On the Fire-Damp of Coal Mines, and on Methods of Lighting the Mines So as to Prevent Its Explosion (Davy) & An Account of an Invention for Giving Light in Explosive Mixtures of Fire-Damp in Coal Mines, by Consuming the Fire-Damp(Davy) in Philosophical Transactions of the Royal Society of London, Volume 106, 1816, pp. 1-22, 23-24 WITH An Essay towards the Calculus of Functions Part I and II (Babbage) in Philosophical Transactions of the Royal Society of London, Volume 105, 1816, Part I pp. 1-22, 23-24, Part II 179-256 WITH On the laws which regulate the polarisation of light by reflection from transparent bodies (Brewster) in Philosophical Transactions of the Royal Society of London, Volume 105, 1815, Parts I and II, pp. 125-159

1st Edition. FIRST EDITION OF THE FIRST ANNOUNCEMENT AND DESCRIPTION of an invention some have argued rescued the Industrial Revolution, Humphrey Davy's Safety Lamp (this published prior to Davy's own 1818 book on the subject).

"Two great events amazed Britain in 1815: the victory of Wellington over Napoleon and the victory of Davy over mine gases. The Industrial Revolution was in danger of stalling in the early 19th c. due to the dangers in mining with contemporary lamps that used flame and ignited explosions. A disaster near Newcastle in 1812 killed 101 miners, and more than two-thirds of the coal mines in England were considered too dangerous to work because of their levels of coal gas.

"In 1815 Davy was invited by the Chairman of a 'Society for Preventing Accidents in Coal Mines' to invent a solution... Davy had earlier studied flames and their propagation and noted that flames could not propagate through small holes. Thus his solution was merely to surround the lamp with a cylinder of wire mesh that still left the flame open to the atmosphere. The mesh conducted away the heat of the flame, thus cooling it so that the temperature methane would encounter at the lamp would be lower than its flash point. The flame itself could not penetrate the mesh...Although the flame and combustible gas were in open contact, there would be no explosion" (Greenberg, A Chemical History Tour, 184-185).

Davy published these two papers in Philosophical Transactions in late 1815 and early 1816. In 1818 he was made a Baronet for his service to Britain's industry.

ALSO in this volume is Part II of Babbage's seminal 'An Essay towards the Calculus of Functions,' his most important mathematical work. "Babbage believed that his new scheme would serve as a generalized calculus to include all problems capable of analytical formulation and it is possible to see here a hint of the inspiration for his concept of the Analytical Engine. While the work on the engines and his other scientific, social and political activities caused him virtually to abandon mathematical research at the age of thirty, the calculus of functions was the area he often yearned to continue. In fact, the calculus of functions was not taken up by other workers, and it is the aspect of Babbage's mathematical work that modern mathematicians find the most fascinating" (Dubbey, The Mathematical Work of Charles Babbage).

ALSO INCLUDED: First editions of Charles Babbage's first papers as well as his most important contribution to mathematics, the calculus of functions.

ALSO INCLUDED: First edition of 'Brewster's Angle, "one of Brewster's most important contributions to the science of physics" (Molecular Expressions Website). CONDITION & DETAILS: Philosophical Transactions Volume for the year MDCCCXV (1815) and MDCCCXVI (1816) Ex-libris bearing only a miniscule "Athenaeum Library, Liverpool" stamp and at the foot (margin) of some of the plates. Quarto. (10.5 x 8.5 inches; 263 x 408mm). [12], 446, [20]; Volume 106 [14], 366, [12]. Volume I includes 8 page index. 16 copperplate engravings; Volume II includes and 8 page index and 21 copperplate engravings. The construction of Davy's lamp is depicted in one of the plates. Full volumes, complete. Handsomely rebound in aged calf. 5 raised bands at the spine, each gilt-ruled; gilt-tooled fleur de lis at the spine. Red and black, gilt-lettered spine labels. Tightly and solidly bound. New endpapers. Occassional light toning and foxing. By any measure, near fine condition.