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2. Note on the extent of our knowledge respecting the Moon's 

 Surface. By Professor C. Piazzi Smyth. 



Taking advantage of the special attention paid at present to 

 certain astronomical disquisitions, the author called attention to a 

 particular point connected with the moon, which was first stated by 

 the author of " The Plurality of Worlds," and then made by him 

 to prove that the moon must be uninhabited, and thence to lead to 

 the conclusion that all the other planets were uninhabited also. 

 This point was, that " observations having been made on the moon 

 abundantly sufficient to detect the change caused by the growth of 

 such cities as Manchester and Birmingham, no such changes hav- 

 ing been perceived, the theory of non-habitation may be in- 

 dulged in." 



But after having indicated the sort of appearance that those col- 

 lections of human habitations would make when transferred to the 

 moon, Pi'ofessor Smyth proceeded to show that the registered and 

 published observations of the moon are by no means sufficiently ac- 

 curate to be used to test this question : and that they do show 

 changes, and often to a far greater amount than the mere building 

 of a lunar Manchester would occasion : but such changes bear the 

 impress of eri'or of observation. More powerfully still was this 

 brought out, on comparing even the best of the published documents 

 with some manuscript drawings of the Mare Crisium in the moon, 

 recently made at the Edinburgh Observatory ; and the author hoped 

 that this statement of the imperfection of existing maps would lead 

 to observers generally applying themselves to improve this important 

 and interesting field of astronomy. 



3. On the Interest strictly Chargeable for Short Periods of 

 Time. By the Rev. Professor Kelland. 



Considerable attention has of late been bestowed on the equitable 

 mode of computing the interest which ought to be charged for frac- 

 tional portions of a year. Various opinions have been offered rela- 

 tive to the solution of the problem. The basis on which they mutu- 

 ally rest, and on which it appears to me that every solution of the 

 problem must rest, is this — " That the interest chargeable for any 

 fractional part of a year shall at the end of the year amount to a 



