ie 
Fune 3, 1886] 
NATORE 
103 
average numbers which constitute the eleven-yearly price 
variation, and to repeat the process on the new means, 
This has been done, and the results are given in 
Table III. 
TABLE III. 
3 Fo | : | 
pred lla lente 5 Aol as 4 
eee) oes erst ese ||) ast) erga edie 
= |/e/eie1s oi i|o |a/] a) Ss 3 
Alsia le (/¥le lela l/ale)/e]4 
Lal 
| £813 | 1783 | 1790| 1825 | 1809 | 1823 | 1824 | 1823 1824) 1811} 1810 
Years, to to to to to to to to to to to 
1877 | 1882] 1882] 1879 | 1882] 1882] 1882 | 1883] 1882 | 1877] 1875 
i} —h = i at i} 
a 93] 93} tOI| 99] 116] 115] 105) 108] 97] 113] 83:2 
2. | 103] 100] 104] 100] 107] 107] ror] 104] 103] 111] 71°7 
3. | 183] 111] 110} 113] 109] 108] 105] 102} 110) 113] 5875 
4 . | 101} 117) 1x13) r2t] £12) 117} 111] 107] 114) 118] 45°1 
5. | 101} 118] 116) 121] 108] roo] 112) 111) 112] 10] 321 
6. | 116} 120] 11z| 112] 97] 85] 102/ 104! 107} 94] 20°1 
7- | 111) 114) 95) 91 83) 75] 92] 87| 101] 82! 12°6 
8. | 97] 94] 80) 82) 81) 36) 95) 93) 95) 77] 16°7 
9. 84) 79} 78) 81) 85) 100) 98} 112 2) 79 35°6 
Io. 79! 78) 89) 84] 94] 109] 100] 112] 91] 91] 6373 
Ir. | 85] 86) 99} 96) 113] 115) 105] 107] 93] 107] 83:2 
These smoothed results are graphically represented 
by the dots connected with black lines in Figs. 1 to ro. 
To show the effect of the smoothing process the original 
unsmoothed numbers, viz. those of Table II., are graphic- 
ally exhibited over the smoothed curves by the dots 
joined with faint dotted lines. It will be seen from these 
figures that the application of the smoothing process has 
got rid of almost all the irregularity. At the same time 
it has somewhat unduly reduced the range of the eleven- 
yearly variations. The amount of this reduction may be 
roughly estimated by applying the same smoothing pro- 
cess to the eleven average sunspot numbers given in the 
last column of Table II. This has been done in the last 
column of Table III. The results are curved in Fig. 11. 
The range of the original unsmoothed numbers is 82°9, 
that of the resulting smoothed numbers is 706; that is 
to say, the range of the smoothed numbers would have to 
be increased by 17 per cent. of itself to obtain the full 
range of the original numbers. From this it may be in- 
ferred that the range of each of the smoothed eleven- 
yearly price variations represented by Figs. 1 to 
10 is too small, and should be increased by about 17 
per cent. of itself to obtain the full range of the variation. 
On the other hand, the extreme range of the unsmoothed 
numbers will probably be somewhat too great in most 
cases, because the data do not extend over a sufficient 
number of years to eliminate completely the effects of 
casual fluctuations. The true mean range of the variation 
caused by solar influence will therefore probably lie some- 
where between the range of the unsmoothed numbers and 
that of the smoothed numbers. The ranges ef both the 
unsmoothed and the smoothed variations are shown below 
for each district. The range of each smoothed variation 
increased by 17 per cent. of itself is also given, 
all ; 
4 Sp Fj s g Fy fal) ee 
Be eS Makeaberein| cu) Eyal |e. It ee 
ey lees lesa Sealey sole 
ajm ys M]a | wa a}Aa |e 
Unsmoothed .| 53 | 49 | 44 | 51 | 51 | 60 | 39 | 51 | 27 | 48 
Smoothed. .| 37 | 42 | 38 | 40 | 35 | 42 | 20 | 25 | 23 | ar 
Smoothed, plus 
17 per cent.) 43 | 49 | 44 | 47 | 41 | 49 | 23 | 29 | 27 | 48 
Now these results reveal the remarkable fact that, amid 
all the apparently irregular fluctuations of the yearly 
prices, there is in every one of the ten districts a periodi- 
cal rise and fall of prices once every eleven years, corre- 
sponding to the regular variation which takes place in the 
number of the sunspots during the same period. They 
also show that in seven out of the ten districts the range 
of the eleven-yearly variation of prices lies between 40 and 
50 per cent. of the average price, and that in the remain- 
ing three districts the range lies between 20 and 30 per 
cent. The ranges are greatest in those districts where 
scarcity and famine are most frequent, smallest in those 
which enjoy the greatest immunity in these respects. In 
Bijapur and the neighbouring districts of Belgaum and 
Dharwar the highest prices occur in the year of minimum 
sunspots ; in Madras, Poona, and Khandesh a year or two 
later; in Kanara, Kaira, and Bhavnagar two or three years 
later ; and in Ahmedabad three years later. The lowest 
prices occur in all the districts from three to five years 
after the year of maximum sunspots, that is to say, three 
years after at the southern stations; four or five years 
after at the northern. Bijapur and Poona are the first to 
show a very decided rise of prices, and this rise takes 
place in the year preceding the year of minimum sunspots. 
At all the other stations a very decided rise takes place a 
year or two later. 
From what has been said it follows that the intervals 
of time between the year of minimum sunspots and the 
years of highest prices are less than the intervals between 
the year of maximum sunspots and the years of lowest 
prices. This shows that the eleven-yearly price variations 
do not exactly correspond to the eleven-yearly sunspot 
variation. The reason may be that on the occurrence of 
scarcity prices rise very rapidly, while on the return of a 
season of plenty they fall much more slowly, because the 
reserve stocks of grain consumed during a period of 
scarcity cannot be fully replaced until good crops for 
several successive years have been secured. If it were 
possible to obtain data showing the actual out-turn of the 
crops of each year, it would perhaps be found that the 
eleven-yearly variations calculated therefrom would corre- 
spond to the sunspot variation even more closely than the 
price variations correspond to it. 
In estimating the significance of these eleven-yearly 
variations it must be remembered that quantity prices, 
not money prices, have been dealt with, and that the 
corresponding money prices would show a much greater 
percentage rise in dear times, and a less percentage fall 
in cheap times than are shown by the quantity prices. 
Indeed, to a person accustomed to thinking of money 
prices the quantity prices are apt to be very misleading 
if the difference is not constantly borne in mind, as may 
be seen from the consideration that if the quantity price, 
that is, the number of pounds for a rupee, becomes 50 per 
cent. less, that is dearer, than usual, the corresponding 
money price is Ioo per cent. higher; while if the quantity 
price becomes 50 per cent. more, that is cheaper, the 
corresponding money price is only 33 per cent. lower, 
From a money point of view, therefore, a fall of 50 per 
cent. in the number of pounds for a rupee is much more 
serious than it seems to be, while a rise of 50 per cent. in 
that number is less advantageous than might at first sight 
be supposed. For financial purposes it would probably 
be best to convert the quantity prices at the beginning 
into their money equivalents, because it is impossible 
accurately to convert results (such as averages and the 
like) worked out in quantity prices into corresponding 
results, expressed in money prices.’ Such conversions 
always give a too favourable appearance as regards cheap- 
1 For purely scientific purposes it would perhaps be test to work with the 
logarithms of the original prices, instead of with the prices themselves, re- 
gardless as to whether the prices are expressed in pounds for a rupee, or in 
rupees for a fixed quantity of grain. It would then be possible to pass 
directly from the results of one system to those of the other, without haying 
to go through the labour of recalculation. 
