However, recent observations have proven the error of this supposed law, especially when applied to large pressure ranges or temperature differences. Neither the research of Arago and Dulong, nor that of the Franklin Institute, nor other modern physicists has been able to solve the mystery to our knowledge, and we have been reduced to date either to direct experiments or to the use of empirical formulas to determine the temperature of a given vapour pressure. or vice versa to determine temperature pressure. There are quite a few formulas for this; But, as I said, they are, without exception, purely empirical; and their results should only be considered as approximate approximations of practical results. Many of these formulas are complex, involve quantities that must be increased to the fifth or sixth power or require extraction of the fifth or sixth root, and combine the use of different constants and coefficients with several rows of decimals attached to them. How much simpler the question is, I will now show and let those interested in the subject judge for themselves whether Mother Nature has long confused mathematicians in this particular case or not. In thinking about the theory which regards heat as a mode of motion, it occurred to me to think of the cause of the well-determined fact that the latent heat of steam decreases with the increase in voltage, and this naturally led me to the conclusion that, in all probability, as the vapour pressure increases, Some of the latent heat is actually converted into this pressure itself. Or, more precisely, the voltage itself is actually just modified latent heat. Mathematically speaking, if this is the case, regardless of the voltage, we have: vapor pressure (a certain amount of motion) + latent heat of the same vapor (a certain amount of motion) = total amount of heat (total motion) in the steam.
To determine whether I was correct in my supposition, I took none of the tables calculated according to the formulas of different authors, but the results of direct experiments conducted by the most reliable scientific authorities, and I soon had the satisfaction of discovering that I had apparently untied the Gordian knot. The tension of the vapour or its elastic force does not represent a simple natural relationship with the thermometric temperature or with the total units of heat to be contained in 1 steam, but is more closely related to its latent heat, part of which is real. In my opinion, the simple law is this: while vapor pressure increases in a geometric progression, latent heat decreases in arithmetic progression and vice versa. If the pressure in atmospheres such as 1, 2, 4, 8, 16, 32, etc., the corresponding reduction in latent heat will be 1, 2, 3, 4; 5, 6, etc. The same would happen with series 3, 6, 12, 24, 48, 96, etc. or 5, 10, 20, 40, 80, etc. or another. If we take 537 C. caloric units as the amount of “latent heat” in the vapor indicating 100 C on the thermometer under atmospheric pressure, we find that the difference between the terms of the above arithmetic progression is 17. or a number that comes close to it in a tiny fraction.
This figure of 17 units of heat is an average of the differences I found between a large number of carefully observed temperatures found by Arago, Dulong and Regnault corresponding to the observed pressures. We exist: pressure in the atmosphere. Latent calories. 1……….537 units. 2…………537 17 4……..537 17 X 2 8…………537 17×3 16…………..537 17 X 4 etc. By interpolation, I formed the following table, which shows the latent heat (which can always be easily calculated from thermometric displays, using Reg-nault`s formula T * 305 + 506 * 5 for degrees Celsius or (T 32) `3O5 + 911-7 for degrees Fahrenheit and the corresponding vapor pressures in atmospheres from 1 to 16. Temperature can also be easily calculated from latent heat by the formula T=606 L-r-*695, where L represents units of latent heat. The letter A denotes units of latent steam heat of 100 C or 212 Fah.
or atmospheric pressure, and b is the number equal to the difference between two arithmetic progression terms. I will only present here the centigrade series in figures. Press accordingly in atmospheres. Einheiten latente Kalorien. Im allgemeinen. 1………………537….. A-0 + 4)! 4……………537 (17 X 2)…………….. The (6+6) 5…………537 [(17 x 2)+ V]…….. A-( + + ) 6…………537 [(17 X 2) + (2 x )]… A (6+6+2J) 7…………587-[(17 X 2) + (3 X )]…. The (6++3) 8………..537 (17X3)………………
A (b+b + b) 9…………537 [(17X3)+ V]. -……. A (36+ ) 10………….537 [(3X17)+ (2 X )]…… A (86 + 2) 11…………537{(3X17) + (3XV)]…… A (30 + 3) 12…………537-[(3X17) + (4X y)]…… A (36 + 4f) 13…………537 [(3X17) +(5X y)]…… A (86+5) 14…………537 [(3X17) +(6X V)]…… A (36+6) 15…………537 [(3X17)+(7 XV)]…… A (3 +7) 16…………537 [(3X17)+(8 Xy)]…… The 46. I am currently busy calculating the latent heat of all pressures from 1 to 16 atmospheres and up to the .000th of a room, which will provide more complete data than all existing ones.
In order to immediately facilitate the verification of my statements by others, I will limit myself to giving an example of how lOths, lOOths and l,000stels are interpolated. PRESSURE OF ONE TO TWO ATMOSPHERES. Tenths, units. Atmospheres 1………………….. 537-U 1-2………………………………9………………………….537_9Xi………. Units. Atmospheres 1……………. -537 1*10…………537 fj 1*11…………….SW-K+J+iMr) 1-1 ……….. 537-( +2XTVTJ)] 1`99………………
537-(9xJ +9*XTy THOUSANDTHS. Units. Atmospheres 1…………537 1-101……..S37-(fk+T*fo) 1-102……..687-(W+*xTWTr) 1-999……..OT-fl`xHWTHf+Ox`dt T) I have applied my formula to most of Begnault`s practical observations, on both large and small scales, and I find the discrepancies really insignificant. For example, it gives a pressure of 1 * 905 atmospheres; observed temperature, 119-16; latent heat, 523; I find 521,615 or a difference of only 1 * 385 units. Another is T=11916; pressure, 1-924 atmospheres; latent heat, 522`2; I find 521`292 units or a difference of 1*008 units. Among the higher pressures we find: pressure, 13 * 344 atmospheres; Temperature, C, 193*8; Latent heat, 472*2. According to our theory, we have 473*662, a difference of only 1*42; and again P=13*625; T=194`8; Latent heat, 471 * 2, if I find 474 * 047, a difference of 2 * 847 units. The above are just a few examples that have been taken to many to serve as a revision of my law, but everything I have tried has come close to the racial results of experience than those we have just cited. I have quickly drafted this communication in order to gather the views of others on this important and interesting topic. In a future article, I will present various practical formulas in this context and enter into the discussion of the relationship between so-called latent heat and the volume of vapour, as well as its connection with the current theory of expansion and condensation, which we all hope to show, which depend most closely on their quantity. Let us conclude by reminding the reader that, in all likelihood, we are rapidly approaching the day when it will be admitted by all sound philosophers that there is only one law in nature, motion, whose modes are known as heat, light, electricity, chemical affinity, molecular forces, gravity, innervation, etc., all of which will be perfectly convertible into each other.