Pleasant Ways in Science. Richard Anthony Proctor
Petersburg. Surely it would be unreasonable to refuse to recognize the weight of evidence which thus tells on both sides at once.
To return, however, to the sun’s influence upon shipwrecks.
Mr. Jeula was “only able to obtain data for two complete cycles of eleven years, namely, from 1855 to 1876 inclusive, while the period investigated by Dr. Hunter extended from 1813 to 1876, and his observations related to Madras and its neighbourhood only, while the losses posted at Lloyd’s occurred to vessels of various countries, and happened in different parts of the world. It was necessary to bring these losses to some common basis of comparison, and the only available one was the number of ‘British registered vessels of the United Kingdom and Channel Islands’—manifestly an arbitrary one. I consequently cast out the percentage of losses posted each year upon the number of registered vessels for the same year, and also the percentage of losses posted in each of the eleven years of the two cycles upon the total posted in each complete cycle, thus obtaining two bases of comparison independent of each other.”
The results may be thus presented:—
Taking the four years of each cycle when sun-spots were least in number, Mr. Jeula found the mean percentage of losses in registered vessels of the United Kingdom and Channel Islands to be 11·13, and the mean percentage of losses in the total posted in the entire cycle of eleven years to be 8·64.
In the four years when sun-spots were intermediate in number, that is in two years following the minimum and in two years preceding the minimum, the respective percentages were 11·91 and 9·21.
Lastly, in the three years when sun-spots were most numerous, these percentages were, respectively, 12·49 and 9·53.
That the reader may more clearly understand what is meant here by percentages, I explain that while the numbers 11·13, 11·91 and 12·49 simply indicate the average number of wrecks (per hundred of all the ships registered) which occurred in the several years of the eleven-years cycle, the other numbers, 8·64, 19·21, and 9·53, indicate the average number of wrecks (per hundred of wrecks recorded) during eleven successive years, which occurred in the several years of the cycle. The latter numbers seem more directly to the purpose; and as the two sets agree pretty closely, we may limit our attention to them.
Now I would in the first place point out that it would have been well if the actual number or percentage had been indicated for each year of the cycle, instead of for periods of four years, four years, and three years. Two eleven-year cycles give in any case but meagre evidence, and it would have been well if the evidence had been given as fully as possible. If we had a hundred eleven-yearly cycles, and took the averages of wrecks for the four years of minimum solar maculation, the four intermediate years, and the three years of maximum maculation, we might rely with considerable confidence on the result, because accidental peculiarities one way or the other could be eliminated. But in two cycles only, such peculiarities may entirely mask any cyclic relation really existing, and appear to indicate a relation which has no real existence. If the percentages had been given for each year, the effect of such peculiarities would doubtless still remain, and the final result would not be more trustworthy than before; but we should have a chance of deciding whether such peculiarities really exist or not, and also of determining what their nature may be. As an instance in point, let me cite a case where, having only the results of a single cycle, we can so arrange them as to appear to indicate a cyclic association between sun-spots and rainfall, while, when we give them year by year, such an association is discredited, to say the least.
The total rainfall at Port Louis, between the years 1855 and 1868 inclusive, is as follows:—
| In | Rainfall. | Condition of Sun. | |
| 1855 | 42·665 | inches | Sun-spot minimum. |
| 1856 | 46·230 | „ | |
| 1857 | 43·445 | „ | |
| 1858 | 35·506 | „ | |
| 1859 | 56·875 | „ | |
| 1860 | 45·166 | „ | Sun-spot maximum. |
| 1861 | 68·733 | „ | |
| 1862 | 28·397 | „ | |
| 1863 | 33·420 | „ | |
| 1864 | 24·147 | „ | |
| 1865 | 44·730 | „ | |
| 1866 | 20·571 | „ | Sun-spot minimum. |
| 1867 | 35·970 | „ | |
| 1868 | 64·180 | „ | |
I think no one, looking at these numbers as they stand, can recognize any evidence of a cyclic tendency. If we represent the rainfall by ordinates we get the accompanying figure, which shows the rainfall for eighteen years, and again I think it may be said that a very lively imagination is required to recognize anything resembling that wave-like undulation which the fundamental law of statistics requires where a cycle is to be made out from a single oscillation. Certainly the agreement between the broken curve of rainfall and the sun-spot curve indicated by the waved dotted line is not glaringly obvious. But when we strike an average for the rainfall, in the way adopted by Mr. Jeula for shipwrecks, how pleasantly is the theory of sun-spot influence illustrated by the Port Louis rainfall! Here is the result, as quoted by the high-priest of the new order of diviners, from the papers by Mr. Meldrum:—
| Three minimum years—total rainfall | 133·340 |
| Three maximum years—total rainfall | 170·774 |
| Three minimum years—total rainfall | 120·721 |
Nothing could be more satisfactory, but nothing, I venture to assert, more thoroughly inconsistent with the true method of statistical research.
May it not be that, underlying the broad results presented by Mr. Jeula, there are similar irregularities?
When we consider that the loss of ships depends, not only on a cause so irregularly variable (to all seeming) as wind-storms, but also on other matters liable to constant change, as the variations in the state of trade, the occurrence of wars and rumours of wars, special events, such as international exhibitions, and so forth, we perceive that an even wider range of survey is required to remove the effects of accidental peculiarities in their case, than in the case of rainfall, cyclones, or the like. I cannot but think, for instance, that the total number of ships lost in divers ways during the American war, and especially in its earlier years (corresponding with two of the three maximum years of sun-spots) may have been greater, not merely absolutely but relatively, than in other years. I think it conceivable, again, that during the depression following the great commercial panic of 1866 (occurring at a time of minimum solar maculation, as already noticed) the loss of ships may have been to some degree reduced, relatively as well as absolutely. We know that when trade is unusually active many ships have sailed,