ON COAL-CUTTING MACHINERY. 175 



Page 



24. Mathematical constants 81 



25. Miscellaneous tables, iigurate numbers, &c •. 83 



§4. Works containing Collections of Tables, arra^igedin alphabetical order 85 



§ 5. List of Works containing 7'ables that are described in this Report, with references 



to the section and article in which the description of their cotitents is to be found 143 



§ 6. Postscript. 

 Art. 1. (Eeport is that presented to the Brighton Meeting enlai-ged) 164 



2. (Alterations since the Brighton Meeting; Report has been made more 



bibliographical) 164 



3. (Reasons for introducing bibliography ; inaccuracy of previous writers) ... 165 



4. (Explanations with regard to the list of books in § 5) 166 



5. (Supplementary explanations referring to § 2, arts. 8 and 9) 167 



6. (The tables of hyperbolic antilogarithms and powers calculated by the Re- 



porter; § 1, and § 3, art. 5) 167 



7. (Slight differences in mode of description observable in the Report) 168 



8. (Why some unimportant works are included) 168 



9. (The Supplementary Report on general tables) 169 



10. (Some books omitted intentionally, as. belonging more properiyto subse- 



quent Reports) 169 



11. (§ 5 has been made an index as well as a list of titles of books) 169 



12. (Statistics with regard to books described in the Report from inspection) ... 169 



13. (Contents of the Report that was intended to be presented to the Bradford 



Meeting) 170 



14. (The tables of the Legendrian functions) 170 



15. (Thelistof errors in Vlacq, 1628 or 1631) 170 



16. (The account of the tabulation of the elliptic functions) 171 



17. (Note on the centesimal division of the degree) 172 



Page 6, line 8 from bottom, for Poggendoff read Poggendorlf. 

 Page 15, line 25 from top, for multiplication read multiplication t; 



ERRATA. 



Poggendorlf. 



table. 



Observations on the Application of Machinery to the Cutting of 

 Coal in Mines. By William Firth, of Birley Wood, Leeds. 



[A Communication ordered by the General Committee to be printed in extenso.'] 



The object of this paper is to submit for consideration some matters toucli- 

 ing the history of the now more than ever absorbing subject of cutting coal 

 in mines by mechanical means. 



It is intended to avoid all technical and scientific symbols, and to convey, 

 in the most simple manner, whatever information is at my command, and to 

 give, from practical experience, spread over long periods, the results derived 

 therefrom, and to show that machinery can be, and is now, applied to the 

 purpose equally to the advantage of the masters and of the men. 



I am aware that there are noiv several distinct modes of doing the work, 

 and doing it well ; but it is not in my power to give any reliable information 

 upon the competitive status which the successfid machines hold towards 

 each other. I shall tlierefore have in this paper to confine myself more 

 particularly to the introduction of coal-cutting machinery driven by com- 

 pressed air, and the results obtained from the invention now known as 

 " Firth's Machine," which was unquestionably the first that ever succeeded 

 in reducing to actual practice the cutting of coal in mines. 



