The nature of this paper may he understood from the following headings:—

(1.) The making and placing of the new thermometers.

(2.) Practically described by Mr Thomas Wedderburn.

(3.) The problem with the old thermometers.

(4.) Their next use in level fluctuations.

(5.) Their employment by Sir Wm. Thomson.

(6.) Their subsequent demonstration of the cycle of supra-annual waves of heat and cold.

(7.) The published predictions in 1872 for 1878–80.

(8.) The spoiled predictions in 1877, under the influence of erroneous sun-spot dates.

(9.) The rectified predictions in 1879, when the true date of sunspot minimum was ascertained by direct observation.

(10.) How to obtain correct dates for future sun-spot minima.