448 THE STATISTICAL METHOD. [BOOK n. 



through which very serious errors were introduced. No comparison 

 of income and output can be considered satisfactory unless at least 

 the carbonic acid produced be directly measured by means of a 

 respiration chamber. And in order that the comparison should be 

 really complete, the water given off by the skin and lungs must be 

 directly measured also ; but this seems to be more difficult than 

 the determination of the carbonic acid. 



In the plan originally adopted by Regnault and Reiset and followed 

 by some other observers, the animal experimented on is allowed to 

 breathe a limited and measured atmosphere. The carbonic acid, as fast 

 as it is formed, is fixed and removed by a strong solution of caustic potash, 

 and the normal percentage of oxygen in the atmosphere is maintained 

 by a supply of this gas from a gasholder. In this way both the oxygen 

 consumed and the carbonic acid produced are directly determined, while 

 the continual supply of fresh oxygen prevents any evil effects due to 

 breathing a confined portion of air. In order however to avoid all 

 possible errors arising from a too restricted atmosphere a different method 

 has been adopted by Pettenkofer and Voit. Their apparatus consists 

 essentially of a large chamber, capable of holding a man comfortably. 

 By means of a steam-engine a current of pure air, measured by a gaso- 

 meter, is drawn through the chamber. Measured portions of the out- 

 going air are from time to time withdrawn and analysed ; and from the 

 data afforded by these analyses, the amounts of carbonic acid (and other 

 gases) and of water given off by the occupant of the chamber during a 

 given time are determined. The oxygen consumed may also be determined 

 by a comparison of the ingoing and outgoing air ; besides if the total 

 amounts of carbonic acid and of water given out by the lungs and skin 

 are thus ascertained and the amount of urine and faeces known, the 

 quantity of oxygen is determined by a simple calculation. For evidently 

 the difference between the terminal weight plus all the egesta and the 

 initial weight plus all the ingesta can be nothing else than the weight of 

 the oxygen absorbed during the period. This method in turn however is 

 also open to objections, since minute errors in the sample determinations 

 acquire by multiplication considerable dimensions. It seems moreover 

 undesirable to leave the quantity used of so important an element as 

 oxygen to be determined by indirect calculations. 



Let us imagine, then, an experiment of this kind to have been 

 completely carried out, that the animal's initial and terminal 

 weights have been accurately determined, the composition of 

 the food satisfactorily known to consist of so much proteid, fat, 

 carbohydrates, salts, and water, and to contain so much nitrogen 

 and carbon, the weight of the faeces and the nitrogen they contain 

 ascertained, the nitrogen of the urine determined, the carbonic 

 acid and water given off by the whole body carefully measured, 

 and the amount of oxygen absorbed calculated what interpreta- 

 tion can be placed on the results ? 



Let us suppose that the animal has gained w in weight during 

 the period. Of what does w consist ? Is it fat or proteid material 

 which has been laid on, or simply water which has been retained, 



