546 



NAT CRE 



[0(T(^r.KU 3, 1S95 



sure reward in its advancement wherever this method might be 

 applied. So much for these objections. 



New notations in the calculus of quaternions must needs be 

 invented from time to time. But since they arc becoming com- 

 plex (though far simpler than in cartesian coordinates) as the 

 problems are getting more complicated, it is highly desirable 

 already at this stage of development, to exchange opinions on 

 the selection or a<Ioplion of new symbols. 



By these and other considerations we have been led to believe 

 that the lime has come for those who are interested in vector 

 analysis to come to the fore and join hands. In order to 

 further this pur|xisc, we venture to suggest the establishing of 

 something like an '" International .\ssociation for Promoting the 

 Calculus of tjuaternions." The following would be amongst its 

 principal objects : — 



( 1 1 That the members should be informed of the publications 

 f'f " nt papers and works re.specting either the theory of 



q r its applications: and if [Mssiblc to have these 



n -le to them. 



!ie memljers should be afforded the means of 

 f ^ [inions on the introduction and adoption of new 



nutations. 



In these few lines we have tried to point out the im)x>rtant 

 task of the As-sociation, but shall be obliged for any suggestion 

 or improvement. All we desire is to assure to the calculus the 

 pLice it deserves, and consecpiently to see it fully developed in 

 its various aspects by the combined efforts of able mathematicians 

 and physicists. It is alnuist needless to say that we are only 

 preparing the way : and once the Association has been started, 

 we shall \yc ready to place it in the hands of |>ersons much more 

 comixrlent than ourselves to further its best interests. 



We earnestly ho|H: that all friends will appreciate our 

 eri ' - r,il show us at once some token of approval. We 



w ■ -e « ho are in Kurii|ie to comnnmicate with the first 



"! 'clow, and those in .\merica with the second. 



I'. Moi.ENBROEK, The Hague, Holland. 

 -SllfSKlcHl KiMfRA, Vale University, U.S.A. 



August 7. 



P.S. —It has been suggested by friends interested in this 

 matter to enlarge the scoix: of the proposed Association so as to 

 include all systems allied to quaternions and to Grassmann's 

 " .Aus<lchnungslehre." This suggestion we are in full sympathy 

 with. The name of the A-ssociatiun might then be " The Inter- 

 n.itional .\ssociation for Promoting the Study of (^Hi.ilernions and 

 .Allied Systems of Mathematics." p. M. 



.SeptemlHrr 17. S. K. 



Artificial Human Milk. 



It is stated in Natire of September 19, that "so far, 

 according to Dr. Uackhaus, no satisfactory substitute has lieen 

 pro<liiced in the jilace of human milk " ; and a methojl is then 

 described by which he has " <|uite recently" succeeded in 

 supplying the deficiency. It appears to differ little from the 

 process first employed and made known by me in 1854, and 

 afterwards published in my '• Kxpcrimental Researches" in 

 1877 ; except that, in omitting to add the necessary amount of 

 milk-sugar to make up for the deficiency in the cow's milk. Dr. 

 liackhaus fails to obtain an artificial milk closely resembling the 

 human in chemical composition. 



-My recipe has, since its first publication, liccn advantageously 

 used in private and hospital practice by the late Prof. W. C. 

 Williamv.n, by Dr. W. Playfair, and others, but it has probably 

 not loniu under the notice of Dr. Uackhaus. 



.My |irocess is Ijased on the fact that by the removal of one- 

 third of the casein from co»"s milk, and the addition of one- 

 third more milk sugar, a liquid is obtained which closely 

 approaches human milk in com|K)silion. The following is the 

 nnHle of preparing the milk, and it is so simple that any 

 •'■' " 'her or nurse can easily carry it out. 



third of a pint of new milk to stand for .iboul 



'*' »e the cream, and add it to two-thirds of a 



P" fresh from the ifiw as |)ossilile. Inlt) the 



'" ' "f blue milk left after the abstr.iclion of the 



cream, put a piece of rennet alxiul one inch s(juare. .Set the 

 veucl in warm water until the milk is fully curdled, an opera- 

 '"' ' " five to fifteen minutes, according to the 



»' ' '. which .•-hoiild lie removed as .so<m as the 



•^"i K ^...^■. anil put into an egg-cup for use on 



Mifwojuent occasion.*, as it may !« employed daily for a week or 



^•■O- 1353. VOL. 52] 



two. Break up the curd repeatedly and carefully separate the 

 whole of the whey, which should then be lapidly heated to 

 boiling in a small tin pan placed over a spirit- or gas-lamp. 

 During the heating, a further quantity of casein .separates, and 

 must be removed by straining through muslin. Now dissolve 

 no grains of powdered milk-suj^ar in the hot whey, and mix it 

 with two-thirds of a pint of new milk to which the cream from 

 the other third of a pint was added, as already described. The 

 artificial milk should be used within twelve hours of its preixara- 

 tion : and it is almost needless to add, that all the vessels 

 employed in its manufacture and administration should be kept 

 scrupulously clean. ' 



In this process only one-third of the milk was sterilised ; but, 

 in the light of modern bacteriologj'. it is desirable to sterilise 

 the whole by finally heating it to boiling. 



The Vews, Reigate. September 29. H. Kkanki.ami. 



The Elements of Architecture. 



Havi.nc, been for some weeks out of the way of seeing [mpers, 

 I have only just seen the review of " .Architecture for Cieneral 

 Readers" in N.\Tl"RE of .\ugust 15. I ought to thank you for 

 devoting so much space to a book which deals rather with art 

 than "nature," and there are one or two criticisms on special 

 |K>ints which I think are just, and which will have attention in 

 the second edition nf the book. But there are three remarks of 

 the reviewer's on which I should like to have a word. 



(1) He refers the reader to Perrot and Chipiez" work on " The 

 .-Vrts of Primitive Greece " for proof of the derivation of the 

 Greek entablature from a wooden origin. In my opinion, 

 Messrs. I'errot andChipie/. prove nothing whatever but their own 

 ingenuity. They argue in a circle. .Assuming the probability of 

 a wooden origin for the Greek entablature, they proceed to con- 

 struct out of their own inner CL>nsciousness a series iif wcioden 

 structures, quite possible but entirely imaginary, in which 

 the origin of all the features of the stone entablature is carefully 

 provided for, and then produce an engraving of the stone (or, 

 rather, marble) entablature to show triumjihantly the result 

 which they have been consciously leading up to all the way. 

 Vou may prove anythint; on that kind of jiiinciple. I ilo not 

 deny that the Greek entablature appears to be of timber origin. 

 I only say it has not been proved to be so, and I am sure 

 Messrs. Perrot and Chipiez have not proved it. 



(2) The reviewer thinks I am captious in objecting to Wren's 

 double cu|X)la at St. Paid's as a sham, and that I might as well 

 object to the vault which hides the interior of the tower over the 

 crossing in a niediaval cathedral. But he misses the main point 

 of my objection, which is that the exterior liml>er dome of St. 

 Paul's is m.ide to appear, to the eye, to carry a ponderous stone 

 lantern which would, in fact, crush it at once, and which is 

 really the termination of a concealed masonic construction 

 thrusting itself through the timber dome. At l''lorence and St. 

 Peter's the stone lantern is really carried by the visible dome 

 which appears to carry it ; at St. I'aul's it is not, and could not 

 be. I consider St. Paul's by f.ir the more beautiful design of 

 the three, but it cannot be denied that it is a consiruclional 

 falsehood in that itspect. (See the block section of it given on 

 p. 99 of the book. ) 



(3) The reviewer objects that I have denied to Italy any 

 S|x.-cimen of true Gothic, and yet that Milan is one of the most 

 impressive Gothic interiors in existence. This maybe true as to 

 general effect ; but the detail of Milan is wretched : and it is by 

 detail that purity of architectural style is chiefly to be judged. 



II. Ukauicoii-; Staiiiam. 



(1) Mk. SlATllAM objects to Perrot and Cliipiez" work, cm 

 primitive Greece being cited for proof of the derivaticm of the 

 Greek entablature from a wooden origin. 



It seems to me that in this matter possibly the main difference 

 between .Mr. .Statham and the reviewer lies in the meaning to 

 be attached to the \sv\A proof, .\bsolule mathematical proof is 

 seldom to be looked for in archix-ological or historical descrip- 

 tions, and we must be often conlented with a sufliciently hiph 

 prolmbility. Taking the word in that sense, it seems to me that 

 the circle in which Perrot and Chipie/. are said to argue, cannot 

 Iw made to re-enter into itself 



Mr. .Sialham allows that the tireek entablature "a|ipears 10 

 Ik: of timber origin." V'itruvius (iv. cap. 2) says distinctly that it 



s 



