138 Dr Pearson, On a neiu hind of self-acting weir. [Feb. 25, 



PAGE 



§ 4. Description of Felkel's table 105 



I 6. Refers to Felkel and Lambert ' . . . 108 



§ 6. Lambert's publications relating to factor tables ...... 109 



§ 7. Correspondence between Lambert and von Stamford and Eoseutbal . 110 



§ 8. Con-espondence between Lambert and Felkel ..... 113 



§ 9. Correspondence between Lambert and Hindenbnrg .... 116 



§ 10. Felkel's iviederauflehende Tafeln ........ 118 



§11. Felkel's account of his work in tbe /Styj^tonmfa. Fate of Ms tables . 119 



§ 12. Remarks on factor tables ......... 122 



§ 13. Marci's and Vega's tables 122 



§ 14. GhexnsLc'H Crib7-umArithmeticuin . . . . . • • • 123 



§ 15. Burckliardt's second and third millions . . . • ■ • 124 



§ 16. Burckhardt's first million 126 



§ 17. Gauss, Base, and Rosenberg (seventh, eighth, and ninth millions) . 128 



§ 18. The tenth miUion 130 



§ 19. The Berlin manuscript of the fourth, fifth, and sixth millions . . 130 



§ 20. Account of the calculation of the fourth million . . . . .131 



§ 21. Example showing the appHcation of a factor table to the calculation of 



logarithms 136 



February 25, 1878. 



Professor Liveing, President, in the chair. 



The following communications were made to the Society by 

 Dr Pearson : 



(1) " On a new kind of self-acting weir recently introduced on 

 the rivers of France and Belgium" 



River navigation in France has for a long time been under the 

 control of the government, and employs a considerable number of 

 engineers belonging to the department of the Fonts et Chaussees. 

 About the year 1835, one of them, M. Poirde, being dissatisfied 

 with the old kind of staunch, then the only artificial system used 

 upon the river Yonne, where he was employed, to facilitate the 

 navigation, resolved on endeavouring to introduce a method which 

 would represent modern progress in mechanics. To carry out this 

 view he erected with the permission of the authorities at Epineau, 

 near Auxerre, a new weir of which the following is the construction. 

 The river at the spot was about 120 yards broad, but had only an 

 average dej)th of about a foot. Having faced the bank adjoining 

 the towing-path with masonry, he constructed a cill or apron 

 diagonal to the course of the stream, about 70 metres long and 

 10 m. broad. At the farther end of this he placed a pile of 



