April 22, 1886] 



NA TURE 



581 



in one way or another, the cavities of the water-conducting 

 elements, and then observing whether the current is inter- 

 rupted. Sachs and Dufour endeavoured to attain this 

 result by sharply bending the stems of actively-transpiring 

 plants, but this method is obviously unsatisfactory, owing 

 to the difficulty of proving that the cavities are completely 

 closed. Elf\ing attacked the problem in a different way. 

 He injected portions of the stem of woody plants with 

 cocoa-butter, melted at a temperature of 30° C, and satis- 

 fied himself that the cavities were really filled up when 

 the injected material had solidified. Under these condi- 

 tions he found that a pressure of 60 cm. of mercury failed 

 to force any water through the wood, though before the 

 injection i cm. of water had sufficed to cause filtration. 



To Elfving's experiment two objections have been made. 

 On the one hand, Dufour urged that the absence of the 

 action of transpiration, rather than the closure of the 

 cavities, might well explain the result of the experiment. 

 On the other hand, it was objected by Scheit that the 

 action of the fatty cocoa-butter on the membranes would 

 probably render them impermeable to water, and thus 

 account for a negative result. Prof. Errera has succeeded 

 in modifying Elfving's method in such a way as to meet 

 both these objections. 



In the first place, actively transpiring branches were 

 emplo)ed for the investigation, Vitis vulpiiia being 

 selected for experiment on account of the large diameter 

 of its vessels. Secondly, instead of cocoa-butter, a solu- 

 tion of gelatine melting at 33° C. was used as the inject- 

 ing material. This was coloured with Indian ink, so 

 that its presence in the vessels might be easily demon- 

 strated. The action of transpiration was in most cases 

 assisted by the pressure of a column of water 50 cm. in 

 height. The experiments were carried out with all pos- 

 sible precautions, and the result in every case was that 

 the injected branches took up no water, and faded in a 

 few hours, while, under precisely similar conditions, un- 

 injected branches remained perfectly fresh for three days 

 at least, and during that time transpired many cubic 

 centimetres of water. For details and numerical results 

 we must refer to the original. 



Prof. Errera's experiments certainly add greatly to the 

 already strong probability that the cavities of the tracheal 

 elements of the wood constitute the channels through 

 which the sap ascends. D. H. S. 



LETTERS TO THE EDITOR 



[ 7 he Editor does Hot hold himself responsibli for opinions express: d 

 by his correspondents. Neither can he undertake to return, 

 or to correspond with the writers of, rejected manuscripts. 

 No notice is taken 0/ anonymous communications, 



[ The Editor urgently requests correspondents to keep their letters 

 as short as possible. The pressure on his space is so great 

 that it is impossible otherwise to insure the appearance even 

 of communications containi72ginteresting and novel facts.'\ 



The Lost Found— Boole Justified and Monge Reinstated 

 in His Rights by Prof. Beman of the University of 

 Michigan, U.S. 



In the report of my public lecture on Reciprocants, published 

 in Nature of January 7 (p. 222), mention is made of a formula, 

 given by Boole in his book on "Differential Equations," which 

 he ascribes to Monge. 



Endeavours were instituted in London, Cambridge, and Paris to 

 ferret out the passage in Monge in which it occurs, and very 

 diligent search was made, as well in the printed works as in the 

 manuscriptsof Monge in the library of the Institute, to accomplish 

 this object. 



But all these researches were fruitless, and the opinion was 

 come to by the compatriots of Monge that Boole had made a 

 misquotation, and that the formula ascribed by him to Monge 

 was not to he found in his works. The formula is one of very 

 great interest, as being the first instance on record of a multi- 

 nomial projective reciprocant. 



Knowing how scrupulous and painstaking Boole was, and the 



least likely of all men to make a quotation at random, I never 

 acquiesced in this belief, but entertained little or no hope that 

 any one would ever succeed in uneai thing a reference which had 

 defied all the endeavours of Monge's own countrymen to verify. 



But fate had designed otherwise, as will be seen from the sub- 

 joined letter. In addition to the satisfaction of a controverted 

 point being settled and Boole's character freed from a rash im- 

 putation of inaccuracy, it is to my mind, and will probably be 

 so to many of the readers of N.'M'URE, a peculiar source oi 

 jjleasure to contemplate the occurrence as an illustration or note 

 of the unity not merely of occupation, but of feeling also, which 

 l)inds together mathematical workers in all parts of the world. 



To think that a task found impossible in London and Paris 

 should have been accomplished in the most satisfactory manner 

 at Yale and Michigan ! 



Without further comment I submit the letter in its entirety as 

 written, for the insertion which it so well merits in the world- 

 wide-diffused c lUmins of Nature, and think that all its readers 

 will join with me in according a cordial vote of thanks to Prof. 

 Beman for his valuable contribution to mathema'ical history. 



University of Michigan, Ann Arbor, Michigan, 

 April z, 1886 

 Prof. J. J. Sylvester, Oxford, England 



Dear Sir, — You will find Monge's form of the differential 

 equation of the conic in his memoir, " Sur les Equations dif- 

 ferentielles des Courbes du Second Degre " (Corresp. sur I'Ecole 

 Polytech. Paris, ii., 1809-13, pp. 51-54), and in Bulhtin de la 

 Soc. Philom,, Paris, 1810, pp. 87, 88 ; the first as having been 

 contributed directly by Monge, and the second as having been 

 copied from the first. 



I have not seen the journals myself, but the references have 

 been verified for me at the Yale College Library. The actual 

 form is " <)q"t - 4Sqrs + 40r^ = o." 



The term " Mongian " can now be used without hesitancy by 

 you. 



I remember noticing this form when I began reading Boole's 

 " Differential Equations," and I also noticed Halphen's method 

 in Jordan's " Cours d'\nalyse." It never occurred to me that 

 Halphen considered the form original with himself ; I thought 

 that his method, probably, of deducing it was different from 

 Monge's. 



With kind recollections of having met you at Johns Hopkins 

 once upon a brief visit when Prof. Cayley was there, 

 I am yours very sincerely. 



W. W. Beman, 

 Assoc. Prof. Math. 



Since writing the above, in fact this very afternoon, I have 

 received a letter from the Universal Knowledge and Informa- 

 tion Office containing the same references as those given by 

 Prof. Beman, which will speak for itself, and cannot fail to draw 

 the attention of the readers of Nature to the important service 

 which this Society is capable of rendering to all engaged in 

 research of whatever nature in enabling them to discover the 

 origins and hunt up the authorities of any subject on which they 

 may desire to obtain information. 



It is certainly a singular coincidence that after the lapse of 

 four months the desired information in this case should have 

 reached me from such widely distant sources at an interval of 

 less than forty-eight hours. The letter, which I inclose, is well 

 deserving of setting out in full. The reference made to the circle 

 at the end is extremely interesting, as it contains an example of 

 a non-homogeneous mixed reciprocant, which in the notation 

 now in use might be written (i + t')b - ya'. Or rather, adopt- 

 ing the improved notation, in which t, a, b, , , . represent 



dy I d-y i d'-'y 

 dx 1.2 fl'jT^' 1.2.3 "'■*"*' 

 it takes the form 



{I -f t')b - 2ta-. 



London, April 15, 1886 

 Dear Sir, — I am instructed by the management to send you 

 the following in reference to your question relating to the attri- 

 bution of the differential equation 



«*-^' 



dx-'] 



d^y d^y d*y 

 5-T— .» ■ -r-« • -7— . + ' 



<S)'==) 



to Monge by Boole in his " Differential Equations." 



