Page:Encyclopædia Britannica, Ninth Edition, v. 17.djvu/193

Rh OF MERCHISTON.] N A P I E K 181 to the Chilias (1617) Briggs states that the reason why his logarithms are different from those introduced by Napier &quot; sperandum, ejus librum posthumum, abunde nobis propediem satisfacturum.&quot; The &quot;liber posthumus&quot; was the Construct (1619), in the preface to which Robert Napier states that he has added an appendix relating to another and more excellent species of logarithms referred to by the inventor himself in the Eabdologia, and in which the logarithm of unity is 0. He also mentions that he has published some remarks upon the propositions in spherical trigonometry and upon the new species of logarithms by Henry Briggs, &quot;qui novi hujus Canonis supputandi laborem gravissimum, pro singular! amicitia quce illi cum Patre meo L. M. intercessit, anirno libentissimo in se suscepit ; creandi methodo, et usuum explanatione Inventori relictis. Nunc autem ipso ex hac vita evocato, totius negotii onus doctis- simi Briggii humeris incumbere, et Sparta liEec ornanda illi sorte quadam obtigisse videtur.&quot; In the address pre fixed to the Arithmetica Logarithmica (1625) Briggs bids the reader not to be surprised that these logarithms are different from those published in the Canon Miriftcus : &quot;Egoenim, cum meis auditoribus Londini, publice in Collegio Greshamensi horum doctrinam explicarem ; animadvert! multo futurum commodius, si Logarithmus sinus totius servaretur (ut in Canone mirifico) Logarithmus autem partis decimse ejusdem sinus totius, nempe sinus 5 graduum, 44, m. 21, s., essct 10000000000. atque ea de re scripsi statim ad ipsum authorem, et quamprimum per anni tempus, et vacationem a publico docendi munere licuit, profectus sum Ediuburgum ; ubi liumanissime ab eo acceptus hsesi per integrum mensem. Cum autem inter nos de horum mutatione sermo haberetur ; ille se idem dudum sensisse, et cupivisse dicebat : veruntamen istos. quos jam paraverat edendos curasse, donee alios, si per negotia et valetudinem liceret, magis commodos confecisset. Istam autem mutationem ita faciendam censebat, ut esset Log arithmus unitatis, et 10000000000 sinus totius : quod ego longe commodissimum esse non potui non agnoscere. Coepi igitur, ejus hortatu, rejectis illis quos antea paraveram, de horum calculo serio cogitare ; et sequent! sestate iterum profectus Edinburgum, horum quos hie exhibeo pnecipuos, illi ostendi. idem etiam tertia restate libentissime facturus, si Deus ilium nobis tamdiu superstitem esse voluisset.&quot; There 13 also a reference to the change of the logarithms on the title-page of the work. 1 These extracts contain all the original statements made by Napier, Robert Napier, and Briggs which have reference to the origin of decimal logarithms. It will be seen that they are all in perfect agreement. Briggs pointed out in his lectures at Gresham College that it would be more convenient that should stand for the logarithm of the whole sine as in the Canon Mirijicus, but that the logarithm of the tenth part of the whole sine (that is to say, of the sine of 5 44 21&quot;) should be 10,000,000,000. He wrote also to Napier at once ; and as soon as he could he went to Edinburgh to visit him, where, as he was most hospitably received by him, he remained for a whole month. When they conversed about the change of system, Napier said that he had felt and desired the same thing, but that he had published the tables which he had already prepared, so that they might be used until he could con struct others more convenient. But he considered that the change ought to be so made that should be the logarithm of unity and 10,000,000,000 that of the whole sine, which Briggs could not but admit was by far the most convenient of all. Rejecting therefore those which he had prepared already, Briggs began, at Napier s advice, to consider seriously the question of the calculation of new tables. In the following summer he went to Edinburgh and showed Napier the principal portion of the logarithms which he published in 1624. These probably included 1 The title runs as follows : Arithmetica Logarithmica, sive Log- arithmorum chiliades triginta,. , . Hos numeros primus invenit clarissimus vir Johannes Neperus Baro Merchistonij ; eos autem ex eiusdem sententia mutavit, eorumque ortum zt usum illustravit Henri- cus Briyrjius. , . . the logarithms of the first chiliad which he published in 1617. Unfortunately Hutton in his history of logarithms, which was prefixed to the early editions of his Mathematical Talks, and was also published as one of his Mathematical Tracts, has charged Napier with want of candour in not telling the world of Briggs s share in the change of system, and he expresses the suspicion that &quot; Napier was desirous that the world should ascribe to him alone the merit of this very useful improvement of the logarithms.&quot; Accord ing to Button s view, the words &quot; it is to be hoped that his posthumous work &quot;. . . . which occur in the preface to the Chilias, were a modest hint that the share Briggs had had in changing the logarithms should be mentioned, and that, as no attention was paid to it, he himself gave the account which appears in the Arithmetica of 1624. There seems, however, no ground whatever for supposing that Briggs meant to express anything beyond his hope that the reason for the alteration would be explained in the posthumous work ; and in his own account, written seven years after Napier s death and five years after the appearance of the work itself, he shows no injured feeling whatever, but even goes out of his way to explain that he abandoned his own proposed alteration in favour of Napier s, and, rejecting the tables he had already constructed, began to consider the calculation of new ones. The facts, as stated by Napier and Briggs, are in complete accordance, and the friendship existing between them was perfect and unbroken to the last. Briggs assisted Robert Napier in the editing of the &quot;posthumous work,&quot; the Constructio, and in the account he gives of the alteration of the logarithms in the Arithmetica of 1624 he seems to have been more anxious that justice should be done to Napier than to himself; while on the other hand Napier received Briggs most hospitably and refers to him as &quot;amico mihi longe charissimo.&quot; Hutton s unfair suggestions are all the more to be regretted as they occur in a history which is the result of a good deal of investigation, and which has been referred to as an authority by many English and foreign writers. He seems to have felt a strong prejudice against Napier for some reason, and all his statements with regard to the origin of logarithms and Napier s connexion with them are untrustworthy. While speaking of the change of the logarithms, it should be noticed that the &quot;Admonitio&quot; on the last page of the Canon Mirificus, containing the refer ence to the new logarithms, does not occur in all the copies. It is printed on the back of the last page of the table itself, and so cannot have been torn out from the copies that are without it. As there could have been no reason for omit ting it after it had once appeared, we may assume that the copies which do not have it are those which were first issued. It is probable therefore that Briggs s copy con tained no reference to the change, and it is even possible that the &quot;Admonitio&quot; may have been added after Briggs had communicated with Napier. As special attention has not been drawn to the fact that some copies have the &quot;Admonitio&quot; and some have not, different writers have assumed that Briggs did or did not know of the promise contained in the &quot;Admonitio&quot; according as it was present or absent in the copies they had themselves referred to, and this has given rise to some confusion. It ought also to be borne in mind that had Napier lived to publish the Constructio himself, he would probably have referred to Briggs in much warmer terms than those used by Robert Napier, who doubtless regarded it as due to his father s memory to simply state the facts as he knew them. The character of Briggs is very amiable and perfect ; he states with modesty and simplicity his own share in the improvement; and with complete loyalty to his friend, and