496 



• KNOWLEDGE . 



[Dkc. 19, 1884. 



Yet we are told that " the performance of work may be 

 looked upm as necessitating a proportionate supply of 

 liitrogenous alimentary matter," and that such material " is 

 split up into two distinct portions, one containing the 

 nitrogen, which is eliminated as useless." This thesis is 

 proved by experiments showing (as asserted) that such 

 •elimination is not so proportioned. 



In short, the modern theory presents us with the follow- 

 ing pretty paradox : — The consumption of nitrogenous food 

 >M proportionate to work done. The elimination of nitrogen 

 ■is W)t proportionate to work done. The elimination of 

 Eitrogen is proportionate to the consumption of nitrogenous 



food. 



I have tried hard to obtiin a rational physiological 

 view of the modern theory. When its advocates compare 

 ciur food to the fuel of an engine, and maintain that its 

 combustion directly supplies the moving power, what do 

 ■i hey mean % 



They cannot suppose that the food is thus oxidised as 

 ■food ; yet such is implied. The work cannot be done in 

 the stomach, nor in the intestinal canal, nor in the mesen- 

 teric glands or their outlet, the thoracic duct. After 

 leaving this, the food becomes organised living material, 

 the blood being such. The question, therefore, as between 

 the new theory and that of Liebig must be whether work is 

 effected by the comhuslmi of the blood itself or the degrada- 

 tion of the working tissues, which are fed and renewed by 

 the blood. Although this is so obviously the true physio- 

 logical question, I have not found it thus stated. 



Such being the case, the supposed analogy to the steam- 

 engine breaks down altogether ; in either case, the food is 

 assimilated, is converted into the living material of the 

 animal itself before it does any work, and therefore it must 

 be the wear and tear of the machine itself which supplies 

 the working power, and not that of the food as mere fuel 

 material shovelled directly into the animal furnace. 



I therefore agree with Playfair, who says that the 

 .modern theory involves a "false analogy of the animal 

 -body to a steam-engine," and that " incessant transforma- 

 won of the acting parts of the animal machine forms the 

 oondition for its action, while in the case of the steam- 

 engine it is the transformation of fuel external to the 

 machine which causes it to move." Pavy says that " Dr. 

 Playfair, in these utterances, must be regarded as writing 

 behind the time." He may be behind as regards the 

 fishion, but I think he is in advance as regards the truth. 



My readers, therefore, need not be ashamed of clinging 

 to the old-fashioned belief that their own bodies are alive 

 throughout, and perform all the operations of working, 

 ifeeling, thinking, ic, by virtue of their own inherent self- 

 -contained vitality, and that in doing this they consume 

 their own substance, which has to be perpetually replaced 

 hj new material, the quality of which depends upon the 

 2nanner of working, and the matter and manner of replace- 

 cnent. We may thus, according to our own daily conduct, 

 fee building iip a better body and a better mind, or one 

 that shall be worse than the fair promise of the original 

 germ. The course of our own evolution depends upon our- 

 selves, and primarily upon the knowledge of our own 

 {)hysical and moral constitution, and their relations to the 

 external world. Of such knowledge even the humble 

 element supplied by "The Chemiatry of Cookery" is one 

 tWt cannot be safely neglected. 



Intimately connected with the preparation of the 

 ir.aterials that internally sustain and renew our bodies, is 

 ihat of protecting them externally. I have accordingly 

 arranged with Mr. Proctor to follow this series (which I 

 ■hope to conclude in my next) with another — necessarily 

 ^h'oitei- — on " The Philosophy of Clothing." 



CHATS ON 

 GEOMETRICAL MEASUREMENT. 



By Richard A- Proctor. 



{Continued from p. 458.) 

 THE CO NIC SECTIONS. 



A. I have been thinking over the method of treating 

 areas which we considered in our last conversation. It 

 seems to me that while the method is sound enough, it is 

 in some degree artificial. Take for instance the example 

 you gave, that of the cycloidal area ; — by a certain arrange- 

 ment you were able to compare the area with that of the 

 generating circle. But, in any case, taken at random, how 

 can you till that this or that particular method of slicing 

 up your area will avail to make the several parts of it com- 

 parable with the several parts of some known area ? 



M. Well ; how can you tell that any particular method 

 of dealing with a complicated algebraical or trigonometrical 

 expression, will result in simplifying it t In geometry, as 

 in other matters (even in business matters), we can but try 

 such methods as seem likely to help us. 



A. But I am told that analytical methods are sure, in 

 these cases. 



^f. That is far from being the case. When you deal 

 with an area by analytical methods, yoa get an algebi-aical 

 or trigonometrical expression, — let us say, — for one of the 

 minute elements into which you have sliced up your area, 

 and you very often see at once from this expression that 

 the area can be obtained by the process known as integra- 

 tion. But often enough the expression you obtain is not 

 one you can deal with as it stands Then you have to 

 apply tentative processes, which may or may not lead to a 

 solution. Of course, the more you know about the ana- 

 lytical treatment of various expressions, the more likely 

 you are to succeed quickly by the analytical methods : but 

 a similar truth holds in regard to geometrical work also. 

 Moreover, you will find that there is no surer help to 

 success with analytical methods, than a knowledge of the 

 various geometrical methods, and practice in their applica- 

 tion. These underlie, in rea'ity, the analytical methods, 

 and later on in your studies you will find great interest in 

 taking your analytical work and seeking the geometrical 

 interpretation of every process, nay of every line in it. 

 However, let us resume our subject. 



A. You promised to take the area of a parabolic segment 

 next. 



M. I did. But on consideration, we had better begin 

 with the more familiar curve, the ellipse. 



A. Can we afterwards go on to the hyperbola t 

 M. Hyperbolic areas are not to be dealt with geometri- 

 cally quite EG easily as the ellipse and parabola. In fact, it 

 is impossible to make any exact geometrical statement 

 about the area of a hyperbolic segment. It has been sug- 

 gested — but, perhaps, mistakenly — that Shakespeare had 

 been working on some hyperliolic area when he wrote the 

 impatient words, " Out hyperbolical fiend ! why vexest 

 tlioi this man ? " 



A. It seems not unlikely. But had we not better turn 

 to the ellipse 1 



M. Let A6 A'6' (Fig. 1) be an el'ipse, axes A A', bV, and 

 let circles be described having these axes as diameters. 

 Now, if any radius as Qq Q is drawn to these concentric 

 circles, then, by a well-known property, Q M and q m (pro- 

 duced) meet at P, a point on the ellipse. We may con- 

 veniently take this property for use in dealing with the 

 area of the ellipse. Complete the diagram, and mark in 

 letters, as in the figure. Now, P M bears to Q M the same 

 ratio that C q bears to C Q, or C i to C B. Hence, if we 



