Fune 3, 1886 | 
NATURE 
IO 
will be affected by the average amount of solar influence, 
and the difference between this average price and the 
actual price for the middle year of the eleven will be 
affected by the difference between the average condition 
of the sun and its actual condition in that middle year. 
This difference of price may also include the effects of 
other extraneous and non-periodic causes. Eleven years 
after the middle year just mentioned the sun will again 
be in its former condition, and a similar price difference 
for that year may be calculated. The same process may 
be carried on to the twenty-second, thirty-third, &c., years, 
and it will then produce a series of price differences 
equally affected by equal periodical solar influence. Non- 
periodic causes will, however, sometimes tend to unduly 
raise these price differences, sometimes to depress them, 
but on the average such disturbances will, in a long series 
of years, tend to balance each other, leaving the periodical 
portion of the solar influence outstanding. If, for instance, 
the years for which the calculations of the price differences 
have been made are those in which the sunspots are at a 
maximum, the average price difference will show how 
much prices tend to be raised or depressed by that con- 
dition of the sun which produces most spots. A similar 
series of calculations may be made for the years in which 
the spots are at a minimum, also for the intermediate 
years when the spots are increasing, and for those years 
when the spots are decreasing. <A set of eleven average 
price differences, one for each year of the sunspot cycle 
of eleven years, will thus be obtained, and_if, on arranging 
them in consecutive order, they show that prices are, on 
the average, decidedly high in those years when there are 
few sunspots, and decidedly low when the sunspots are 
numero«s, or if they show any other decided and system- 
atic variation in the sunspot period, the conclusion will be 
that the sunspot cycle does really affect the prices. If, 
on the other hand, the prices do not change in any system- 
atic manner in the different years of the sunspot cycle, the 
conclusion will be against the hypothesis of a periodical 
variation of the prices corresponding to the periodical 
variation of the sunspots. 
There is one point of view from which this method of 
taking differences is open to some objection. Suppose, 
merely for the sake of illustration, that the average price 
of millet throughout some particular sunspot period of 
eleven years is 50 pounds for a rupee, but that in the 
year of maximum sunspots the solar influence is such as 
to double the crop and lower the money price or raise 
the quantity price proportionately, that is, to 100 pounds 
forarupee. The price difference for that year would be 
50. If, however, by reason, say, of a more plentiful 
supply of money, the average price of millet for the whole 
of another sunspot period of eleven years is only 25 pounds 
for a rupee, and the crop in the year of maximum sunspots 
is, through solar influence, similarly doubled, the quantity 
price would only rise to 50 pounds, and the price differ- 
ence would be only 25, although the solar influence, which 
is supposed to have produced the change, is the same as 
before. The difference between the two results would be 
due simply to the more plentiful supply of money, not at 
all to a difference of solar influence. This shows that it 
is needful to adopt some modification of the method, 
which will allow for gradual changes in the amount of 
money in use, and other similar causes of alteration of 
price. Such a modification will be made if, instead of 
taking price differences, the actual price of the middle 
year of the eleven is expressed as a percentage of the 
average price. Expressed in this way, the percentage for 
the year of maximum sunspots in each of the above ex- 
amples would be 200, that is to say, in each case the 
number of pounds for a rupee would be 100 per cent. 
greater than the average number. 
Table I. contains the Bhavnagar price list expressed in 
the percentage form in the manner just described. Inthe 
original table the prices are expressed in pounds for a 
rupee. If, therefore, the number for any year in Table I. 
is 125, it means that the number of pounds of grain for a 
rupee is 25 per cent. greater than the corresponding 
eleven-yearly average ; and if the number is 75 it means 
that the number of pounds for a rupee is 25 per cent. less. 
In other words the excess above or the defect below 109 
shows how much per cent. the number of pounds for a 
rupee is above or below the corresponding eleven-yearly 
average. 
TABLE 1.—Percentages, Bhavnagar. 
Years. peer eet IM) oe Soll ey) exsyil| Be: 
1783 to 1793 . . | 57] 66) 56 143/157 172|185|104] 24] 60) 61 
1794 to 1804 . . | 66) 69/140 163/145|/131|108| 82) 78) 75) 63 
1805 to18i5 . . | 70) 117 97/139|124|115|106| 78] 38) 69] 85 
1816 to 1826 . , |118)159)162/103| 68 81] 78|x11| 71) 51) 74 
1827 to 1837 . . |14I 98|137| 96)121)131/135| 71| 78] 79} St 
1838 to 1848 . gt| 58100] 92!) 81/141|164| 93) 86)107| 66 
1849 to1859 . . |132) 96) 96,102) 104/100} 106) 112/109) 84\122 
1860 to 1870 . . |103/100;103] 86] 52] 62) 87|105|104) 92) 84 
1871 to1881 . . | 93] 93/133/126 126|107| 89] 75) 71) So|118 
1882 =. St Airs | 
Means, including 
1863 to 1866 . | 97] 95|114\117|109|116|118| 92) 73) 78) 84 
Means, excluding 
1863 to 1866 . | 97| 95|114|120|116|122|121) 92) 73 78| 84 
Smoothed means. | 93|100|111|117|118/120|114| 94) 79) 78) 86 
The numbers of Table I. are arranged in lines of eleven 
numbers each, so that the numbers occurring at equal 
intervals of eleven years, beginning with 1783, all fall in 
the first column, those occurring at equal intervals begin- 
ning with 1784, all fall in the second column, and so on. 
Now if there is any decided tendency for high or low 
prices to recur at more or less regular intervals of about 
eleven years, the great majority of the high prices should 
be found in a few contiguous columns in one part of the 
table, and the great majority of the low prices in a few 
contiguous columns in another part of the table. An 
examination of the numbers of Table I. shows that this is 
the case, for in columns 9, 10, and 11, no less than twenty- 
two out of the twenty-seven numbers are below Ioo, and 
only five of them are above 100 ; while in columns 3 to 7 
the great majority of the numbers are above 100. 
The average results are given at the foot of the table. 
They show that there is a decided tendency for years of 
high and low prices to recur, with some regularity, in a 
period of eleven years, five consecutive years being good 
years, when money prices are below the average ; and the 
six following years being bad years, when money prices 
are above the average. The years which give the highest 
average money price, or the smallest number of pounds 
for a rupee, are those in column 9. The average number 
of pounds for a rupee in those years is 27 per cent. below 
the eleven-yearly average. The years which give the 
lowest average money prices are those in columns 4, 6, 
and 7. The average number of pounds for a rupee in 
those years is about 17 per cent. greater than the eleven- 
yearly average. There is thus an average difference of 
44 per cent. between the years of low prices and those of 
high prices. This percentage difference would have been 
considerably greater if the prices had been reckoned in 
rupees for a fixed quantity of grain, instead of in pounds 
of grain fora rupee. To show that this is the case it is 
only necessary to convert the three prices 117, 100, and 
73 regarded as pounds for a rupee, into their correspond- 
ing rupee prices, that is to say, into the number of rupees 
which would in each case be required to purchase 100 
pounds. These are 0°85, 1°00, and 1°37 respectively, 
