MATHEMATICAL SECTION. 93 
1218 MEETING. Marca 5, 1884. 
The Chairman presided. 
‘Fifteen members present. 
Mr. A. Hatt read the following paper on 
THE FORMULZ FOR COMPUTING THE POSITION OF A SATELLITE. 
The method of rectangular co-ordinates in space furnishes a very 
simple and at the same time a general method of treating many 
questions in astronomy. This method was introduced into practical 
astronomy by Lagrange in his memoir on the Transit of Venus, 
June 3, 1769 (Berlin Academy Memoirs, 1766). Whenever we 
have to consider the relations of three points in space, we may take 
the origin of co-ordinates at one of the points, and then forming 
the values of the rectangular co-ordinates of the other points in 
terms of the polar co-ordinates, the sum or difference of two of the 
x co-ordinates being equal to the third x co-ordinate, we have an 
equation between the three polar co-ordinates. Similar relations 
hold for the axes of y and z, and hence result three equations be- 
tween the two angles and the distance that are required to be 
found. This method is extremely useful, and can be applied to a 
great number of questions in parallax, aberration, eclipses, and to 
those that occur in nearly every part of spherical astronomy. A 
great recommendation of this method is its simplicity, and the fact 
that it is so closely connected with first principles that it can be 
applied with the greatest ease. After the equations are formed 
they have only to be transformed by known rules, and the whole 
work is thus reduced to algebraic and trigonometric transformations 
which can be safely made. These advantages are so great that it 
is not surprising that this method of treating astronomical ques- 
tions has come so largely into use, and the generality and elegance 
of the process are in marked contrast with the old methods which 
proceed by spherical trigonometry.. Perhaps a disadvantage of the 
new method is that it is too mechanical, and one is apt to forget or 
never know the meaning of the quantities that areemployed. The 
old geometrical methods have therefore their value in calling to 
mind a more exact knowledge of the quantities that are used in 
the solution of a problem. 
