424 PHILOSOPHICAL TRANSACTIONS. [aNNO I67O. 



always cold. From a wound made in a walnut-tree in January, and the be- 

 ginning of this present March, in mild weather, nothing issued ; but the weather 

 changing and growing colder, it bled plentifully : which seems not well to con- 

 sist with that hypothesis, and must be better examined. 



Last year, the 6th and 7th of March, we made the experiments of the bleed- 

 ing of poles, held perpendicular at both ends, in willow, birch and sycamore : 

 which may so easily and certainly be found to succeed, that there needs no such 

 exact niceness in the observation of those particulars. The 1 1 th of March, 

 roots of birch, great and small, bled both ways ; and about the same time syca- 

 more roots also. Of all which I doubt not but Dr. Tonge is by this time 

 fully satisfied by his own experiments. The same birch which first began to 

 bleed the 3d of March this year, bled three weeks sooner last year. 



Some Considerations on M. Cassjnis Method of finding the Apogees, 

 Excentricities, and Anomalies of the Planets; by M. Nic. Mercator. 

 Translated from the Latin. N" 57, j^^. 1168. 



1 . M. Cassini supposes two lines drawn from both foci to the planet, revolv- 

 ing in an ellipsis, one of which is the line of the mean motion, and the other 

 that of the true. 



Construction. (Fig. 2, PI. xi.) 



L is the centre of the concentric 

 ABCDE. 



BLD its diameter. 



BA, BC, BP apparent distances. 



DE, DF, DQ distances of mean mo- 

 tion. 



BE, BF, BQ, DA, DC, DP right 

 lines. 



BE cuts DA in H; BF cuts DC in 

 G; BQcutsDPinR. 



RHG is a right line. 



BI is perpendicular to RHG. 



I the centre of the ellipse. 



LI is the excentricity. 



IO = LL 



O the focus, or centre of mean mo- 

 tion. 



L the other focus, or centre of the 

 true motion. 



IM = IN = LB. 



M the apogeum; N the perigeum; 

 BLM the true anomaly. 



Demonstration. — Bishop Ward, in his Examination of the Philolaic Astro- 

 nomy, published at Oxford l653, in chap. 6, gives a method of finding the 

 true anomaly of the planets from their mean anomaly ; which is this : 



In fig. 3, C is the centre of the ellipsis AEP; F the focus and centre of the 

 mean motion ; S the focus or centre of the true motion ; A the apogeum ; P 

 the perigeum; E the planet; AFE the mean anomaly ; ASE the true anomaly; 

 FET a right line; ET = ES; ST a right line. 



