VOL. XLVIII.] PHILOSOPHICAL TRANSACTIONS. 469 



distance of the object. As the telescope must be lengthened, or drawn out far- 

 ther, for short distances ; the scale, which depends on that length, is thereby in- 

 creased ; which renders the measure of the angle very uncertain : whereas, in 

 this micrometer, the scale is the same at all distances : so that the angle may be 

 measured with the utmost certainty, without any regard to the distance of the 

 objects. 



On the whole, it may be concluded, that this micrometer is a complete instru- 

 ment in its kind ; having many advantages above the common sort, without any 

 of their disadvantages : and there is no doubt but, when brought into practice, 

 it will tend much to the advancement of astronomy. 



LXXF. Of an Earthquake felt at York, ^pril IQ, 1754. By Mr. David 



Erskine Baker, p. 564. 



This small shock felt by Mr. B. at York, lasted about 3 seconds. It gave an 

 undulating motion to the buildings, made the windows, &c. rattle, and was pre- 

 ceded by a rumbling noise, like a carriage over a pavement. Its direction seemed 

 to be from s.w. to n.e., and it was felt at several other places, at many miles 

 distance. 



LXXVI. An Investigation of some Theorems which suggest some Remarkable 

 Properties of the Circle, and are of Use in Resolving Fractions, whose Denomi- 

 nators are certain Multinomials, into more Simple ones. By Mr. John Lan- 

 den.* p. 566. 



That the principal theorems, below investigated, will be of considerable use in 

 the doctrine of fluxions, by rendering, in many cases, the business of computing 



* Mr. Landen, who was born at Peakirk near Peterborough, in Northamptonshire, in I719» was 

 in a great measure a self-taught mathematician, a branch of learning in which he rose to the first 

 rank of eminence. He became a respectable contributor to the mathematical part of the Ladies* 

 Diary so early as the year 1744 ; to which work he continued his contributions, either in his own 

 name, or under various fictitious ones, till within a very few years of his death. His first paper in 

 the Phil. Trans, above printed for the year 1754, is no mean specimen of his taste and skill in that 

 line. Besides this, and several other valuable papers printed at different times in these Transactions, 

 he published some curious and separate works himself. As, 1. Mathematical Lucubrations in 1755; 

 containing a variety of tracts relating to the rectification of curve lines, the summation of series, the 

 finding of fluents, 8lC. 2 A Discourse on the Residual Analysis, 1758; being a new branch of the 

 algebraic art, of very extensive use, both in pure mathematics and natural philosophy. 3. The 1st 

 book of the same Residual Analysis, in 1704 ; explaining the principles, and applying them in a number 

 of curious speculations. 4. Animadversions on Dr. Stewart's Computation of the Sun's Distance from 

 the Earth, 1771. 5. Mathematical Memoirs, 17S0, vol. i. ; on a variety of subjects; with an ap- 

 pendix containing a very extensive collection of forms for finding fluents. 6". Several Observations on 

 converging Series, in 1781, 1782, 1783. 7. And lastly the 2d vol, of the Mathematical Memoirs, 

 in the latter end of 1789 ; containing, besides a solution of the general nroblem concerning rotatory 



