26 J. H. Gore — Decimal System of Seventeenth Century. 



lengths and with balls of various sizes. The indiscriminate 

 mean of these four series is 1252 ±0*047, a result which reflects 

 great credit upon the observer. On the margin of a page is 

 given the length of a virgula, with the naive confession that it 

 is not given with such accuracy that we can take copies from 

 it as if it were the standard — a remark made unnecessary by 

 the careless trimming of the bookbinder. 



The facts here established are : 1. Mouton devised a system 

 of measure, arranged upon the scale of tens. 2. He derived 

 his unit from the length of a minute of the terrestrial arc. 3. 

 He showed how this unit could be expressed in terms of the 

 seconds pen<fulum. It is now added, that this is the earliest 

 decimal system proposed, that the French Academicians knew 

 of this system, took from it its best features, and never gave 

 credit where credit was due. Chronology shows it to be the 

 earliest. As already stated, the two units, virga and virgula 

 are more convenient lengths than the yard and foot, meter and 

 decimeter ; and so far as names are concerned, decuria, by tens, 

 is as good as dekameter, while decima, the tenth part is better 

 than decimeter. Again, the virga is an exact part of a minute, 

 and is therefore an exact division of degree, quadrant and cir- 

 cumference, while the meter has nine degrees as its smallest 

 exact multiple. 



The only remaining point to be considered is : to what 

 extent was Mouton known to his contemporaries and succes- 

 sors ? As to the former it is impossible to even surmise. 



His system forms pages 427-448 of his treatise " Observa- 

 tions Diametrorum Solis et Lunse . . . Una cum Nova Men- 

 snrarum G-eometricarum Idea." Lugduni [Lyons] 1670. This 

 small quarto was published with the " approval and permission 

 of superiors," who, judging from the names appearing on the 

 page which contains these approvals and consent, are the chair- 

 man of the Faculty of Paris, a Carmelite monk who announces 

 that the book is orthodox, and a Procureur du Roy. This 

 would give the book at least three readings before it was 

 printed, and by men of such ability that they would appreciate 

 the system proposed and discuss it with others. 



Picard saw the book soon after its publication, nor did he 

 soon forget it. This is shown in a report, published in vol. vii 

 of the Memoirs of the Paris Acad., 1729, of observations made 

 in 1672, 1673, and 1674. Picard, elated over the success 

 which he had achieved in his geodetic work, sought new glory 

 in making accurate astronomic observations at some of the 

 principal cities of France. One of these places was Lyons, and 

 while discussing his observations made when there he says : 

 M. Mouton in his discussion of a universal measure, said that 

 at Lyons a simple pendulum whose length was equal to a Paris 



