R Dataset / Package HistData / Langren.all
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On this Picostat.com statistics page, you will find information about the Langren.all data set which pertains to van Langren's Data on Longitude Distance between Toledo and Rome. The Langren.all data set is found in the HistData R package. You can load the Langren.all data set in R by issuing the following command at the console data("Langren.all"). This will load the data into a variable called Langren.all. If R says the Langren.all data set is not found, you can try installing the package by issuing this command install.packages("HistData") and then attempt to reload the data. If you need to download R, you can go to the R project website. You can download a CSV (comma separated values) version of the Langren.all R data set. The size of this file is about 2,123 bytes. van Langren's Data on Longitude Distance between Toledo and RomeDescriptionMichael Florent van Langren (15981675) was a Dutch mathematician and astronomer, who served as a royal mathematician to King Phillip IV of Spain, and who worked on one of the most significant problems of his time— the accurate determination of longitude, particularly for navigation at sea. In order to convince the Spanish court of the seriousness of the problem (often resulting in great losses through ship wrecks), he prepared a 1dimensional line graph, showing all the available estimates of the distance in longitude between Toledo and Rome, which showed large errors, for even this modest distance. This 1D line graph, from Langren (1644), is believed to be the first known graph of statistical data (Friendly etal., 2010). It provides a compelling example of the notions of statistical variability and bias. The data frame Usagedata(Langren1644) data(Langren.all) Format
DetailsIn all the graphs, Toledo is implicitly at the origin and Rome is located relatively at the value of
SourceThe longitude values were digitized from images of the various graphs, which may be found on the Supplementary materials page for Friendly etal. (2009). ReferencesFriendly, M., ValeroMora, P. and Ulargui, J. I. (2010). The First (Known) Statistical Graph: Michael Florent van Langren and the "Secret" of Longitude. The American Statistician, 64 (2), 185191. Supplementary materials: http://datavis.ca/gallery/langren/. Langren, M. F. van. (1644). La Verdadera Longitud por Mar y Tierra. Antwerp: (n.p.), 1644. English translation available at http://www.math.yorku.ca/SCS/Gallery/langren/verdadera.pdf. Lelewel, J. (1851). G?ographie du Moyen ?ge. Paris: Pilliet, 1851. Examplesdata(Langren1644)#################################################### # reproductions of Langren's graph overlaid on a map ####################################################if (require(jpeg, quietly=TRUE)) { gimage < readJPEG(system.file("images", "googletoledorome3.jpg", package="HistData")) # NB: dimensions from readJPEG are y, x, colors gdim < dim(gimage)[1:2] ylim < c(1,gdim[1]) xlim < c(1,gdim[2]) op < par(bty="n", xaxt="n", yaxt="n", mar=c(2, 1, 1, 1) + 0.1) # NB: necessary to scale the plot to the pixel coordinates, and use asp=1 plot(xlim, ylim, xlim=xlim, ylim=ylim, type="n", ann=FALSE, asp=1 ) rasterImage(gimage, 1, 1, gdim[2], gdim[1]) # pixel coordinates of Toledo and Rome in the image, measured from the bottom left corner toledo.map < c(131, 59) rome.map < c(506, 119) # confirm locations of Toledo and Rome points(rbind(toledo.map, rome.map), cex=2) text(131, 95, "Toledo", cex=1.5) text(506, 104, "Roma", cex=1.5) # set a scale for translation of lat,long to pixel x,y scale < data.frame(x=c(131, 856), y=c(52,52)) rownames(scale)=c(0,30) # translate from degrees longitude to pixels xlate < function(x) { 131+x*726/30 } # draw an axis lines(scale) ticks < xlate(seq(0,30,5)) segments(ticks, 52, ticks, 45) text(ticks, 40, seq(0,30,5)) text(xlate(8), 17, "Grados de la Longitud", cex=1.7) # label the observations with the names points(x=xlate(Langren1644$Longitude), y=rep(57, nrow(Langren1644)), pch=25, col="blue", bg="blue") text(x=xlate(Langren1644$Longitude), y=rep(57, nrow(Langren1644)), labels=Langren1644$Name, srt=90, adj=c(.1, .5), cex=0.8) par(op) }### Original implementation using ReadImages, now deprecated & shortly to be removed ## Not run: if (require(ReadImages)) { gimage < read.jpeg(system.file("images", "googletoledorome3.jpg", package="HistData")) plot(gimage) # pixel coordinates of Toledo and Rome in the image, measured from the bottom left corner toledo.map < c(130, 59) rome.map < c(505, 119) # confirm locations of Toledo and Rome points(rbind(toledo.map, rome.map), cex=2) # set a scale for translation of lat,long to pixel x,y scale < data.frame(x=c(130, 856), y=c(52,52)) rownames(scale)=c(0,30) lines(scale) xlate < function(x) { 130+x*726/30 } points(x=xlate(Langren1644$Longitude), y=rep(57, nrow(Langren1644)), pch=25, col="blue") text(x=xlate(Langren1644$Longitude), y=rep(57, nrow(Langren1644)), labels=Langren1644$Name, srt=90, adj=c(0, 0.5), cex=0.8) }## End(Not run)### First attempt using ggplot2; temporarily abandonned. ## Not run: require(maps) require(ggplot2) require(reshape) require(plyr) require(scales)# set latitude to that of Toledo Langren1644$Latitude < 39.68# x/long y/lat bbox < c( 38.186, 9.184, 43.692, 28.674 ) bbox < matrix(bbox, 2, 2, byrow=TRUE)borders < as.data.frame(map("world", plot = FALSE, xlim = expand_range(bbox[,2], 0.2), ylim = expand_range(bbox[,1], 0.2))[c("x", "y")])data(world.cities) # get actual locations of Toledo & Rome cities < subset(world.cities, name %in% c("Rome", "Toledo") & country.etc %in% c("Spain", "Italy")) colnames(cities)[4:5]<c("Latitude", "Longitude")mplot < ggplot(Langren1644, aes(Longitude, Latitude) ) + geom_path(aes(x, y), borders, colour = "grey60") + geom_point(y = 40) + geom_text(aes(label = Name), y = 40.1, angle = 90, hjust = 0, size = 3) mplot < mplot + geom_segment(aes(x=4.03, y=40, xend=30, yend=40))mplot < mplot + geom_point(data = cities, colour = "red", size = 2) + geom_text(data=cities, aes(label=name), color="red", size=3, vjust=0.5) + coord_cartesian(xlim=bbox[,2], ylim=bbox[,1])# make the plot have approximately aspect ratio = 1 windows(width=10, height=2) mplot## End(Not run) ########################################### # show variation in estimates across graphs ###########################################library(lattice) graph < paste(Langren.all$Author, Langren.all$Year) dotplot(Name ~ Longitude, data=Langren.all)dotplot( as.factor(Year) ~ Longitude, data=Langren.all, groups=Name, type="o")dotplot(Name ~ Longitudegraph, data=Langren.all, groups=graph)# why the gap? gap.mod < glm(Gap ~ Year + Source + Latitude, family=binomial, data=Langren1644) anova(gap.mod, test="Chisq")  Dataset imported from https://www.rproject.org. 
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