Regnault, the celebrated chemist and natural philosopher, in the published results of his admirable researches on steam, undertaken at the requisition of the French Government, while speaking of the intimate relation existing between the pressure and the temperature of steam, says : " The question we are at present studying is probably one of the least complex of the theory of heat, and if the law which governs it has not been made manifest by our experiments, this depends probably on the empirical definition given of temperatitre, which definition, in all likelihood, does not establish any simple relation between various temperatures and absolute quantities of heat." He further says : " We are at present totally unacquainted with the theoretical law which connects the elastic forces of vapors with their temperatures." Dalton, long before Regnault, propounded a law, stating that, while the pressures increased in geometrical ratio, the temperatures did so in an arithmetical one; and Faraday, to a certain extent, corroborated Dalton's theory during his investigations on the expansion of gases. More recent observations have, however, proved the fallacy of this supposed law, especially when applied to long ranges of pressures or to great differences in temperature. Neither the researches of Arago and Dulong, nor those of the Franklin Institute, nor of other modern physicists have, to our knowledge, been able to solve the mystery, and we have, to this day, been reduced either to direct experiment or to the use of empirical formulae in order to determine the temperature of any given pressure of steam, or, vice versa, to determine the pressure from the temperature. The formulae for this purpose are quite numerous; but -as I have said before, they are, without exception, purely empirical; and their results must be considered only as rough approximations to practical results. Many of these formulas are complex, involving quantities to be raised to the fifth or sixth power or require the extraction of the fifth or sixth root, and combine the uie of various constants and coefficients with multitudinous rows of decimals attached to them. How much more simple the matter really is, I shall now proceed to show, leaving those who take interest in the subject to judge for themselves, whether or not Dame Nature has long mystified the mathematicians in this special case. While reflecting on the theory which regards heat as a mode of motion, it occurred to me to think of the cause of the well-ascertained fact, that the latent heat of steam- decreases as the tension increases, and this naturally led me to the conclusion, that, in all probability, as the pressure of steam increases so is a portion of the latent heat really converted into this pressure itself, or, more properly speaking, the tension is in reality itself only modified latent heat. Expressed mathematically, if such be the case, no matter what the tension is, we have: Tension of steam (a certain amount of motion) + latent heat of same steam (a certain amount of motion) = total amount of heat (total motion] in steam. In order to ascertain if I was right in my supposition I took up not any of the tables calculated by the formulae of various authors, but the results of direct experiments mad* by the most reliable scientific authorities and I soon hac the satisfaction of discovering that I had, to all appearance solved the gordian knot. The tension of steam, or its elastic force, does not present any natural simple relation to either thermometric tempera- ture or to the total units of heat supposed to be contained in 1 steam, but is most intimately related to its latent heat, a portion of which, in fact, it really is. According to my views, the simple law reads as follows: While the pressure of steam increases in a geometrical progression, the latent heat decreases in an arithmetical progression, and vice versa. If the pressure in atmospheres be as 1, 2, 4, 8, 16, 32, etc., the corresponding diminution in latent heat will be, respectively, as 1, 2, 3, 4; 5, 6, etc. The same would occur with the series 3, 6,12, 24, 48, 96, etc., or 5, 10, 20, 40, 80, etc., or any other If we take 537 C. units of caloric as the quantity of " latent heat" in steam, indicating 100 C. on the thermometer under atmospheric pressure, we find that the difference between the terms of the above arithmetical progression is 17, or a number which approximates to it within a very minute fraction. This number of 17 units of heat is an average of the differences found by me to exist between a large number of the carefully observed temperatures, noted by Arago, Dulong, and Regnault, as corresponding to observed pressures. It gives us: Pressure in atmosphere. Latent caloric. 1..............................537 units. 2..............................537 17 4..............................537 17 X 2 8..............................537 17x3 16..............................537 17 X 4, etc. By interpolation, I have formed the following table, showing the latent heat (which may always be readily calculated from the thermometric indications, by means of Reg-nault's formula T *305 + 506*5 for Centigrade degrees, or (T 32)'3O5 + 911-7 for Fahrenheit degrees, and the corresponding pressures of steam in atmospheres, from 1 to 16. The temperature is also readily calculated from the latent heat by the formula T=606 L-r-*695, in which L represents the units of latent heat. The letter A indicates the units of latent heat of steam of 100 C, or 212 Fah. or of atmospheric pressure, and b indicates the number corresponding to the difference between two terms of the arithmetical progression. I shall here only exhibit the Centigrade series in numerals. Pressures Corresponding in atmospheres. units of latent caloric. In general. 1............537. .........................A o 2............537 17........................A 3............537-(17+V).................A-0 + 4)! 4............537 (17 X 2)...................A (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 )]....... A (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)]........A 46. I am at present occupied in computing the latent heat of all pressures, from 1 to 16 atmospheres and up to l,000ths parts, which will furnish more complete data than any extant. In order to facilitate at once to others the verification of my statements, I will limit myself to showing how the lOths, lOOths, and l,000ths are interpolated by an example. PRESSURE FROM ONE TO TWO ATMOSPHERES. TENTHS, Units. Atmospheres 1.................................537 l'l...............................537-U 1-2...............................537 2X 1-9...............................537_9Xi 2.................................537 17 HUNDREDTHS. 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, taken high and low in the scale, and find the discrepancies to be really insignificant. He gives, for instance, pressure 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. We here, by our theory, have 473*662, a difference of 1*42 only; and again, P=13*625; T=194'8; latent heat, 471*2, when I find 474*047, a difference of 2*847 units. The above are only a few examples, taken at random from among many, to serve as a verification of my law, but all those I have tried have approximated as closely to the )ractical results of experiment as those we have just quoted. I have rapidly penned the present notice for the purpose of eliciting the opinion of others upon this important and interesting subject. In a future article I may furnish various practical formulae in connection with it, and will enter into the discussion of the relation existing between, so-called, latent heat and the volume of steam, as also its connection with the present theory of expansion and condensation, all of which we hope to show, have the most intimate dependence on its amount. Let us conclude by reminding the reader, that we are, in all probability, fast approaching the day when it will be admitted by all sound philosophers, that only one law exists in nature, motion, the modes of which are familiarly known as heat, light, electricity, chemical affinity, molecular forces, gravitation, innervation, etc., all of which will be found to be perfectly convertible into one another. This will constitute a sufficient proof of their identity.