary method of balancing a chemical 

 equation algebraically is a very simple pro- 

 cedure. In the following equation, let a, b, c, 

 etc., represent the coefficients of the balanced 

 equation : 



oAg^AsO^ -|- 6Zn -|- cH^SO^ = 

 dAsH + eAg -f /ZnSO -f ^H^O 



It is obvious that one may write algebraic 

 equations expressing the number of gram atoms 

 of each element involved in the reaction. Thus : 



For silver: 2a := e 



For arsenic: a ^ d 



For oxygen: ia -{- io ^ if -\- g 



For zinc: 6 =; / 



For hydrogen: 2c = 3(J -|- 2g 



For sulphur: o := f 



Since this results in six equations amongst 



