“Having recently computed the remaining observations of our earth-thermometers here, and prepared a new projection of all the observations from their beginning in 1837 to their calamitous close last year [1876]—results generally confirmatory of those arrived at in 1870 have been obtained, but with more pointed and immediate bearing on the weather now before us.
“The chief features undoubtedly deducible for the past thirty-nine years, after eliminating the more seasonal effects of ordinary summer and winter, are:—
“1. Between 1837 and 1876 three great heat-waves, from without, struck this part of the earth, viz., the first in 1846·5, the second in 1858·0, and the third in 1868·7. And unless some very complete alteration in the weather is to take place, the next such visitation may be looked for in 1879·5, within limits of half a year each way.
“2. The next feature in magnitude and certainty is that the periods of minimum temperature, or cold, are not either in, or anywhere near, the middle time between the crests of those three chronologically identified heat-waves, but are comparatively close up to them on either side, at a distance of about a year and a half, so that the next such cold-wave is due at the end of the present year [1877].
“This is, perhaps, not an agreeable prospect, especially if political agitators are at this time moving amongst the colliers, striving to persuade them to decrease the out-put of coal at every pit’s mouth. Being, therefore, quite willing, for the general good, to suppose myself mistaken, I beg to send you a first impression of plate 17 of the forthcoming volume of observations of this Royal Observatory, and shall be very happy if you can bring out from the measures recorded there any more comfortable view for the public at large.
“Piazzi Smyth,
“Astronomer-Royal for Scotland.”
If this prediction shall be confirmed [this was written in autumn, 1877], it will afford an argument in favour of the existence of the cyclic relation suggested, but no argument for the endowment of solar research. Professor Smyth’s observations were not solar but terrestrial.
[The prediction was not confirmed, the winter of 1877–78 being, on the contrary, exceptionally mild.]
[9] The reader unfamiliar with the principles of the telescope may require to be told that in the ordinary telescope each part of the object-glass forms a complete image of the object examined. If, when using an opera-glass (one barrel), a portion of the large glass be covered, a portion of what had before been visible is concealed. But this is not the case with a telescope of the ordinary construction. All that happens when a portion of the object-glass is covered is that the object appears in some degree less fully illuminated.
[10] It may be briefly sketched, perhaps, in a note. The force necessary to draw the earth inwards in such sort as to make her follow her actual course is proportional to (i) the square of her velocity directly, and (ii) her distance from the sun inversely. If we increase our estimate of the earth’s distance from the sun, we, in the same degree, increase our estimate of her orbital velocity. The square of this velocity then increases as the square of the estimated distance; and therefore, the estimated force sunwards is increased as the square of the distance on account of (i), and diminished as the distance on account of (ii), and is, therefore, on the whole, increased as the distance. That is, we now regard the sun’s action as greater at this greater distance, and in the same degree that the distance is greater; whereas, if it had been what we before supposed it, it would be less at the greater distance as the square of the distance (attraction varying inversely as the square of the distance). Being greater as the distance, instead of less as the square of the distance, it follows that our estimate of the sun’s absolute force is now greater as the cube of the distance. Similarly, if we had diminished our estimate of the sun’s distance, we should have diminished our estimate of his absolute power (or mass) as the cube of the distance. But our estimate of the sun’s volume is also proportional to the cube of his estimated distance. Hence our estimate of his mass varies as our estimate of his volume; or, our estimate of his mean density is constant.