Explanation of Rain Gauge, Summer 1809

From Daily Record, 1 November 1802-25 May 1826 (Massachusetts Historical Society).

In Jefferson’s hand in available spaces in margin alongside entries for June-August 1809.

I shall begin with the next month to use my rain gauge. The diam. of it's tube is <.9875 I. that of the glass funnel 3.255 consequently as 3.2552 : .9752 or as> .9875 I. that of the glass funnel is 3.2187 consequently as 3.21872 : .98752 or as 10.36 : .975 :: <so is the depth of water in the graduated tube : to the depth fallen> so is the area of the funnel to the area of the tube & so is the depth of water in the tube to the depth fallen on the earth. <therefore the depth in the tube divided & .975 : 10.36 : : 10.87 therefore the depth in the tube divided by 10.87 = the depth fallen. The tube being but 7. I. deep will be filled by a fall of .644 I. of rain. The area of the mouth of the tube is to the area of the tube as 2.066 : .975>

the diam. of the tube of the rain gage being .9875 & that of it’s mouth 1.4375 I. the square of 1.4375 will be to that of .9875 or 2.066 : .975 as the height of rain in the tube to that fallen on the ground. then in the tube

the diam. of the tube of the rain-gage being .9875 & that of the small glass funnel <exactly double to wit [...]> 2. I the height of water in the tube will be <exactly 4 times> to that fallen on the earth, to wit