After carrying these experiments to a successful conclusion, I found that it was yet necessary to prove that, on reducing the vapor pressure of boiling oxygen, to a minimum, no corresponding fall of temperature takes place. The vessel, e, was partially filled with liquid oxygen, and, by means of a small siphon, a small quantity of the liquid was allowed to flow into the tube, a. The inner vessel, a, was then connected with the air pump and manometer, and the pressure was reduced to 2 mm. of mercury. The oxygen remained liquid and quite clear. In a second experiment the temperature of the liquid oxygen, boiling under 2 mm. of mercury pressure, was measured by means of a thermometer. The temperature indicated lay above -220° C., a temperature easily arrived at by means of liquid air. I, therefore, concluded that liquid air was a much more efficient cooling agent than liquid oxygen, and that it would be quite unnecessary to make further experiments on the liquefaction of helium. In every single instance I have obtained negative results, and, as far as my experiments go, helium remains a permanent gas, and apparently much more difficult to liquefy than even hydrogen. The small quantity of the gas at my disposal, and, indeed, the extreme rarity of the minerals from which it is obtained, compelled me to carry out my investigation on a very small scale. Using a larger apparatus, and working at a much higher pressure, I could have submitted the gas to greater expansion. Further, I should have been able to measure the temperature of the gas at the moment of expansion by means of a platinum thermometer, as I did when working with hydrogen; but to make such experiments I should have required 10, if not 100, liters of the gas. As I was unable to determine the temperatures to which I cooled the gas, by any experimental means, I have been obliged to calculate them from Laplace's and Poisson's formula for the change of temperature in a gas during adiabatic expansion. T/T1 = (p/p1)^{(k - 1/k)} Where: T, p are the initial temperature and pressure of the gas. T1, p1 are the final temperature and pressure of the gas. k is the ratio (cp/cv) which, for a monatomic gas, is 1.66. In the first series of experiments the gas, under a pressure of 128 atmospheres, was cooled down to -210° C. p T p1 T1 At. Deg. At. Deg. Deg. 125 -210 C. 50 -229.3 C. 43.7 A. ... ... 20 -242.7 C. 30.3 A. ... ... 10 -250.1 C. 22.9 A. ... ... 5 -255.6 C. 17.4 A. ... ... 1 -263.9 C. 9.1 A.