June 7, 1877J 



NA TURE 



103 



did not receive this letter until May 14, when he sought 

 in vain for the comet. Pingr^ who wrote before any sus- 

 picion liad been raised with respect to D'Angos, attri- 

 buted this to its having in the interval receded to too 

 great a distance from the earth, or having attained too 

 great south declination. It appears that Messier did not 

 receive any further observations from Malta, but D'Angos 

 some time afterwards communicated to him elements of 

 the orbit, calculated by himself, and it was to be presumed 

 with the aid of further positions. The observatory at 

 Malta was burnt at a subsequent period, and the whole of 

 the papers, &lc., of D'Angos were stated to have fallen a 

 prey to the llames, so that it was supposed in France that 

 the observations were irrecoverably lost. Burckhardt had 

 endeavoured by successive hypotheses to extract some 

 idea of the nature of the orbit from the two rough observa- 

 tions which he had received, and as his results differed 

 widely from those of D'Angos, and even the elements of 

 the latter did not represent these observations, Delambre, 

 at the instance of JBurckhardt, wrote for further particu- 

 lars. In reply, D'Angos stated that he had only saved 

 from the fire his meteorological journal, in which, under 

 date April 22, was mentioned an observation of the 

 zodiacal light, without any reference to the comet, whence 

 he concluded that on this date the latter was no longer 

 visible. 



This assertion will appear a most extraordinary one 

 when it is stated that so far from the observations being 

 lost, they had appeared in a memoir drawn up by D'Angos 

 himself, in a periodical conducted by Bernoulli and 

 Hindenberg, entitled — Lcipcigcr Magaziii fiir leiiie und 

 angcwandte Matltcmatik, Leipzig, 1786, where they were 

 discovered by Olbers, as he mentions in a letter to Encke, 

 inviting his discussion of them. Positions of the comet 

 in longitude and latitude are there given for fourteen 

 nights between April 10 and May i, and they are followed 

 by the elements of the orbit, which D'Angos says he had 

 calculated from them. 



Zach in 1S12 had suspected that the observations of 

 the second comet of 1784 were imaginary, and had 

 suggested that the orbit should be omitted from the cata- 

 logues, but he adds as he had only great probabilities 

 and mortl, not mathematical, proofs to support his view, 

 he did not insist upon it. To provoke an explanation, 

 however, he states he had enveloped " ce mystire 

 d'iniquitd " in a problem in vol. iii. of his Corj-cspondaiice 

 Astronoiniqiic, where he printed a series of positions of a 

 body, whicti he invited his readers to explain, and which 

 puzzled Olbers and Bessel who failed, like others, to dis- 

 cover Zach's meaning. Burckhardt also on receiving 

 intimation from Olbers of his having brought to light 

 what purported to be the observations of D'Angos, re- 

 marked upon the importance attaching to the circum- 

 stance, since it might lead to proof that they had been 

 fabricated. 



It remains to describe in a future note or notes, the 

 results of Encke's investigation and of later inquiries 

 relative to the comet of D'Angos. 



PROF. SYLVESTER ON TEACHING AND 

 " RESEARCHING " 



IN the address of Prof. Sylvester at the Johns Hopkins 

 University, to which we have already referred, he 

 spoke as follows on the above subject : — 



Let me take this opportunity of making my profession 

 of faith on a subject much mooted at the present day, as 

 to whether the highest grade of university appointments 

 should be conferred with or without the condition of 

 teaching annexed. 



I hesitate not to say that, in my opinion, the two 

 functions of teaching and working in science should 

 never be divorced. I believe that none are so well fitted 



to impart knowledge (if they will but recognise as existing, 

 and take the necessary pains to acquire, the art of pre- 

 sentation) as those who are engaged in reviewing its 

 methods and extending its boundaries — and I am sure 

 that there is no stimulus so advantageous to the original 

 investigator as that which springs from contact with other 

 minds and the necessity for going afresh to the founda- 

 tions of his knowledge, which the work of teaching im- 

 poses upon him. I look forward to the courses of 

 lectures that I hope to deliver in succession within the 

 walls of this university as marking the inauguration of a 

 new era of productivity in my own scientific existence ; 

 nor need I consider any subject too low (as it is some- 

 times foolishly termed) for me to teach, when I remember 

 to have seen the minutes of the conversation held between 

 the delegates of the Convention, at the time of the French 

 Revolution, and the illustrious Lagrange, the son of the 

 pastry-cook of Turin, possibly the progenitor of the 

 Marquis Lagrange, of turf celebrity (Citoyen Lagrange, 

 as he is styled in the record), who, when asked what 

 subject he would be wiUing to profess for the benefit of 

 the community, answered meekly, " I will lecture on 

 Arithmetic." 



At this moment I happen to be engaged in a research 

 of fascinating interest to myself, and which, if the day 

 only responds to the promise of its dawn, will meet, I 

 believe, a sympathetic response from the Professors of 

 our divine Algebraical art wherever scattered through the 

 world. 



These are things called Algebraical Forms. Prof 

 Cayley calls them Ouantics. These are not, properly 

 speaking. Geometrical Forms, although capable, to some 

 extent, of being embodied in them, but rather schemes of 

 processes, or of operations for forming, for calling into 

 existence, as it were, algebraic quantiiies. 



To every such Ouantic is associated an infinite variety 

 of other forms that may be regarded as engendered from 

 and floating, like an atmosphere, around it — but infinite in 

 number as are these derived existences, these emanations 

 from the parent form, it is found that they admit of being 

 obtained by composition, by mixture, so to say, of a 

 certain limited number of fundamental forms, standard 

 rays, as they might be termed in the Algebraic Spectrum 

 of the Quantic to which they belong. And, as it is a 

 leading pursuit of the Physicists of the present day to 

 ascertain the fixed lines in the spectrum of every chemical 

 substance, so it is the aim and object of a great school of 

 mathematicians to make out the fundamental derived 

 forms, the Covariants and Invariants, as they are called, 

 of these Ouantics. 



This is the kind of investigation in which I have, for the 

 last month or two been immersed, and which I entertain 

 great hopes of bringing to a successful issue. 'Why do I 

 mention it here ? It is to illustrate my opinion as to the 

 invaluable aid of teaching to the teacher, in throwing him 

 back upon his own thoughts and leading him to evolve 

 new results from ideas that would have otherwise re- 

 mained passive or dormant in his mind. 



But for the persistence of a student of this University 

 in urging upon me his desire to study with me the modern 

 Algebra 1 should never have been led into this investiga- 

 tion ; and the new facts and principles which I have dis- 

 covered in regard to it (important facts, I believe,) would, 

 so far as I am concerned, have remained still hidden in 

 the womb of time. In vain I represented to this inquisi- 

 tive student that he would do better to take up some other 

 subject lying less off the beaten track of study, such as 

 the higher parts of the Calculus or Elliptic Functions, or 

 the theory of Substitutions, or I wot not what besides. 

 He stuck with perfect respectfulness, but with invincible 

 pertinacity, to his point. He would have the New 

 Algebra (Heaven knows where he had heard about it, for 

 it is almost unknown in this continent), that or nothing. 

 I was obliged to yield, and what was the consequence .' 



