386 PHILOSOPH.ICAL TRANSACTIONS. [aNNO 1/78. 



appears, that if this rule be true in the equation (e), it must hold also in the 

 next equation (d) of superior dimensions; and as we know that it is true in 

 simple and quadratic equations, it must therefore be true in cubics, in biqua- 

 dratics, and so on. This is one of the best rules we have in algebra. Dr. Sauu- 

 derson (vol. 2, p. 683, Algeb.) saw such an infinity of cases in equations of high 

 dimensions, that he scarcely hoped for a general proof. Maclaurin's method 

 (p. 145, Algeb.) is plainly impracticable when the roots are numerous, and 

 therefore this concise demonstration will perhaps be acceptable to mathematicians. 



XIX. Journal of a Voyage to the East Indies, in the Ship Grenville, Capt. 

 Burnet Abercro7nbie, in the Y'ear 1775. By Alexander Dalrymple, Esq. 

 F. R. S. p. 380. 



This journal of a voyage to the East-Indies, was kept and arranged in the form 

 of tables, the matter in which being now useless, they are omitted, but as the 

 manner in which they were arranged was ingenious, the following explanation 

 of the different columns is given. 



Explanation of the Columns. — 1st. The date. "A. The height of tlie tliermometer, according to 

 Fahrenheit's scale. This thermometer belonged to Mr. Russell, and hung in the open air in the 

 balcony. 



3d. Including 4 columns, contains the register of the marine barometers, all of which, as well as 

 the thermometers, were made by Nairne and Blunt : those marked a and d are quicksilver, of the 

 kind usually made by them. That marked S is compounded of quicksilver, and of a lighter fluid, 

 for the purpose of making tlie alterations more visible, which \s a great convenience at sea ; a quick- 

 silver thermometer being fixed to it for the sake of correcting its height, the heat by which is set 

 down in the column marked Th. next to that marked s. 



4th. The weather and winds in 4 lines : 1st line from noon to 6 p. m. ; i?d, from 6 p. m. to mid- 

 night ; 3d, from midnight to 6 a. m. ; 4th, from 6 a. m. to noon. In the column of weather, f. de- 

 notes fair ; sq. squally ; c. cloudy ; h. hazy ; r. rain ; hr. hard rain ; sr. small rain ; dr. r. drizling 

 rain; sh. showers ; th. thunder ; 1. lightning. Also the winds are set down according to tlie com- 

 pass, witliout any allowance for the variation. 



5Lh in i.>. The difference between the daily alteration of latitude by account and observation ; n. 

 denoting iJiat the observation was to the northward of the account ; s. that it was to the soxithward. 



6th in J. The ditference between the daily alteration of longitude by tlie account and time-keeper ; 

 w. denoting tliat the longitude by the time-keeper was to the westward of account ; e. that it was to 

 the eastward. The result of tliose differences indicates the daily effect of current ; however an error 

 in the course sailed, or distance run by log, would make tlie current appear different from what it 

 really was. 



7th. The longitude from Greenwich, in 7 columns. 1st. The longitude by account. 2d. The 

 longitude by the time-keeper, which was made by Arnold, but without his late improvements. 3d. 

 The difference between the longitudes deduced from observations of (he moon and from ihe time- 

 keeper uncorrected ; v. denoting the time- keeper to be to the east of d ; w denoting time-keeper to 

 west of 5 . This, admitting tlie time-keeper not to be liable to any sudden changes in its rate of 

 going, indicates the precision with which the observations of the moon may be relied on, all circum- 

 stances of weather and of the ship's motion considered. 4th. The longitude by obsenations of the 

 moon's distance from the sun or stars, adjusted, by the log, to the noon nearest tlie time of observa- 

 tion. 5th. The number of sights or distances ubserM'd. Olii. Tlie object w hose distance from tlie 



