On some Results of the Earth's Contraction from Cooling. 41 



which is borne out by the Table of reciprocals calculated by 

 means that are totally independent of series. 



From the values that have been thus obtained and verified for 

 the imitates of the reciprocals of 1, 2, 4, 5, 7, 8, it follows that, 

 in any division sum which has these unitates in the divisor, the 

 corresponding unitates of their reciprocals may be written as 

 multipliers to find the unitate of the quotient. For instance, in 



25 



—- = 5, as above given, the following is the readiest process of 

 o 



25 



unitation — the unitate of — = 7 x 2 = 14=5, and the unitate of 



o 



5 = 5. This substitution of multiplication for division cannot 

 be made in the case of the unitates of the reciprocals of 3, 6, or 

 9 ; therefore in the cases in which 3, 6, or 9 is in the denomi- 

 nator, and in these cases only, it is necessary to preserve the 

 fractional form of the unitate during the whole of the process of 

 unitation. 



Thus, considered in extenso, subtraction gives birth to co-uni- 

 tates or negative unitates, and inverse powers, or the operation 

 of division, to fractional unitates, or unitates that are irreducible 

 to the whole number form. 



74 Brecknock Road, N., 

 June 1873. 



IV. On some Results of the Earth's Contraction from Cooling, in- 

 cluding a discussion of the Origin of Mountains. By James 

 D. Dana*. 



Part I. 



iREPABATORY to a discussion of some questions connected 

 with the earth's contraction, I here present a statement of 

 the views which I have entertained with regard to the prominent 

 results of this agency. They first appeared in 1846 and 1847, 

 in volumes ii., iii., and iv. of the Second Series of the American 

 Journal of Science, and were somewhat extended in 1856 in 

 vol. xxii.f Full credit is given to earlier writers in connexion 

 with the articles referred to. The views are as follows J : — 



* From the American Journal of Science and Arts, vol. v. June 1873. 

 Communicated by the Author, with additional notes. 



-r Vol. ii. p. 385, iii. pp. 94, 176, 380, iv. p. 88, xxii. pp. 305, 335. 



X I may add in this place that a sight of Madler's chart of the moon 

 in 1846, six years after my visit to the crater of Kilauea, in the Wilkes 

 Exploring Expedition, prompted to the first of the articles on the subject 

 (that on the Volcanoes of the Moon, vol. ii. pp. 335, 1846), in which the 

 origin of continents and oceanic basins is considered. The most important 



