Jan. 16, 18S5.] 



♦ KNOWLEDGE ♦ 



45 



»k'- 1 /ImY 



the principle we have adopted (i.t' , all the rectauglcs like 

 Q /, R lit, equal) shall briug ua to E. We have found an 

 arithmetical relation which hajipcns to serve our purpose, 

 because we /lajijiin to have desired and utilised the arith- 

 metical function known as a logarithm : if we decline to 

 avail ourselves of this knowledge, we can go no f\irther. 



.1. Let us do so, then, by all means. After all, it was I 

 who invited you to the task. 



M. Taking logarithms, then, we have (using Neperian 

 or natural logarithms), — 



, CE , Ow 

 log^=,<log-^^; 



i Im 1 llm^ 



wherefore, when n is very large, so that I m is very 

 small, and all the terms but the tirst in the above series 

 may be neglected compared with the first, 



C / CE 



H = ; — . log -77-r 



Xow we have divided the space P Z E K into 71 rectangles, 



each equal to Q ,ti . in /, or to F I . I m (it is the same thing 



when H is very large). Hence we have, when n is very 



large, 



sum of rectangles in P / E K = /t . P ? . I m ; or 



CE r.w 1 /CE\ 



^squareDDMog/ — j; 



— =- I ; and 



area A P K L= 1 (sq. on C L - sq. on CD- sq. on E N) 



^^, , CE 

 -sq. ^^' '- 



area P ; E K=C /. P ?. log r_^: 



° CI 



D D'. log : 



CD 

 A. Can the oblique hyperbola be similarly dealt with 1 



Fig. 2. 



J/. Quite easily. I recommend you to go througli the 

 reasoning for yourself, using Fig. 2 instead of Fig. 1, and 

 making such changes as the oblique hyperbola requires and 

 the figure suggests. You will obtain the following 

 results : — 



Area P I E K = rhombus D D' . log (^\ ■ 



area 



ADE K=rhombos D D' . log (—\ : and 



:l= acln- acda- 



-rhombus D D' log/^V 



area APKL= aCLN- aCDA-ANEK 



(To he continued.) 



THE CHKi\118TRY OK COOK Eli Y. 



Bv N\'. Mattiku Williams. 

 I.T.-M.M.TOSE AS A CdOKlXC. AGKMT. 



A FEW years ago the " farmer's friends " were very 

 sanguine on the subject of using lualt as a cattle 

 food, and at agricultural meetings throughout the country 

 the iniquitous mult tax was eloquently denounced because 

 it stood in the way of the great fodder reform. The malt 

 tax was rejiciiled, and the subject fell out of sight anj 

 hearing immediately thereafter. Why was this ? 



The idea of nuilt feeding was theoretically sound. By 

 the malting of barley or other graiu its diastase is made to 

 act upon its insoluble starch, and to convert it more or loss 

 completely into soluble dextrin, a change which is abso- 

 lutely necessary as a part of the business of digestion. 

 Therefore, if you feed cattle on malted grain instead of raw 

 grain, you supply them with a food so prepared that a part 

 of the business of digestion is already done for them, and 

 their nutrition is thereby advanced. 



From what I am able to learn, the reason why this 

 hopeful theory has not been carried out is simply that it 

 does not " pay." The advantage to the cattle is not 

 sufficient to remunerate the farmer for the extra cost of 

 the malted food. 



This may be the case with oxen, but it does not follow 

 that it .should be so with human beings. Cattle feed on 

 grass, mangold-wurzels, &o., in their raw state, but we 

 cannot ; and, as I have already shown, we are not even 

 graminivorous as they are — we cannot digest raw wheat, 

 barley, oats, or maize. 



We cannot do this because we are not supplied with .such 

 natural grinding apparatus as they have in their mouths, 

 and we have a much smaller supply of saliva, besides a 

 shorter alimentary canal. 



We can easily supply our natural deficiencies in the 

 matter of grinding, and do so in our flour-mills ; but at 

 first thought the idea of finding an artificial substitute^for 

 saliva does not recommend itself. When, however, it is 

 understood that the chief active princii)le of the saliva so 

 closely resembles the diastase of grain, that it has received 

 the name of animal diastase, and is probably the same 

 compound, the aspect of the problem changes. 



Not only is this the case with the secretion from the 

 glands surrounding the mouth, but the pancreas, which is 

 concerned in a later stage of digestion, is a gland so similar 

 to the salivary glands, that in ordinary cookery both are 

 dressed and served as " sweetbreads," and its secretion, the 

 pancreatic juice, is a liquid closely resembling saliva and 

 containing a similar diastase, or substance that converts 

 starch into dextrine, and from dextrine to sugar. Lehmann 

 says " it is now indubitably established that the pancreatic 

 juice possesses this sugar-forming power in a far higher 

 degree than the saliva." Besides this there is another 

 sugar-forming secretion, the "intestinal juice," which assists 

 the graminivorous animals in the digestion of raw grain. 

 Thisbeing the case, we should, by exercising our privilege 

 as cooking animals, be able to assist the digestive functions 

 of the saliva and the pancreatic and intestinal secretion, 

 just as we help our teeth in the flour-mill ; the means of 

 doing this is offered by the diastase of malt. 



In accordance with this reasoning I have made some 

 experiments oir a variety of our common vegetable foods, by 

 Eimjily raising them (in contact with water) to the tempera- 

 ture most favourable to the converting action of diastase 

 (140° to 150° Fabr.), and then adding a little malt extract 

 or malt flour. This extract naay be purchased ready made 

 or may be prepared by soaking crushed or ground malt in 



