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starting from the first telescopic sunspot observations by david and johannes fabricius , galileo galilei , thomas harriot and christoph scheiner , the 400-year sunspot record is one of the longest directly recorded scientific data series , and forms the basis for numerous studies in a wide range of research such as , e.g. , solar and stellar physics , solar - terrestrial relations , geophysics , and climatology . during the 400-year interval , sunspots depict a great deal of variability from the extremely quiet period of the maunder minimum @xcite to the very active modern time @xcite . the sunspot numbers also form a benchmark data series , upon which virtually all modern models of long - term solar dynamo evolution , either theoretical or ( semi)empirical , are based . accordingly it is important to review the reliability of this series , especially since it contains essential uncertainties in the earlier part . the first sunspot number series was introduced by rudolf wolf who observed sunspots from 1848 until 1893 , and constructed the monthly sunspot numbers since 1749 using archival records and proxy data @xcite . sunspot activity is dominated by the 11-year cyclicity , and the cycles are numbered in wolf s series to start with cycle # 1 in 1755 . when constructing his sunspot series wolf interpolated over periods of sparse or missing sunspot observations using geomagnetic proxy data , thus losing the actual detailed temporal evolution of sunspots @xcite . sunspot observations were particularly sparse in the 1790 s , during solar cycle # 4 which became the longest solar cycle in wolf s reconstruction with an abnormally long declining phase ( see fig . [ fig : wsn]a ) . the quality of wolf s sunspot series during that period has been questioned since long . based on independent auroral observations , it was proposed by elias loomis already in 1870 that one small solar cycle may have been completely lost in wolf s sunspot reconstruction in the 1790 s @xcite , being hidden inside the interpolated , exceptionally long declining phase of solar cycle # 4 . this extraordinary idea was not accepted at that time . a century later , possible errors in wolf s compilation for the late 18th century have been emphasized again based on detailed studies of wolf s sunspot series @xcite . recently , a more extensive and consistent sunspot number series ( fig . [ fig : wsn]b ) , the group sunspot numbers ( gsn ) , was introduced by @xcite , which increases temporal resolution and allows to evaluate the statistical uncertainty of sunspot numbers . we note that the gsn series is based on a more extensive database than wolf s series and explicitly includes all the data collected by wolf . however , it still depicts large data gaps in 17921794 ( this interval was interpolated in wolf s series ) . based on a detailed study of the gsn series , @xcite revived loomis idea by showing that the lost cycle ( a new small cycle started in 1793 , which was lost in the conventional wolf sunspot series ) agrees with both the gsn data ( fig . [ fig : wsn]b ) and indirect solar proxies ( aurorae ) and does not contradict with the cosmogenic isotope data . the existence of the lost cycle has been disputed by @xcite based on data of cosmogenic isotope and sunspot numbers . however , as argued by @xcite , the lost cycle hypothesis does not contradict with sunspots or cosmogenic isotopes and is supported by aurorae observations . using time series analysis of sparse sunspot counts or sunspot proxies , it is hardly possible to finally verify the existence of the lost solar cycle . therefore , the presence of the lost cycle has so far remained as an unresolved issue .    here we analyze newly restored original solar drawings of the late 18th century to ultimately resolve the old mystery and to finally confirm the existence of the lost cycle . most of wolf s sunspot numbers in 1749 - 1796 were constructed from observations by the german amateur astronomer johann staudacher who not only counted sunspots but also drew solar images in the second half of the 18th century ( see an example in fig .  [ fig : staud ] ) . however , only sunspot counts have so far been used in the sunspot series , but the spatial distribution of spots in these drawings has not been analyzed earlier . the first analysis of this data , which covers the lost cycle period in 1790 s , has been made only recently @xcite using staudacher s original drawings . additionally , a few original solar disc drawings made by the irish astronomer james archibald hamilton and his assistant since 1795 have been recently found in the archive of the armagh observatory @xcite . after the digitization and processing of these two sets of original drawings @xcite , the location of individual sunspots on the solar disc in the late 18th century has been determined . this makes it possible to construct the sunspot butterfly diagram for solar cycles # 3 and 4 ( fig . [ fig : wsn]c ) , which allows us to study the existence of the lost cycle more reliably than based on sunspot counts only .      despite the good quality of original drawings , there is an uncertainty in determining the actual latitude for some sunspots ( see @xcite for details ) . this is related to the limited information on the solar equator in these drawings . the drawings which are mirrored images of the actual solar disc as observed from earth , can not be analyzed by an automatic prodecure adding the heliographic grid . therefore , special efforts have been made to determine the solar equator and to place the grid of true solar coordinates for each drawing ( see fig . [ fig : staud ] ) . depending on the information available for each drawing , the uncertainty in defining the solar equator , @xmath0 , ranges from almost 0@xmath1 up to a maximum of 15@xmath1 @xcite . the latitude error of a sunspot , identified to appear at latitude @xmath2 , can be defined as @xmath3 where @xmath0 is the angular uncertainty of the solar equator in the respective drawing , and @xmath4 is the angular distance between the spot and the solar disc center . accordingly , the final uncertainty @xmath5 can range from 0@xmath1 ( precise definition of the equator or central location of the spot ) up to 15@xmath1 . we take the uncertain spot location into account when constructing the semiannually averaged butterfly diagram as follows . let us illustrate the diagram construction for the second half - year ( jul - dec ) of 1793 ( fig . [ fig : dist ] ) . during this period there were only two daily drawings by staudacher with the total of 8 sunspots : two spots on august 6th , which were located close to the limb near the equator , and six spots on november 3rd , located near the disc center at higher latitudes . the uncertainty in definition of the equator was large ( @xmath6 ) for both drawings . because of the near - limb location ( large @xmath4 ) of the first two spots , the error @xmath5 of latitude definition ( eq .  [ eq : delta ] ) is quite large . the high - latitude spots of the second drawing are more precisely determined because of the central location of the spots . the latitudinal occurrence of these eight spots and their uncertainties are shown in fig . [ fig : dist ] as stars with error bars . the true position of a spot is within the latitudinal band @xmath7 , where @xmath5 is regarded as an observational error and @xmath2 as the formal center of the latitudinal band . accordingly , when constructing the butterfly diagram , we spread the occurrence of each spot within this latitudinal band with equal probability ( the use of other distribution does not affect the result ) . finally , the density of the latitudinal distribution of spots during the analyzed period is computed as shown by the histogram in fig . [ fig : dist ] . this density is the average number of sunspots occurring per half - year per 2@xmath1 latitudinal bin . each vertical column in the final butterfly diagram shown in fig . [ fig : wsn]c is in fact such a histogram for the corresponding half - year .      typically , the sunspots of a new cycle appear at rather high latitudes of about 2030@xmath1 . this takes place around the solar cycle minimum . later , as the new cycle evolves , the sunspot emergence zone slowly moves towards the solar equator . this recurrent `` butterfly''-like pattern of sunspot occurrence is known as the _ sprer law _ @xcite and is related to the action of the solar dynamo ( see , e.g. * ? ? ? it is important that the systematic appearance of sunspots at high latitudes unambiguously indicates the beginning of a new cycle @xcite and thus may clearly distinguish between the cycles . one can see from the reconstructed butterfly diagram ( fig . [ fig : wsn]c ) that the sunspots in 17931796 appeared dominantly at high latitudes , clearly higher than the previous sunspots that belong to the late declining phase of the ending solar cycle # 4 . thus , a new `` butterfly '' wing starts in late 1793 , indicating the beginning of the lost cycle . since sunspot observations are quite sparse during that period , we have performed a thorough statistical test as follows . the location information of sunspot occurrence on the original drawings during 17931796 ( summarized in table  [ tab1 ] ) allows us to test the existence of the lost cycle . the observed sunspot latitudes were binned into three categories : low ( @xmath8 ) , mid- ( @xmath9@xmath10 ) and high latitudes ( @xmath11 ) , as summarized in column 2 of table  [ tab2 ] . we use all available data on latitude distribution of sunspots since 1874 covering solar cycles 12 through 23 ( the combined royal greenwich observatory ( 18741981 ) and usaf / noaa ( 19812007 ) sunspot data set : http://solarscience.msfc.nasa.gov/greenwch.shtml ) as the reference data set . we tested first if the observed latitude distribution of sunspots ( three daily observations with low - latitude spots , one with mid - latitude and three with only high - latitude spots , see table  [ tab2 ] ) is consistent with a late declining phase ( d - scenario , i.e. the period 17931796 corresponds to the extended declining phase of cycle # 4 ) or with the early ascending phase ( a - scenario , i.e. , the period 17931796 corresponds to the ascending phase of the lost cycle ) . we have selected two subsets from the reference data set : d - subset corresponding to the declining phase which covers three last years of solar cycles 12 through 23 and includes in total 11235 days when 33803 sunspot regions were observed ; and a - subset corresponding to the early ascending phase which covers 3 first years of solar cycles 13 through 23 and includes 10433 days when 47096 regions were observed . first we analyzed the probability to observe sunspot activity of each category on a randomly chosen day . for example , we found in the d - subset 4290 days when sunspots were observed at low latitudes below 8@xmath1 . this gives the probability @xmath12 ( see first line , column 3 in table  [ tab2 ] ) to observe such a pattern on a random day in the late decline phase of a cycle . similar probabilities for the other categories in table  [ tab2 ] have been computed in the same way . next we tested whether the observed low - latitude spot occurrence ( three out of seven daily observations ) corresponds to declining / ascending phase scenario . the corresponding probability to observe @xmath13 events ( low - latitude spots ) during @xmath14 trials ( observational days ) is given as @xmath15 where @xmath16 is the probability to observe the event at a single trial , and @xmath17 is the number of possible combinations . we assume here that the results of individual trials are independent on each other , which is justified by the long separation between observational days . thus , the probability to observed three low - latitude spots during seven random days is @xmath18 and 0.07 for d- and a - hypotheses , respectively . the corresponding probabilities are given in the first row , columns 56 of table  [ tab2 ] . the occurrence of three days with low latitude activity is quite probable for both declining and ascending phases . thus , this criterion can not distinguish between the two cases . the observed mid - latitude spot occurrence ( one out of seven daily observations ) is also consistent with both d- and a - scenarios . the corresponding confidence levels ( 0.06 and 0.22 , respectively , see the second row , columns 56 of table  [ tab2 ] ) do not allow to select between the two hypotheses . next we tested the observed high - latitude spot occurrence ( three out of seven observations ) in the d / a - scenarios ( the corresponding probabilities are given in the third row of table  [ tab2 ] ) . the occurrence of three days with high - latitude activity is highly improbable during a late declining phase ( d - scenario ) . thus , the hypothesis of the extended cycle # 4 is rejected at the level of @xmath19 . the a - scenario is well consistent ( confidence 0.26 ) with the data . thus , the observed high - latitude sunspot occurrence clearly confirms the existence of the lost cycle . we also noticed that sunspots tend to appear in northern hemisphere ( 13 out of 16 observed sunspots appeared in the northern hemisphere ) . despite the rather small number of observations , the statistical significance of asymmetry is quite good ( confidence level 99% ) , i.e. it can be obtained by chance with the probability of only 0.01 , in a purely symmetric distribution . nevertheless , more data are needed to clearly evaluate the asymmetry . thus , a statistical test of the sunspot occurrence during 17931796 confirms that :    * the sunspot occurrence in 17931796 contradicts with a typical latitudinal pattern in the late declining phase of a normal solar cycle ( at the significance level of @xmath19 ) . * the sunspot occurrence in 17931796 is consistent with a typical ascending phase of the solar cycle , confirming the start of the lost solar cycle . we note that it has been shown earlier @xcite , using the group sunspot number , that the sunspot number distribution during 17921793 was statistically similar to that in the minimum years of a normal solar cycle , but significantly different from that in the declining phase . * the observed asymmetric occurrence of sunspots during the lost cycle is statistically significant ( at the significance level of 0.01 ) . therefore , the sunspot butterfly diagram ( fig . [ fig : wsn]c ) unambiguously proves the existence of the lost cycle in the late 18th century , verifying the earlier evidence based on sunspot numbers @xcite and aurorae borealis @xcite . an additional cycle in the 1790 s changes cycle numbering before the dalton minimum , thus verifying the validity of the _ gnevyshev - ohl _ rule of sunspot cycle pairing @xcite and the related 22-year periodicity @xcite in sunspot activity throughout the whole 400-year interval . another important consequence of the lost cycle is that , instead of one abnormally long cycle # 4 ( min - to - min length @xmath2015.5 years according to gsn @xcite ) there are two shorter cycles of about 9 and 7 years ( see fig .  [ fig : wsn]d ) . note also that some physical dynamo models even predict the existence of cycles of small amplitude and short duration near a grand minimum @xcite . the cycle # 4 ( 17841799 in gsn ) with its abnormally long duration dominates empirical studies of relations , e.g. , between cycle length and amplitude . replacing an abnormally long cycle # 4 by one fairly typical and one small short cycle changes empirical relations based on cycle length statistics . this will affect , e.g. , predictions of future solar activity by statistical or dynamo - based models @xcite , and some important solar - terrestrial relations @xcite . the lost cycle starting in 1793 depicts notable hemispheric asymmetry with most sunspots of the new cycle occurring in the northern solar hemisphere ( fig . [ fig : wsn]c ) . this asymmetry is statistically significant at the confidence level of 99% . a similar , highly asymmetric sunspot distribution existed during the maunder minimum of sunspot activity in the second half of the 17th century @xcite . however , the sunspots during the maunder minimum occurred preferably in the southern solar hemisphere @xcite , i.e. , opposite to the asymmetry of the lost cycle . this shows that the asymmetry is not constant , contrary to some earlier models involving the fossil solar magnetic field @xcite . interestingly , this change in hemispheric asymmetry between the maunder and dalton minimum is in agreement with an earlier , independent observation , based on long - term geomagnetic activity , that the north - south asymmetry oscillates at the period of about 200 - 250 years @xcite . concluding , the newly recovered spatial distribution of sunspots of the late 18th century conclusively confirms the existence of a new solar cycle in 17931800 , which has been lost under the preceding , abnormally long cycle compiled by rudolf wolf when interpolating over the sparse sunspot observations of the late 1790 s . this letter brings the attention of the scientific community to the need of revising the sunspot series in the 18th century and the solar cycle statistics . this emphasizes the need to search for new , yet unrecovered , solar data to restore details of solar activity evolution in the past ( e.g. , * ? ? ? the new cycle revises the long - held sunspot number series , restoring its cyclic evolution in the 18th century and modifying the statistics of all solar cycle related parameters . the northern dominance of sunspot activity during the lost cycle suggests that hemispheric asymmetry is typical during grand minima of solar activity , and gives independent support for a systematic , century - scale oscillating pattern of solar hemispheric asymmetry . these results have immediate practical and theoretical consequences , e.g. , to predicting future solar activity and understanding the action of the solar dynamo . we are grateful to dr . john butler from armagh observatory for his help with finding the old notes of hamilton s data . support from the academy of finland and finnish academy of sciences and letters ( visl foundation ) are acknowledged .
because of the lack of reliable sunspot observation , the quality of sunspot number series is poor in the late 18th century , leading to the abnormally long solar cycle ( 17841799 ) before the dalton minimum . using the newly recovered solar drawings by the 1819th century observers staudacher and hamilton , we construct the solar butterfly diagram , i.e. the latitudinal distribution of sunspots in the 1790 s . 
 the sudden , systematic occurrence of sunspots at high solar latitudes in 17931796 unambiguously shows that a new cycle started in 1793 , which was lost in traditional wolf s sunspot series . 
 this finally confirms the existence of the lost cycle that has been proposed earlier , thus resolving an old mystery . 
 this letter brings the attention of the scientific community to the need of revising the sunspot series in the 18th century . 
 the presence of a new short , asymmetric cycle implies changes and constraints to sunspot cycle statistics , solar activity predictions , solar dynamo theories as well as for solar - terrestrial relations .