Temperature is more variable in winter than in summer , and hence we should expect the curve of temperature to experience more violent oscillations in the former season .sx To show to what extent this expectation is realised , two smooth curves have been added to Fig. 2 , the distances of which above and below the central horizontal line arc equal to 0.4 times the mean standard deviation of the five-day means about the corresponding 30-year average .sx The figure 0.4 was chosen merely for convenience in constructing the diagram .sx The figure shows clearly that while the curves of the five-day temperatures have a greater range of variation in summer than in winter , the standard deviation is greater in winter than in summer .sx Relative to the standard deviation the variations of the five-day curves are much greater in summer than in winter , and are especially small during the months January to March .sx The only explanation of this curious discrepancy which occurs to us is that although over the long series of 59 years there is very little tendency for warm or cold spells to recur at the same time each year , yet in the shorter periods of 30 years some such tendency manifests itself in summer but not in winter .sx In this connexion we may recall a statement in an article on " Parallel Weather Sequences " by Miss W. A. Quennell , that in a period of 45 years she found that the tendency for similar types of pressure distribution to recur in the same months in different years was greatest in the four months beginning in late spring or early summer .sx There are only three periods in which the two curves both show marked abnormalities of the same sign at about the same time .sx At the end of May and beginning of June and again at the end of October both curves indicate a warm spell and at the end of July and beginning of August both curves show a marked minimum .sx The agreement between the two pairs of maxima is not exact , but the minima on August 1 are in remarkably close approximation .sx For these three periods the departures from the 59-year smoothed curve of Fig. 1 were found year by year in order to test the regularity of the occurrences .sx The five-day period May 31 to June 4 was above the smooth curve on 32 occasions and below it on 27 occasions so that there is obviously no support for the assumption of the regular occurrence of a warm spell at this time .sx The five-day period October 28 to November 1 was above the smooth curve on 37 occasions and below it on 22 occasions , which is little better .sx On the other hand , the five-day period July 30 to August 3 was below the smooth curve on 43 occasions , above it on 15 and exactly on the curve once .sx This gives a chance of nearly three to one that the temperature of London at this period will be unseasonably low .sx 5 A POSSIBLE COLD PERIOD AT THE END OF JULY .sx Ignoring the year in which the temperature exactly fitted the smooth curve we have 58 temperatures for the five days July 30 to August 3 .sx We may regard these as 58 shots fired at a targetformed by a line , and it is a simple matter to calculate the odds against a distribution of 43 shots falling on one side of the line and 15 on the other arising by chance .sx The probability that in any one attempt at least 43 shots will fall to the same side of the target is .sx 00045 , or less than one in 2,000 , assuming that the frequency distribution of the shots falling at different distances from the target follows the normal curve of errors .sx But the period July 30 to August 3 has been selected from 365 overlapping five-day .sx periods , and though only 73 of these are independent of each other , we may regard them without great error as equivalent to 365 trials .sx The probability that out of 365 sets of 58 shots each , one set will give a distribution so abnormal that at least 43 shots fall on one side of the target and not more than 15 on the other side is .sx 165 or one in six .sx This suggests that the cold period at the end of July and beginning of August is probably real , but the probability is not sufficiently great to be regarded as in any way approaching proof .sx Moreover , as stated above , this calculation assumes that the frequency curve is of the " normal " type .sx The actual frequencies of different mean temperatures during this five-day period are shown in Fig. 3 .sx Actually the distribution in Fig. 3 is not quite normal , .sx but indicates a closer aggregation about the lower temperatures than about the higher , with the result that if we compare the mean temperature of July 30 to August 3 in each year with the average of those five days during the whole 58 , instead of with the smooth curve , we still find that more than half ( actually 53 per cent ) are below the average .sx When this asymmetry is taken into account it decreases still further the probability that the cold period at the end of July and beginning of August is a real permanent feature of our climate .sx In order to obtain further light on the permanence of this cool period in summer , the average daily temperatures at Greenwich for the 25 years 1841-65 during the months of July and August were examined .sx Overlapping five-day means were formed as for the Kew temperatures ; these are plotted as the upper inset .sx in Fig. 1 .sx The Greenwich curve is quite unlike the Kew curve for 1871 to 1900 , but has a rather close resemblance to that for .sx 1901 to 1929 , except that the maximum on August 12 is of quite minor importance , and hence there is no suggestion of a definite minimum on August 3 .sx The impression left by a comparison of .sx the three curves , 1841-65 , 1871-1900 and 1901-29 , is that the crest .sx of the annual wave of temperature tends to be flattened out between mid-July and mid-August , and replaced by a series of irregular oscillations , but that it is not possible to pick on any one five-day period as the August cold period .sx 6 THE POSSIBLE WARM PERIODS IN MID-JULY AND MID-AUGUST .sx The peaks on either side of this summer cool period were next examined in the same way .sx The peaks on the two curves of five-day means for 1871-1900 and 1901-29 do not synchronise exactly , but the periods July 15-19 and August 14-18 may be taken as representative of both curves .sx On comparing the five-day means for these two periods with the corresponding values from the smooth curve for the whole interval 1871-1929 , we find that in July 15-19 the five-day period was above the smooth curve 28 times , coincided with it once , and fell below it 30 times .sx The fact that the average for the whole period is above the smooth curve is due to the fact that in four years these five days were very hot , the means being 71.1 in 1876 , 72.7 in 1881 , 71.1 in 1900 and 71.2 in 1921 .sx It is evident , however , that no warm spell falls regularly on these dates , for the chances of a warm spell or a cold spell are almost equal .sx During the period August 14-18 the five-day mean was above the smooth curve on 32 occasions and below it on 27 occasions .sx The difference of five is too small to justify the assumption of a regular warm period , especially as during no fewer than 16 years the excess did not exceed 2F .sx In fact the outstanding occurrence in this period was not heat but cold , the year 1888 having a mean for the five days of only 53.9F. Thus none of Buchan's warm periods are regular features of the annual variation of temperature in London .sx 7 POSSIBLE WARM PERIOD AT THE END OF MAY .sx At this stage , it seems desirable to return for a moment to the possible warm period at the end of May .sx Although this cannot be regarded as a permanent feature of our climate , yet Fig. I shows that since 1901 at least this part of the year has on the whole been abnormally warm .sx A study of the records for the individual years shows that in 23 years out of the 29 at least one of the five-day means centred on one of the days from May 23 to May 31 inclusive has been 2F .sx or more above the normal value represented by the smooth curve for 1901-29 inset in Fig. 1 .sx On the other hand , in 13 years out of the 29 at least one of these five day means has been 2F .sx or more below the smooth curve .sx The distribution is as follows ( the words " Excess " and " Deficit .sx refer to a departure of 2F .sx or more ) :sx - .sx The only conclusion which can be drawn from these figures is that even the most pronounced warm spell of the present century , when examined in detail , shows very little indication of even an approximate regularity .sx The fact that in eight years out of 29 smoothed temperatures can change so rapidly that a period of nine days includes both a warm spell and a cold spell suggests that the oscillations of temperature are so rapid that any day selected at random will in most years come either in or within two or three days of a five-day cold spell .sx Thus any one of Buchan's " cold spells " stands an excel-lent chance of being hailed as a success in any particular year , but its chance of " success " would probably have been equally great had it been designated as a warm period .sx 8 BUCHAN'S COLD PERIODS IN INDIVIDUAL YEARS .sx With a view to investigating in greater detail the occurrence of Buchan's first three cold spells in individual years curves were constructed showing the smoothed five-day means of temperature in each year from 1881 to 1923 , over the six months January to June .sx On these curves every maximum of temperature was marked which was separated by at least five days from another maximum and was above the smooth curve of Fig. 1 .sx The minima were marked in a similar way .sx There were found to be 444 maxima and 409 minima in the 43 half-years giving one maximum and one minimum to every eighteen days .sx The most interesting feature of the distribution , however , was the relation to the first three of Buchan's cold spells .sx This is shown in the following table , which sets out the frequencies with which minima and maxima on the five-day temperature curve have been centred ( a ) between the limiting dates given by Buchan ; ( b ) within the interval from two days before Buchan's first date to two days after his last date .sx That is , in these 43 years Buchan's first three cold spells were verified 39 times and falsified 39 times an exactly even chance of verification or falsification .sx If we allow two days grace on either side the three cold spells were verified 62 times and falsified 75 times , a balance of 13 on the wrong side .sx 9 SUMMARY OF CONCLUSIONS .sx We may summarise the results of this investigation as follows :sx 1 .sx There is no apparent tendency for any of the six periods .sx designated by Buchan as cold periods to be regularly cold in London .sx 2 .sx There is no apparent tendency for any of the three periods designated by Buchan as warm periods to be regularly warm in London .sx 3 .sx There appears to be a definite tendency for the summer rise of temperature to ease towards the end of July , and to give place to a period of variable temperatures which continues until the autumn fall sets in about the middle of August .sx 4 .sx Since 1900 there has been a remarkable tendency for winter temperatures to be abnormally high , but this applies to the whole winter and not to any specific part of it .sx 5 .sx Since 1900 there has been a general tendency for the last ten days of May to be abnormally warm , but the variations within this ten-day period have been considerable .sx