Why is the International Sunspot Number always lower than simultaneous Wolf numbers published by other sources ? (The 0.6 factor)
Other sunspot numbers, like the Boulder sunspot number or Wolf numbers provided by individual stations, are often 20 to 50% higher than the International Sunspot Number. You may thus wonder if anything is wrong with either data set. In fact, this difference is easy to understand and find its roots in the past origins of the sunpot number.
Back in 1849, when he started producing the sunspot from his own sunspot counts, Rudolph Wolf considered essential to keep his spot counts on the same scale as all ancient telescopic observations made before him. Knowing that the crude early telescopes could only show rather large sunspots, he thus decided to deliberately ignore the smallest short-lived spots and also the internal spot structure (multiple umbrae in a large common penumbra), although he could perfectly see them with own 80mm Fraunhofer doublet-lens refractor.
At the end of Wolf's carreer, his assistant and successor, Alfred Wolfer, considered that this elimination introduced unnecessary personal subjectivity in the resulting counts and that it was dropping very useful information. He thus started counting all sunspots that he could actually detect. Of course, his counts were systematically higher than Wolf's counts. However, he consistenly made his counts in parallel with Wolf during 17 years (1875 - 1892) until Wolf's death.
Based on this long simulataneous series spanning more than one full solar cycle, he derived an stable average ratio between the new counts and the original Wolf counts. In order to bring the new higher counts to the Wolf scale, they had to be multiplied by a factor 0.6.
Since that time, all modern raw sunspot counts used to produce the sunspot number have been multiplied by this constant 0.6 factor to reduce them to the scale of the original series established by Wolf before 1892.
Therefore, before other sunspot numbers can be compared to the international sunspot number, they should be multiplied by this 0.6 factor.