April 20. 1893] 



NA TURE 



593 



in either Hamilton or Tait. The truth is it is all there. 

 Hamilton showed long ago that if 



then 

 where 



<^p = aSKp + ySSjUp + ySyp, 



<p-^p = AjSojP + fiiSfiiP + v^Syip, 



a^Safiy = V0y, &c., X^SK/xv =z V/tv, &C. 



Now Heaviside fusses greatly over this method of inverting (p, 

 and any reader of § 172 ("Electromagnetic Theory," in the 

 Electrician), would infer that the invention of the name 

 dyadic suggestion this demonstration which Hamilton and 

 Tait had somehow missed in their development of " the very 

 clumsy way " of expressing (p-'^p in terms of p, <pp, and <p'^p. But 

 the whole thin<j is given in Hamilton's " Elements" (p. 438, 

 equation xxvii.), and in Tail's "Quaternions" (p. 89, second 

 edition : p. 123, third edition). I would also refer to § 174 of 

 Tait's third edition (§ 162 of the second), a comparison of which 

 with. Heaviside's tall talk in the Electrician of November 18, 

 1892 (§ 171), will show that, on the most lenient hypothesis 

 available, our self-appointed critic of Tait's methods has never 

 really read Tait's "Quaternions." . . . 



All through his system Prof. Gibbs has refused to consider 

 the complete product of two vectors. He has used the form o)3 

 to mean a " dyad " or operator of the form oS;8 or )3So. What, 

 then, can he mean us to understand by the equations — 



md 



\^{da,^ = j J fclvvco ( (2) of § 164), 

 / <lp(o = I \d<T X vw ( (2) of § 165). 



In quaternion notation the last would be written 



/ dpu = j \{dav)i> 



Both equations ate quite correct if and only if dau>, dpw, and 

 Vw are taken in their quaternion meaning of quantities, but 

 Gibbs has wilfully cut himself adrift from this interpretation. 

 How, then, does he interpret these equations ? 



The chief arguments of the paper may be briefly summarised 

 thus :— 



(1) It is maintained that the quaternion is as fundamental a 

 geometrical conception as any that Prof. Gibbs has named. 



(2) In every vector analysis so far developed, the versorial 

 character of vectors in product CDmbinations is implied if not 

 explicitly stated. 



(3) This being so, it follows as a natural consequence that the 

 .>-quare of a unit vector is equal to negative unity. 



(4) The assumption that the square of a unit vector is positive 

 unity leads to an a'gebra whose characteristic quantities are 

 non-associative, and whose v is not the real efficient Nabla of 

 quaternions. 



(5) The invention of new names and new notations has added 

 practically nothing of importance to what we have already 

 learned from quaternions. 



EXPERIMENTAL MEDICINES 



'T'HIS volume is the fourth number of this remarkable pub- 

 ^ lication, and will prove of surpassing interest to the bac- 

 teriologist, physiologist, and physician, chiefly on account of 

 the first paper which it contains." 



In 1877 Dr. N. V. Eck invented an operation by which it 

 was possible to alter the circulation in such a manner that the 

 blood flowed from the portal vein into the inferior vena cava 

 without passing through the liver. He succeeded in establish- 

 ing an artilicial opening between these veins in several dogs, 

 and then tied the portal vein near the liver ; unfortunately, 

 only one dog lived for any length of time (two and a half months), 

 and, owing to an accident. Dr. Eck was unable to control the 

 result by post-mortem examination. The operation has now 

 been repeated at the St. Petersburg Institute, and it has been 



' "Archives des Sciences biolo;iques publicds par I'institut imperial de 

 m^decine experimentale Ji St. Pe'tersbourg," vol. i. no. 4. 



'■' "La fistule d'Eck de la veine cave infirieure et de la veine porte, et 

 sescons<iquencespourrorKanisme,parMM. les Drs. M. Hahn, V. Massen, 

 ^ Nencki, et J. Pawlow." 



1235. 



47] 



fonnd that in successful cases the blood passed entirely from the 

 portal vein into the inferior vena cava. 



The animals which successfully resisted this severe operation 

 .•showed no alteration in the appetite, though after a period of 

 ten days or so 1 heir temper underwent marked changes. Although 

 perfectly docile before the operation, they now became bad- 

 tempered, bit everything that came in their way, and showed 

 undue excitement on trifling provocation. The animals became 

 weak, and their gait ataxic, whilst ihe sensory apparatus was 

 also greatly disturbed, as they often became blind, and appeared 

 to lose all sensation of pain. In a further stage convulsions 

 and coma supervened ; though the animals occasionally re- 

 covered perfectly after a time, many of them died v\ hen the 

 first attack of excitement and convulsions occurred, or suc- 

 cumbed to subsequent attacks, although, on the whole, the latter 

 rarely proved fatal. The temperature showed no changes 

 attributable to the veinous fistula, but the weight generally 

 diminished until death supervened, although, in animals which 

 recovered it reached, or even exceeded, the original weight. 

 The appetite was good, though capricious ; but a distinct rela- 

 tion was found to exist between the state of the alimentary 

 canal and the attacks of excitement before mentioned. The 

 animals which absolutely refused to eat meat remained free 

 from the attacks, while the "crises" invariably occurred in the 

 dogs that ate meat voraciously. It is a remarkable fact that 

 many of ihem learnt by experience that meat was bad for them, 

 and declined to take it. 



Some dogs recovered perfectly, and at the postmortem it was 

 found that a collateral circulation had been set up, so that the 

 portal blood again circulated through the liver. 



It would appear from further observations that these symptoms 

 are due to the toxic action of the products of the transformation 

 of nitrogenous food, the liver being unable to convert them into 

 urea and uric acid. Carbamic acid was found in the urine of 

 these animals, and carbamate of sodium or calcium, when intro- 

 duced into a healthy animal's stomach, produced exactly the 

 same symptoms as the fistula above described. On the other 

 hand, it was found impossible to poison healthy dogs with the 

 same salt, provided the setting free of carbamic acid was pre- 

 vented by the simultaneous introduction of carbonate of soda 

 into the stomach, while the introduction of both salts gave rise 

 to all the symptoms of carbamic acid poisoning, when the circu- 

 lation through the liver had been interrupted. The authors 

 conclude, therefore, that the carbamates formed during digestion 

 in passing through the liver are transformed into a harmless 

 substance, and that this substance is most probably urea. 



In some cases the experimenters removed the entire liver ; but 

 the animals never lived more than six hours, and fell at once into 

 a comatose state, followed by convulsions, tetanus, and death 

 through arrest of the respiration. Similar results were obtained 

 by establishing a veinous fistula in the first place and tyuig the 

 hepatic artery afterwards. 



According to Messrs. Hahn and Nencki, who performed the 

 chemical part of these observations, the reaction of the urine 

 remained normal until one of the attacks of excitement set in, 

 when it became alkaline. If the hepatic artery were tied at the 

 same time, the urine contained a little albumin and hivma- 

 globin, together with small quantities of urobilin and biliary 

 pigment, provided the gall-bladder had not been emptied before 

 the operation. The quantity of urea was always greatly lessened 

 if the hepatic artery were also tied, or the greater part of the 

 liver removed. The relation of the nitrogen in urea to the 

 total quantity of nitrogen excreted was much smaller than 

 normal, being only 77 per cent, instead of 89 per cent. On the 

 other hand, the uric acid in the urine ultimately increased in 

 quantity, even when the hepatic artery was not tied, althf ugh 

 the total quantity of nitrogen excreted was not greater than 

 normal, the increase in the uric acid corresponding to the 

 setting in of the convulsions. With regard to the ammonia 

 contained in urine, the authors have come to the following con- 

 clu'ions : — (i) Eck's operation, combined with the ligature of 

 the hepatic artery, causes in dogs an increase in the excretion of 

 ammonia. In some cases this increase is relative only with 

 regard to the nitrogen of urea or the total nitrogen, whereas in 

 other cases it is absolute, and this absolute increase takes place 

 when the animals survive the operation for twenty hours at 

 least ; (2) the secretion of ammonia increases rapidly in animals 

 which have been subjected to Eck's operation as soon as the 

 first symptoms set in. 



In a further series of researches the authors showed that car- 



