October 25 marks the passing of Evangelista Torricelli. Torricelli was the Italian mathematician and physicist who invented the barometer.
Torricelli was sent as a young man to study under his uncle, a Camaldolese monk. Once he learned all his uncle could teach, his uncle arranged to have him educated at a Jesuit college. Early on, Torricelli had an aptitude for mathematics and science. His uncle arranged to have Torricelli study under the Benedictine monk Benedetto Castelli who was experimenting with running water and hydraulics under a grant from Pope Urban VIII. This put Torricelli in all the correct social circles for Italian science.
When he came across a copy of Galileo’s Dialogues of the New Science, he became an instant admirer of Galileo. He wrote many letters to Galileo and was eventually invited to visit. Torricelli did eventually accept the invitation to visit and served as Galileo’s personal assistant for the last three months of Galileo’s life. After Galileo’s death, Torricelli assumed the position of court mathematician held by Galileo to Grand Duke Ferdinando II of Tuscany.
One project Torricelli was working on was trying to prove the existence of a vacuum. Common scientific theory believed the existence of a vacuum was a contradiction of logic. “Nature abhors a vacuum” was taught to Renaissance students. Torricelli constructed meter long glass tubes with one end sealed. He filled the tubes with mercury and held his finger over the closed end. He then inverted the tube into a basin of mercury and removed his finger. The mercury fell out of the tube, but not all the way. The level of the mercury dropped only to a point approximately one-quarter of the length of the tube. Torricelli reasoned the empty part of the tube contained a vacuum and thus, proved vacuum exists. While investigating this phenomenon, he saw the level of the mercury in the tube would vary as the weather changed. He found the pressure of the air was related to the level in the mercury filled tube. He could calibrate the tube to measure fluctuations in air pressure and created the first barometer.
Much of Torricelli’s scientific work has not survived to present day. He arranged to have a friend publish his works after his death, but the friend never completed the task. It is known he was an excellent lens maker and a source of great income for him throughout his life. He gave the first scientific explanation for wind as the difference of air temperatures and densities of air between two regions creating different pressures that tried to equalize.
Torricelli’s mathematical contributions include the discovery of the Gabriel’s Horn paradox. This was a three-dimensional shape that had an infinite surface area but finite volume. The horn was formed by the equation y = 1/x between the values x=1 and x=a. This curve was rotated around the x-axis to form the horn. The volume for this solid can be shown to be π( 1 – 1/a ) and the surface area to be 2π(ln a). As the value of a approaches infinity, the volume approaches π and the surface area approaches infinity. The idea a shape could have an infinite surface area but a definite volume was the apparent paradox and had many mathematicians questioning the nature of infinity. This line of reasoning would eventually lead others to the invention of calculus.
Torricelli passed away at the age of 39 after contracting typhoid in Florence. Many have speculated he would have made many more contributions to mathematics had he lived. The pressure unit torr is named in his honor.
Notable Science History Events for October 25
1922 – Oskar Hertwig died.
Erik Nordenskiöld, The history of biology: a survey. Knopf, New York, 1935
Hertwig was a German biologist who was the first to determine the fusion of the nuclei of sperm and ovum cells was the beginning point of fertilization. He was investigating the transmission of hereditary information between cells when he made the discovery.
Hertwig is also known for Hertwig’s Rule or the ‘long axis rule’ of cell division. He noted cells divide along their longest axis instead of randomly.
1877 – Henry Norris Russell was born.
Russell was an American astrophysicist who is best known for the Hertzsprung-Russell diagram which shows the relationship between star brightness and spectral type. He developed a method to compute the distance to binary star systems and used the light from eclipsing binary stars to calculate their mass. He also described the coupling of electron angular momentum and spin quantum numbers known as Russell-Saunders coupling.
He also described the coupling of electron angular momentum and spin quantum numbers known as Russell-Saunders coupling. This coupling is also known as LS coupling since it combines the ℓ and s quantum numbers to form the j quantum value. This is done to account for the total angular momentum state of a particle.
1827 – Marcellin Berthelot was born.
Berthelot was a French chemist who believed all chemical reactions depended on the action of physical forces that could be measured. He was also partly responsible for the end of the vitalism theory of organic chemistry. It was generally believed that organic compounds could only be formed from other organic sources and required some ‘vital spark’. He synthesized hydrocarbons, natural fats, and sugars from inorganic sources to disprove this theory. He was responsible for the Thomsen-Berthelot principle in thermochemistry that postulated chemical changes produce heat and will produce the change that generates the most heat. This theory would be modified later by Helmholtz to consider not just heat, but the reaction’s free energy.