VOL. LVIII,] PHILOSOPHICAL TRANSACTIONS. 547 



= the limit of i -3.5(1) X 6"; 



3z+-i.3z + 7.3z+ 10(2) 



which, by art. 4, is = 2~*. Therefore g is = -. 

 It also appears, that 



I is = the limit of ^ „ .' ^\ Z. , — ^ X — - — ; which, by art. 3, = 

 2 . 3 . 5 . 7 • 8 . 10 (2a) '^ 2 ' ' •' ' 



2s s *2c 



4 X sine of 60" 3^ 34* 



Moreover it appears, that 



BXK. .. 1- -^ r 1 •*-7 (:) X 5.11. I7(z) ^^ 1 

 is = the limit of ^ ^ „ ) -' — ; — - — -~ X 



I 2 . 5 . 8 (z) X 1 . 3 . 5 (z) 3* - > 



*u 1- •<. r 32 + 2. 3z + 5.3z + 8(z) ^^ 1 u- u \, ,. . ■ 



= the limit of — ?— r-,-; ^ X ; which, by art. 4, is 



1 . 3 . 5 (z) 2* ■ 3* ~ ' 



3 rj^u r . 3i 2*.3ic 



= —r. Iherefore k is ^ -7- ^ . 



And in like manner may a great number of other areas be compared. 

 Note. — All the whole areas above-mentioned are supposed to begin where x 

 begins, and to stand on a base = 1 . 



XXVIl. Experiments and Observations on a Blue Substance, found in a Peat-' 

 moss in Scotland. By Sylvester Douglas, Esq. p. 181. 



The blue coloured substance, which is tlie subject of the following observa- 

 tions, was accidentally dug up in the summer 1759, to mix with some other 

 materials for the purpose of manure, to be laid on some ground, then in 

 Mr. D.'s possession, in the north of Scotland, about 12 miles from Aberdeen. 

 Mr. D. had not met with a description of this substance in any naturalist. 

 Kentman indeed in a few lines mentions a blue earth, which he calls coeruleum 

 patavinum, which agrees with this substance in one remarkable circumstance; 

 that it is at first of a white colour, and becomes blue only by being exposed to 

 the air. Mr. Da Costa's ochra friabilis coerulea, Nat. Hist, of Foss. p. 103, 

 would also have been found probably to correspond with it, if a more particular 

 account could have been given of the circumstances in which it was found, and 

 its appearance before the air had acted on it. Mr. Cronsledt, in his late System 

 of Mineralogy, mentions a blue substance, which seems to be of the same kind, 

 and which, he says, is found somewhere in Prussia. 



The place, where it is dug up, is of a marshy nature, in the corner of an ex- 

 hausted peat-moss. Immediately under the sward lies a stratum, about a foot 

 deep, of common peat; next to that is the substance itself, with irregular striae 

 of a peaty matter all through it, to the depth of near another foot; and below 

 this, he thinks, there is clay. While it is thus wet, and shut out from the air, 

 it is of a white colour, and seemingly of a fatty consistence, not unlike lime 

 that has been prepared for cement. All the water in the neighbourhood of the 



4 A a 



